weiss

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Author name code: weiss
ADS astronomy entries on 2022-09-14
author:"Weiss, Nigel O."

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Title: On long-term modulation of the Sun's magnetic cycle
Authors: Beer, J.; Tobias, S. M.; Weiss, N. O.
2018MNRAS.473.1596B Altcode:
We utilize reconstructions based on cosmogenic radionuclides as well
as direct observations of solar magnetic activity, to argue that
the solar dynamo has operated similarly to the present day for at
least the past 10 000 yr. The persistence of the 87-yr Gleissberg
cycle throughout supermodulation events suggests that the Hale and
Schwabe cycles continue independently of the modulational mechanism
for activity. We further analyse behaviour of solar activity during
the Spörer and Maunder Minima. Such grand minima recur with the
characteristic de Vries period of approximately 208 yr but their
incidence is modulated by the Hallstatt cycle with a characteristic
period of around 2300 yr. We ascribe the latter to supermodulation,
caused by breaking the symmetry of the dynamo pattern. Finally, we
emphasize the need for further calculations in order to determine the
effects of changes in solar field morphology and symmetry on the solar
wind and on cosmic ray deflection.

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Title: Supermodulation of the Sun's magnetic activity: the effects
of symmetry changes
Authors: Weiss, N. O.; Tobias, S. M.
2016MNRAS.456.2654W Altcode:
In this paper, we argue that the solar activity record, as revealed by
telescopic observations and proxy data from the abundances of cosmogenic
isotopes, is consistent with the action of a deterministic non-linear
chaotic dynamo. In particular, we claim that the long time-scale
`supermodulation' apparent in the isotopic record can be ascribed to
switching of the dynamo between two different modulational patterns. The
first (which is currently in operation) involves deep grand minima and
occasional changes in symmetry triggered by these minima. The second,
which exhibits only weak modulation and no grand minima, arises as
a consequence of symmetry breaking. These processes are demonstrated
for highly idealized simple models of the non-linear dynamo equations.

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Title: Solar Activity in the Past and the Chaotic Behaviour of
the Dynamo
Authors: Arlt, Rainer; Weiss, Nigel
2014SSRv..186..525A Altcode: 2014SSRv..tmp...27A; 2014arXiv1406.7628A
The record of solar activity is reviewed here with emphasis on
peculiarities. Since sunspot positions tell us a lot more about the
solar dynamo than the various global sunspot numbers, we first focus on
the records of telescopic observations of sunspots leading to positional
information. Then we turn to the proxy record from cosmogenic isotope
abundances, which shows recurrent grand minima over the last 9500
years. The apparent distinction between episodes of strong modulation,
and intervening episodes with milder modulation and weaker overall
activity, hints at the solar dynamo following a variety of solutions,
with different symmetries, over the course of millennia.

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Title: Sunspots and Starspots
Authors: Thomas, John H.; Weiss, Nigel O.
2012sust.book.....T Altcode:
Preface; 1. The sun among the stars; 2. Sunspots and starspots:
a historical introduction; 3. Overall structure of a sunspot;
4. Fine structure of the umbra; 5. Fine structure of the penumbra;
6. Oscillations in sunspots; 7. Sunspots and active regions; 8. Magnetic
activity in stars; 9. Starspots; 10. Solar and stellar activity cycles;
11. Solar and stellar dynamos; 12. Solar activity, space weather,
and climate change; 13. The way ahead; Appendices; References; Index.

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Title: Convectively driven dynamo action in the quiet Sun
Authors: Bushby, P. J.; Favier, B.; Proctor, M. R. E.; Weiss, N. O.
2012GApFD.106..508B Altcode:
Observations of the quiet solar surface indicate that localised
concentrations of vertical magnetic flux tend to accumulate in the
convective downflows. Furthermore, there is some evidence to suggest
that mesogranular boundaries are preferred locations for the formation
of these flux concentrations. This implies that these magnetic fields
are organised on scales that are larger than the granular scale. One
possible explanation for the existence of quiet Sun magnetic features is
that they are continuously regenerated by the near-surface convective
motions. Motivated by this, we consider dynamo action in a local
Cartesian model of convection in a compressible electrically conducting
fluid. The horizontal scale of this domain is large enough to model
mesoscale behaviour. Dynamo action occurs provided that the magnetic
Reynolds number exceeds some critical value. In the kinematic regime
the presence of mesogranules seems to be beneficial for dynamo action:
compared to similar smaller aspect ratio calculations, we find higher
kinematic growth rates for the magnetic energy, as well as a lower
value for the critical magnetic Reynolds number. In the nonlinear
regime the peak magnetic field strengths compare very favourably
to observations, greatly exceeding the equipartition value at the
surface, as observed in the quiet Sun. However, there is no evidence
to suggest that the presence of mesogranules significantly increases
the saturation level of the dynamo in this nonlinear regime, which
(in the highest magnetic Reynolds number case) is comparable to that
found in similar calculations in smaller domains.

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Title: Reflections on magnetoconvection
Authors: Weiss, N. O.
2012GApFD.106..353W Altcode:
The interaction between magnetic fields and convection can be observed
directly in stars like the Sun. This selective review uses idealized
numerical experiments to illustrate and extend results obtained
from bifurcation theory. It covers a wide variety of steady and
time-dependent behaviour, in incompressible and compressible fluids,
in two and three dimensions. These results illuminate behaviour that
appears in recent "realistic" simulations of solar magnetoconvection.

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Title: Magnetic buoyancy instabilities in the presence of magnetic
flux pumping at the base of the solar convection zone
Authors: Barker, Adrian J.; Silvers, Lara J.; Proctor, Michael R. E.;
Weiss, Nigel O.
2012MNRAS.424..115B Altcode: 2012arXiv1204.5432B
We perform idealized numerical simulations of magnetic buoyancy
instabilities in three dimensions, solving the equations
of compressible magnetohydrodynamics in a model of the solar
tachocline. In particular, we study the effects of including a
highly simplified model of magnetic flux pumping in an upper layer
('the convection zone') on magnetic buoyancy instabilities in a lower
layer ('the upper parts of the radiative interior - including the
tachocline'), to study these competing flux transport mechanisms at
the base of the convection zone. The results of the inclusion of this
effect in numerical simulations of the buoyancy instability of both a
preconceived magnetic slab and a shear-generated magnetic layer are
presented. In the former, we find that if we are in the regime that
the downward pumping velocity is comparable with the Alfvén speed of
the magnetic layer, magnetic flux pumping is able to hold back the
bulk of the magnetic field, with only small pockets of strong field
able to rise into the upper layer. In simulations in which the
magnetic layer is generated by shear, we find that the shear velocity
is not necessarily required to exceed that of the pumping (therefore
the kinetic energy of the shear is not required to exceed that of the
overlying convection) for strong localized pockets of magnetic field
to be produced which can rise into the upper layer. This is because
magnetic flux pumping acts to store the field below the interface,
allowing it to be amplified both by the shear and by vortical fluid
motions, until pockets of field can achieve sufficient strength to
rise into the upper layer. In addition, we find that the interface
between the two layers is a natural location for the production of
strong vertical gradients in the magnetic field. If these gradients
are sufficiently strong to allow the development of magnetic buoyancy
instabilities, strong shear is not necessarily required to drive them
(cf. previous work by Vasil &amp; Brummell). We find that the addition
of magnetic flux pumping appears to be able to assist shear-driven
magnetic buoyancy in producing strong flux concentrations that can
rise up into the convection zone from the radiative interior.

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Title: The Solar Tachocline
Authors: Hughes, D. W.; Rosner, R.; Weiss, N. O.
2012sota.book.....H Altcode:
Preface; Part I. Setting the Scene: 1. An introduction to the solar
tachocline D. O. Gough; 2. Reflections on the solar tachocline
E. A. Spiegel; Part II. Observations: 3. Observational results
and issues concerning the tachocline J. Christensen-Dalsgaard and
M. J. Thompson; Part III. Hydrodynamic Models: 4. Hydrodynamic models of
the tachocline J.-P. Zahn; 5. Turbulence in the tachocline M. S. Miesch;
6. Mean field modelling of differential rotation G. Rudiger and
L. L. Kitchatinov; Part IV. Hydromagnetic Properties: 7. Magnetic
confinement of the solar tachocline P. Garaud; 8. Magnetic confinement
and the sharp tachopause M. E. McIntyre; 9. ß-Plane MHD turbulence
and dissipation in the solar tachocline P. H. Diamond, K. Itoh,
S.-I. Itoh and L. J. Silvers; Part V. Instabilities: 10. Global
MHD instabilities of the tachocline P. A. Gilman and P. S. Cally;
11. Magnetic buoyancy instabilities in the tachocline D. W. Hughes;
12. Instabilities, angular momentum transport and magnetohydrodynamic
turbulence G. I. Ogilvie; Part VI. Dynamo Action: 13. The solar dynamo
and the tachocline S. M. Tobias and N. O. Weiss; Part VII. Overview:
14. On studying the rotating solar interior R. Rosner; Index.

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Title: Global model of differential rotation in the Sun
Authors: Balbus, Steven A.; Latter, Henrik; Weiss, Nigel
2012MNRAS.420.2457B Altcode: 2011arXiv1111.3809B
The isorotation contours of the solar convective zone (SCZ) show three
distinct morphologies, corresponding to two boundary layers (inner and
outer), and the bulk of the interior. Previous work has shown that the
thermal wind equation (TWE) together with informal arguments on the
nature of convection in a rotating fluid could be used to deduce the
shape of the isorotation surfaces in the bulk of the SCZ with great
fidelity, and that the tachocline contours could also be described by
relatively simple phenomenology. In this paper, we show that the form
of these surfaces can be understood more broadly as a mathematical
consequence of the TWE and a narrow convective shell. The analysis
does not yield the angular velocity function directly; an additional
surface boundary condition is required. However, much can already
be deduced without constructing the entire rotation profile. The
mathematics may be combined with dynamical arguments put forth in
previous works to the mutual benefit of each. An important element of
our approach is to regard the constant angular velocity surfaces as
an independent coordinate variable for what is termed the 'residual
entropy', a quantity that plays a key role in the equation of thermal
wind balance. The difference between the dynamics of the bulk of the
SCZ and the tachocline is due to a different functional form of the
residual entropy in each region. We develop a unified theory for the
rotational behaviour of both the SCZ and the tachocline, using the
solutions for the characteristics of the TWE. These characteristics
are identical to the isorotation contours in the bulk of the SCZ,
but the two deviate in the tachocline. The outer layer may be treated,
at least descriptively, by similar mathematical techniques, but this
region probably does not obey thermal wind balance.

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Title: Solar and Stellar Dynamos
Authors: Weiss, Nigel O.
2011IAUS..271..247W Altcode:
Records of the solar magnetic field extend back for millennia,
and its surface properties have been observed for centuries, while
helioseismology has recently revealed the Sun's internal rotation and
the presence of a tachocline. Dynamo theory has developed to explain
these observations, first with idealized models based on mean-field
electrodynamics and, more recently, by direct numerical simulation,
notably with the ASH code at Boulder. These results, which suggest
that cyclic activity relies on the presence of the tachocline, and that
its modulation is chaotic (rather than stochastic), will be critically
reviewed. Similar theoretical approaches have been followed in order
to explain the magnetic properties of other main-sequence stars,
whose fields can be mapped by Zeeman-Doppler imaging. Of particular
interest is the behaviour of fully convective, low-mass stars, which
lack any tachocline but are nevertheless extremely active.

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Title: The influence of stratification upon small-scale
convectively-driven dynamos
Authors: Bushby, Paul J.; Proctor, Michael R. E.; Weiss, Nigel O.
2011IAUS..271..197B Altcode:
In the quiet Sun, convective motions form a characteristic granular
pattern, with broad upflows enclosed by a network of narrow
downflows. Magnetic fields tend to accumulate in the intergranular
lanes, forming localised flux concentrations. One of the most plausible
explanations for the appearance of these quiet Sun magnetic features
is that they are generated and maintained by dynamo action resulting
from the local convective motions at the surface of the Sun. Motivated
by this idea, we describe high resolution numerical simulations of
nonlinear dynamo action in a (fully) compressible, non-rotating layer of
electrically-conducting fluid. The dynamo properties depend crucially
upon various aspects of the fluid. For example, the magnetic Reynolds
number (Rm) determines the initial growth rate of the magnetic energy,
as well as the final saturation level of the dynamo in the nonlinear
regime. We focus particularly upon the ways in which the Rm-dependence
of the dynamo is influenced by the level of stratification within
the domain. Our results can be related, in a qualitative sense, to
solar observations.

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Title: Chaotic behaviour in low-order models of planetary and
stellar dynamos
Authors: Weiss, N. O.
2011GApFD.105..256W Altcode:
The behaviour of the geodynamo and the solar cycle can be modelled
by low-order systems of coupled nonlinear differential equations. The
Earth's magnetic field reverses aperiodically, and similar behaviour
is exhibited by disc dynamos that are described by the Lorenz
equations. Chaotic behaviour is also a characteristic feature of
coupled disc dynamos. In stars like the Sun, magnetic activity varies
cyclically, with regular reversals of magnetic fields, but the cyclic
activity is modulated on longer timescales. This behaviour can be
described by normal form equations that account for symmetry-breaking
as well as for variations in amplitude. The Von Kármán Sodium
(VKS) experiment has successfully demonstrated magnetic reversals
in the laboratory, and these results can be represented by evolution
equations also.

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Title: Effects of boundary conditions on the onset of convection
with tilted magnetic field and rotation vectors
Authors: Proctor, M. R. E.; Weiss, N. O.; Thompson, S. D.; Roxburgh,
N. T.
2011GApFD.105...82P Altcode:
The problem of the onset of thermal convection is considered, firstly
when a uniform tilted magnetic field is present, and secondly in a frame
rotating about an oblique axis. If up-down symmetry is broken we expect
to find only bifurcations that lead to travelling waves. Numerical
studies show, however, that in a Boussinesq fluid the spectrum of
eigenvalues can be symmetrical about the real axis, even when the
boundary conditions are asymmetrical. Here we show analytically that
this symmetry property indeed holds for a wide range of boundary
conditions and hence that both steady solutions and standing waves
are allowed.

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Title: Small-scale Dynamo Action in Compressible Convection
Authors: Bushby, P. J.; Proctor, M. R. E.; Weiss, N. O.
2010ASPC..429..181B Altcode:
Motivated by observations of magnetic fields at the surface of the
Sun, we consider direct numerical simulations of dynamo action in
highly-stratified, three-dimensional compressible convection. Whether
or not a convective flow can drive a dynamo depends crucially upon
the magnetic Reynolds number. If this parameter is large enough that
the inductive effects of the fluid motions outweigh the dissipative
effects of magnetic diffusion, then dynamo action can occur. Simulating
convection with a Reynolds number of approximately 150, we find that
it is possible to excite a dynamo with computationally accessible
values of the magnetic Reynolds number. In the kinematic regime,
the growth rate of the dynamo has a logarithmic dependence upon the
magnetic Reynolds number. Following these dynamos into the nonlinear
regime, we find that intense, partially-evacuated concentrations of
vertical magnetic flux form near the upper surface of the computational
domain. This partial evacuation has a profound influence upon the
efficiency of the (explicit) numerical scheme that is used in these
calculations. These results can be related (in a qualitative sense)
to recent observations of magnetic fields in the quiet Sun.

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Title: Modulation of the sunspot cycle
Authors: Weiss, Nigel
2010A&G....51c...9W Altcode:
Solar activity has been abnormally high for the last half-century,
but the extremely feeble start of the latest 11-year cycle suggests
that this episode is probably coming to an end. This prospect raises
some fascinating and important issues, involving an extremely wide
range of timescales, writes Nigel Weiss.

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Title: Differential rotation in fully convective stars
Authors: Balbus, Steven A.; Weiss, Nigel O.
2010MNRAS.404.1263B Altcode: 2010MNRAS.tmp..279B; 2010arXiv1001.3542B
Under the assumption of thermal wind balance and effective entropy
mixing in constant rotation surfaces, the isorotational contours of the
solar convective zone may be reproduced with great fidelity. Even at
this early stage of development, this helioseismology fit may be used
to put a lower bound on the mid-latitude radial solar entropy gradient,
which is in good accord with standard mixing length theory. In this
paper, we generalize this solar calculation to fully convective stars
(and potentially planets), retaining the assumptions of thermal wind
balance and effective entropy mixing in isorotational surfaces. It
is found that each isorotation contour is of the form R2
= A + BΦ(r), where R is the radius from the rotation axis, Φ(r)
is the (assumed spherical) gravitational potential, and A and B
are constants along the contour. This result is applied to simple
models of fully convective stars. Both solar-like surface rotation
profiles (angular velocity decreasing toward the poles) as well as
`antisolar' profiles (angular velocity increasing toward the poles)
are modelled; the latter bear some suggestive resemblance to numerical
simulations. We also perform exploratory studies of zonal surface
flows similar to those seen in Jupiter and Saturn. In addition to
providing a practical framework for understanding the results of
large-scale numerical simulations, our findings may also prove useful
in dynamical calculations for which a simple but viable model for the
background rotation profile in a convecting fluid is needed. Finally,
our work bears directly on an important goal of the CoRoT programme:
to elucidate the internal structure of rotating, convecting stars.

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Title: Summary and Perspective
Authors: Weiss, N. O.
2010ASSP...19..346W Altcode: 2010mcia.conf..346W
This meeting celebrated a double anniversary. A 100 years ago, George
Ellery Hale had a hunch: he had noticed the vortical structure in Hα
above sunspots, and he interpreted this as evidence for a vortex flow,
which (he supposed) carried electric charges round a spot, and so
provided an azimuthal electric current that would generate a magnetic
field like that in a solenoid (Hale 1908a). His hunch was actually
wrong since (as we now know) the solar plasma is electrically neutral
- but when he looked for spectroscopic evidence of a magnetic field,
using the recently discovered Zeeman effect, he found that there were
kilogauss magnetic fields in sunspots (Hale 1908b). This was the first
demonstration that magnetic fields were present outside the earth.

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Title: Differential rotation and convection in the Sun
Authors: Balbus, Steven A.; Bonart, Julius; Latter, Henrik N.; Weiss,
Nigel O.
2009MNRAS.400..176B Altcode: 2009arXiv0907.5075B
We show that the differential rotation profile of the solar convection
zone, apart from inner and outer boundary layers, can be reproduced with
great accuracy if the isorotation contours correspond to characteristics
of the thermal wind equation. This requires that there be a formal
quantitative relationship involving the entropy and the angular
velocity. Earlier work has suggested that this could arise from
magnetohydrodynamic stability constraints; here, we argue that purely
hydrodynamical processes could also lead to such a result. Of special
importance to the hydrodynamical solution is the fact that the thermal
wind equation is insensitive to radial entropy gradients. This allows
a much more general class of solutions to fit the solar isorotation
contours, beyond just those in which the entropy itself must be a
function of the angular velocity. In particular, for this expanded
class, the thermal wind solution of the solar rotation profile remains
valid even when large radial entropy gradients are present. A clear
and explicit example of this class of solution appears to be present
in published numerical simulations of the solar convective zone. Though
hydrodynamical in character, the theory is not sensitive to the presence
of weak magnetic fields. Thus, the identification of solar isorotation
contours with the characteristics of the thermal wind equation appears
to be robust, accommodating, but by no means requiring, magnetic
field dynamics.

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Title: The Solar Dynamo
Authors: Weiss, N. O.; Thompson, M. J.
2009SSRv..144...53W Altcode: 2008SSRv..tmp..155W
It is generally accepted that the strong toroidal magnetic fields that
emerge through the solar surface in sunspots and active regions are
formed by the action of differential rotation on a poloidal field,
and then stored in or near the tachocline at the base of the Sun’s
convection zone. The problem is how to explain the generation of
a reversed poloidal field from this toroidal flux—a process that
can be parametrised in terms of an α-effect related to some form
of turbulent helicity. Here we first outline the principal patterns
that have to be explained: the 11-year activity cycle, the 22-year
magnetic cycle and the longer term modulation of cyclic activity,
associated with grand maxima and minima. Then we summarise what has
been learnt from helioseismology about the Sun’s internal structure
and rotation that may be relevant to our subject. The ingredients
of mean-field dynamo models are differential rotation, meridional
circulation, turbulent diffusion, flux pumping and the α-effect:
in various combinations they can reproduce the principal features
that are observed. To proceed further, it is necessary to rely on
large-scale computation and we summarise the current state of play.

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Title: The Solar Dynamo
Authors: Weiss, N. O.; Thompson, M. J.
2009odsm.book...53W Altcode:
It is generally accepted that the strong toroidal magnetic fields that
emerge through the solar surface in sunspots and active regions are
formed by the action of differential rotation on a poloidal field,
and then stored in or near the tachocline at the base of the Sun's
convection zone. The problem is how to explain the generation of
a reversed poloidal field from this toroidal flux—a process that
can be parametrised in terms of an α-effect related to some form
of turbulent helicity. Here we first outline the principal patterns
that have to be explained: the 11-year activity cycle, the 22-year
magnetic cycle and the longer term modulation of cyclic activity,
associated with grand maxima and minima. Then we summarise what has
been learnt from helioseismology about the Sun's internal structure
and rotation that may be relevant to our subject. The ingredients
of mean-field dynamo models are differential rotation, meridional
circulation, turbulent diffusion, flux pumping and the α-effect:
in various combinations they can reproduce the principal features
that are observed. To proceed further, it is necessary to rely on
large-scale computation and we summarise the current state of play.

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Title: Oded Regev (2006): Chaos and Complexity in
Astrophysics. Cambridge University Press, 468 pp., $89. ISBN-13
978-0-521-85534-1 (ISBN-10 0-521-85534-9)
Authors: Weiss, Nigel
2008ThCFD..22..485W Altcode: 2008ThCFD.tmp...16W
No abstract at ADS

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Title: Sunspots and Starspots
Authors: Thomas, John H.; Weiss, Nigel O.
2008sust.book.....T Altcode:
Preface; 1. The sun among the stars; 2. Sunspots and starspots:
a historical introduction; 3. Overall structure of a sunspot;
4. Fine structure of the umbra; 5. Fine structure of the penumbra;
6. Oscillations in sunspots; 7. Sunspots and active regions; 8. Magnetic
activity in stars; 9. Starspots; 10. Solar and stellar activity cycles;
11. Solar and stellar dynamos; 12. Solar activity, space weather,
and climate change; 13. The way ahead; Appendices; References; Index.

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Title: For how long will the current grand maximum of solar activity
persist?
Authors: Abreu, J. A.; Beer, J.; Steinhilber, F.; Tobias, S. M.;
Weiss, N. O.
2008GeoRL..3520109A Altcode:
Understanding the Sun's magnetic activity is important because of its
impact on the Earth's environment. The sunspot record since 1610 shows
irregular 11-year cycles of activity; they are modulated on longer
timescales and were interrupted by the Maunder minimum in the 17th
century. Future behavior cannot easily be predicted - even in the
short-term. Recent activity has been abnormally high for at least
8 cycles: is this grand maximum likely to terminate soon or even to
be followed by another (Maunder-like) grand minimum? To answer these
questions we use, as a measure of the Sun's open magnetic field, a
composite record of the solar modulation function Φ, reconstructed
principally from the proxy record of cosmogenic 10Be
abundances in the GRIP icecore from Greenland. This Φ record extends
back for almost 10,000 years, showing many grand maxima and grand
minima (defined as intervals when Φ is within the top or bottom 20%
of a Gaussian distribution). We carry out a statistical analysis of
this record and calculate the life expectancy of the current grand
maximum. We find that it is only expected to last for a further 15-36
years, with the more reliable methods yielding shorter expectancies,
and we therefore predict a decline in solar activity within the next
two or three cycles. We are not able, however, to predict the level
of the ensuing minimum.

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Title: Flux Pumping and Magnetic Fields in the Outer Penumbra of
a Sunspot
Authors: Brummell, Nicholas H.; Tobias, Steven M.; Thomas, John H.;
Weiss, Nigel O.
2008ApJ...686.1454B Altcode:
The filamentary structure of a sunspot penumbra is believed to be
magnetoconvective in origin. In the outer penumbra there is a difference
in inclination of up to 30°-40° between the magnetic fields associated
with bright and dark filaments, and the latter fields plunge downward
below the surface toward the edge of the spot. We have proposed that
these fields are dragged downward by magnetic pumping caused by the
external granular convection. In this paper we model this process in
a more elaborate idealized configuration that includes the curvature
force exerted by an arched magnetic field in addition to magnetic
buoyancy, and demonstrate that magnetic pumping remains an efficient
mechanism for holding flux submerged. We discuss the implications of
these results for the magnetic structure of the outer penumbra.

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Title: Convective intensification of magnetic fields in the quiet Sun
Authors: Bushby, P. J.; Houghton, S. M.; Proctor, M. R. E.; Weiss,
N. O.
2008MNRAS.387..698B Altcode: 2008arXiv0804.1238B
Kilogauss-strength magnetic fields are often observed in intergranular
lanes at the photosphere in the quiet Sun. Such fields are stronger
than the equipartition field Be, corresponding to a
magnetic energy density that matches the kinetic energy density of
photospheric convection, and comparable with the field Bp
that exerts a magnetic pressure equal to the ambient gas pressure. We
present an idealized numerical model of three-dimensional compressible
magnetoconvection at the photosphere, for a range of values of the
magnetic Reynolds number. In the absence of a magnetic field, the
convection is highly supercritical and characterized by a pattern of
vigorous, time-dependent, `granular' motions. When a weak magnetic
field is imposed upon the convection, magnetic flux is swept into the
convective downflows where it forms localized concentrations. Unless
this process is significantly inhibited by magnetic diffusion, the
resulting fields are often much greater than Be and the high
magnetic pressure in these flux elements leads to their being partially
evacuated. Some of these flux elements contains ultraintense magnetic
fields that are significantly greater than Bp. Such fields
are contained by a combination of the thermal pressure of the gas and
the dynamic pressure of the convective motion, and they are constantly
evolving. These ultraintense fields develop owing to non-linear
interactions between magnetic fields and convection; they cannot be
explained in terms of `convective collapse' within a thin flux tube
that remains in overall pressure equilibrium with its surroundings.

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Title: Convection-driven Emergence of Small-Scale Magnetic Fields
and their Role in Coronal Heating and Solar Wind Acceleration
Authors: Isobe, H.; Proctor, M. R. E.; Weiss, N. O.
2008ApJ...679L..57I Altcode:
Recent observations by the Solar Optical Telescope (SOT) on board
Hinode have revealed that the surface of the Sun is, on average,
covered with small-scale horizontal magnetic fields. Frequent emergence
of horizontal magnetic flux on a granular scale is found in the quiet
Sun and in plage regions. In this Letter we present the results of
magnetohydrodynamic simulations that cover the upper convection zone
and the corona. It is found that, even when the initial magnetic field
is uniform and vertical, a disordered magnetic field is produced in the
convection zone. The photospheric magnetic field is then characterized
by strong vertical fields concentrated in the intergranular lanes and
relatively weak, horizontal fields both in the granules and in the
intergranular lanes. Occasionally, fragments with large magnetic fluxes
are driven above the photosphere by the upward convective flows. These
characteristics are consistent with the SOT observations. Moreover,
the simulated flux emerging on a granular scale undergoes magnetic
reconnection with the expanding vertical magnetic concentrations in the
chromosphere. These reconnection events heat the local plasma and emit
high-frequency waves that propagate into the corona. Such an interplay
between the small-scale horizontal fields and the vertical flux may
play an important role in coronal heating and wind acceleration in
the Sun and stars.

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Title: The Solar Tachocline
Authors: Hughes, D. W.; Rosner, R.; Weiss, N. O.
2007sota.book.....H Altcode:
Preface; Part I. Setting the Scene: 1. An introduction to the solar
tachocline D. O. Gough; 2. Reflections on the solar tachocline
E. A. Spiegel; Part II. Observations: 3. Observational results
and issues concerning the tachocline J. Christensen-Dalsgaard and
M. J. Thompson; Part III. Hydrodynamic Models: 4. Hydrodynamic models of
the tachocline J.-P. Zahn; 5. Turbulence in the tachocline M. S. Miesch;
6. Mean field modelling of differential rotation G. Rudiger and
L. L. Kitchatinov; Part IV. Hydromagnetic Properties: 7. Magnetic
confinement of the solar tachocline P. Garaud; 8. Magnetic confinement
and the sharp tachopause M. E. McIntyre; 9. ß-Plane MHD turbulence
and dissipation in the solar tachocline P. H. Diamond, K. Itoh,
S.-I. Itoh and L. J. Silvers; Part V. Instabilities: 10. Global
MHD instabilities of the tachocline P. A. Gilman and P. S. Cally;
11. Magnetic buoyancy instabilities in the tachocline D. W. Hughes;
12. Instabilities, angular momentum transport and magnetohydrodynamic
turbulence G. I. Ogilvie; Part VI. Dynamo Action: 13. The solar dynamo
and the tachocline S. M. Tobias and N. O. Weiss; Part VII. Overview:
14. On studying the rotating solar interior R. Rosner; Index.

---------------------------------------------------------
Title: Sunspot Structure and Dynamics
Authors: Weiss, N. O.
2007sdeh.book...13W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: The Solar Tachocline
Authors: Hughes, David W.; Rosner, Robert; Weiss, Nigel O.
2007sota.conf.....H Altcode:
No abstract at ADS

---------------------------------------------------------
Title: The solar dynamo and the tachocline
Authors: Tobias, Steven; Weiss, Nigel
2007sota.conf..319T Altcode:
No abstract at ADS

---------------------------------------------------------
Title: The Puzzling Structure of a Sunspot
Authors: Weiss, N. O.
2006ASPC..354..213W Altcode:
Sunspots are characterized by the presence of a filamentary penumbra
but it is only within the last few years that the fine structure of
penumbral magnetic fields, and of the associated Evershed outflow,
has been definitively established. High resolution observations show
that bright filaments in the inner penumbra possess slender dark cores
with fields and flows that are nearly horizontal, while the ambient
fields are inclined at 40° to the vertical. In the outer penumbra
the fields in bright and dark filaments differ in inclination by
about 30° and recent observations confirm that the Evershed flow is
along the almost horizontal fields in dark filaments. Moreover, these
two families of field lines remain distinct. This intricate magnetic
geometry poses major theoretical problems. How can such a structure be
maintained and how does it originate? How do penumbral fields relate
to the photospheric granulation outside the spot? What drives the
Evershed flow within dark filaments? What form does convection take
in the umbra, in bright filaments and in dark filaments? What causes
the fine structure within bright filaments? What is the subsurface
structure of a sunspot and how does it relate to outflows and inflows
in the moat cell that surrounds it? Although a general theoretical
picture is beginning to emerge, these questions can only be properly
answered through detailed computational investigations, guided by
further observations both from the ground and from space.

---------------------------------------------------------
Title: Unpredictable Sun leaves researchers in the dark
Authors: Tobias, Steven; Hughes, David; Weiss, Nigel
2006Natur.442...26T Altcode:
No abstract at ADS

---------------------------------------------------------
Title: On the fine structure of magnetic fields in sunspot penumbrae
Authors: Thomas, J. H.; Weiss, N. O.; Tobias, S. M.; Brummell, N. H.
2006A&A...452.1089T Altcode:
Recent observations have revealed the interlocking-comb structure of
the magnetic field in the outer penumbra of a sunspot. We have argued
that this structure owes its origin in part to downward pumping of
magnetic flux by vigorous granular convection in the region surrounding
the spot. Here we stress the difference between the inner and outer
penumbra, and correct some misleading assertions in a recent paper by
Spruit &amp; Scharmer.

---------------------------------------------------------
Title: Sunspot Structure and Dynamics
Authors: Weiss, N. O.
2006SSRv..124...13W Altcode: 2006SSRv..tmp...87W
Sunspots are the most prominent magnetic features on the Sun but it
is only within the last few years that the intricate structure of
their magnetic fields has been resolved. In the penumbra the fields
in bright and dark filaments differ in inclination by 30°. The field
in the bright filaments is less inclined to the vertical, while the
field in dark filaments becomes almost horizontal at the edge of the
spot. Recent models suggest that this interlocking-comb structure is
maintained through downward pumping of magnetic flux by small-scale
granular convection, and that filamentation originates as a convective
instability. Within the bright filaments convection patterns travel
radially owing to the inclination of the field. A proper understanding
of these processes requires new observations, from space and from the
ground, coupled with large-scale numerical modelling.

---------------------------------------------------------
Title: Hughes, Rosner, Weiss: Stellar MHD: Magnetohydrodynamics of
stellar interiors
Authors: Hughes, David; Rosner, Robert; Weiss, Nigel
2005A&G....46d..35H Altcode:
David Hughes, Robert Rosner and Nigel Weiss describe what was
achieved during a programme on stellar magnetic fields at the Isaac
Newton Institute in Cambridge. Over a four-month period more than
90 participants visited the Institute for a mixture of structured
workshops and informal collaboration.

---------------------------------------------------------
Title: Linear and nonlinear dynamos
Authors: Weiss, N. O.
2005AN....326..157W Altcode:
More than eighty years have passed since the idea of a solar dynamo was
first put forward, and almost fifty years since Parker's pioneering
paper. Yet dynamo theory remains a fertile subject and continues
to raise new challenges, both physical and mathematical. So far,
nearly all treatments have relied on mean field electrodynamics. The
earliest models were linear but recent treatments have been nonlinear
and increasingly sophisticated. During his career, Michael Stix has
made major contributions to all branches of this subject. In this
survey I shall review the historical development of dynamo theory, as
applied to stars like the Sun, and then focus on some issues of current
interest, ranging from axisymmetric calculations in spherical geometry
to low-order models. Finally, I shall look ahead to what is needed in
order to develop fully consistent, three-dimensional numerical models
of the solar cycle.

---------------------------------------------------------
Title: Book review of The magnetic universe, geophysical and
astrophysical dynamo theory, by G. Rüdiger and R. Hollerbach,
Wiley-VCH, Weinheim, 2004, XI+332 pp., £90.00, $161.00,
&amp;euro;135.00, hardback (ISBN: 3-527-40409-0).
Authors: Weiss, Nigel
2005GApFD..99..347W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Fluid Dynamics and Dynamos in Astrophysics and Geophysics:
reviews emerging from the Durham Symposium on Astrophysical Fluid
Mechanics held July 29 to August 8, 2002
Authors: Soward, Andrew M.; Jones, Christopher A.; Hughes, David W.;
Weiss, Nigel O.
2005fdda.conf.....S Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Solar and stellar physics - II
Authors: Weiss, N. O.
2004Obs...124..348W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Fine Structure in Sunspots
Authors: Thomas, John H.; Weiss, Nigel O.
2004ARA&A..42..517T Altcode:
Important physical processes on the Sun, and especially in sunspots,
occur on spatial scales at or below the limiting resolution of
current solar telescopes. Over the past decade, using a number of
new techniques, high-resolution observations have begun to reveal
the complex thermal and magnetic structure of a sunspot, along with
associated flows and oscillations. During this time remarkable advances
in computing power have allowed significant progress in our theoretical
understanding of the dynamical processes, such as magnetoconvection,
taking place within a sunspot. In this review we summarize the latest
observational results and theoretical interpretations of the fine
structure in sunspots. A number of projects underway to build new solar
telescopes or upgrade existing ones, along with several promising new
theoretical ideas, ensure that there will be significant advances in
sunspot research over the coming decade.

---------------------------------------------------------
Title: Sunspots: The puzzling structure of a sunspot
Authors: Tobias, Steven; Weiss, Nigel
2004A&G....45d..28T Altcode:
High-resolution observations of fine structure in sunspots have at
last made it possible to answer a very old question: what causes the
filamentary structure of the penumbra, with magnetic fields forming an
interlocking comb-like configuration, that surrounds the dark central
umbra of a sunspot? This unexpected geometry can only be explained
by an understanding of the interaction between magnetic fields and
small-scale turbulent convection outside the spot. This interaction
leads to downwards transport of magnetic flux, submerging magnetic
flux tubes below the solar surface and resulting in a strongly fluted
structure. An idealized version of this process can be demonstrated
in numerical experiments.

---------------------------------------------------------
Title: On the origin of filamentary structure in sunspot penumbrae:
non-linear results
Authors: Tildesley, M. J.; Weiss, N. O.
2004MNRAS.350..657T Altcode:
As the magnetic flux in a pore increases, it grows in radius and the
magnetic field at its outer edge becomes increasingly inclined to
the vertical. It is believed that this increased field inclination
causes filamentary convection to set in and that this new pattern
of convection eventually develops into the highly fluted azimuthal
structure of sunspots. The linear instability was investigated in a
highly idealized Boussinesq model by Tildesley. A non-linear extension
of this work is carried out here and the saturation of the instability
is explored. These solutions are contrasted with those obtained when the
upper-boundary condition is modified by matching the magnetic field to
a potential field above the convecting layer. In the non-linear regime
an alternating pattern of hot and cool stripes is produced at the
upper surface. The results from these model calculations are related
to the transition from pores to protospots and to the development of
penumbral filaments in sunspots.

---------------------------------------------------------
Title: Global Magnetorotational Instability with Inflow. I. Linear
Theory and the Role of Boundary Conditions
Authors: Kersalé, Evy; Hughes, David W.; Ogilvie, Gordon I.; Tobias,
Steven M.; Weiss, Nigel O.
2004ApJ...602..892K Altcode:
We formulate a model system suitable for the systematic numerical
investigation of global aspects of the magnetorotational instability
and nonlinear dynamo action in accretion disks. The model consists
of a cylindrical annulus occupied by an incompressible fluid with
explicit viscosity and resistivity. Boundary conditions are imposed
that permit an accretion flow appropriate to the stresses acting within
the fluid to develop freely through the annulus. A steady basic state
is identified in which a slow, steady accretion flow is driven by the
explicit viscosity. We investigate the linear theory of this state
subject to different choices of boundary conditions. The choice of
boundary conditions is a crucial factor in determining the nature and
growth rate of the instabilities. It is found that very rapidly growing
wall modes occur generically, drawing energy artificially from outside
the computational domain. However, by carefully selecting boundary
conditions for which the total pressure is constrained at the radial
boundaries, the wall modes are found to have growth rates bounded
by the local properties of the magnetorotational instability. The
resulting model provides the basis for a systematic exploration of
nonlinear behavior in our future work.

---------------------------------------------------------
Title: The Origin of Penumbral Structure in Sunspots: Downward
Pumping of Magnetic Flux
Authors: Weiss, Nigel O.; Thomas, John H.; Brummell, Nicholas H.;
Tobias, Steven M.
2004ApJ...600.1073W Altcode:
This paper offers the first coherent picture of the interactions
between convection and magnetic fields that lead to the formation of
the complicated filamentary structure of a sunspot penumbra. Recent
observations have revealed the intricate interlocking-comb structure
of the penumbral magnetic field. Some field lines, with associated
Evershed outflows, plunge below the solar surface near the edge of
the spot. We claim that these field lines are pumped downward by
small-scale granular convection outside the sunspot. This mechanism
is demonstrated in numerical experiments. Magnetic pumping is a key
new ingredient that links several theoretical ideas about penumbral
structure and dynamics; it explains not only the abrupt appearance of
a penumbra as a pore increases in size but also the behavior of moving
magnetic features outside a spot.

---------------------------------------------------------
Title: The Sun, An Introduction, by M. Stix, Astronomy and
Astrophysics Library, Springer Berlin, Heidelberg, New York,
Barcelona, Hong Kong, London, Milan, Paris, Tokyo, 2nd ed. 2002,
XVI+490 pp., EUR 79,95, hardback (ISBN: 3-540-42886-0)
Authors: Weiss, Nigel
2003GApFD..97..421W Altcode:
Available from <A
href="http://taylorandfrancis.metapress.com/openurl.asp?genre=article&amp;issn=0309-1929&amp;volume=97&amp;issue=5&amp;spage=421">http://taylorandfrancis.metapress.com/openurl.asp?genre=article&amp;issn=0309-1929&amp;volume=97&amp;issue=5&amp;spage=421</A>

---------------------------------------------------------
Title: On the Interaction between Convection and Magnetic Fields
Authors: Cattaneo, Fausto; Emonet, Thierry; Weiss, Nigel
2003ApJ...588.1183C Altcode:
Turbulent convection in the solar photosphere can act as a small-scale
dynamo, maintaining a disordered magnetic field that is locally
intense. On the other hand, convection is inhibited in the presence
of a strong, externally imposed magnetic field, as for instance,
in a sunspot. Large-scale, three-dimensional, numerical experiments
on highly nonlinear magnetoconvection in a Boussinesq fluid show
that there is a continuous transition from a dynamo regime through
a convective regime to an oscillatory regime as the strength of the
imposed magnetic field is progressively increased. The patterns found
in these different regimes are described and analyzed.

---------------------------------------------------------
Title: Modelling solar and stellar magnetoconvection
Authors: Weiss, Nigel
2003safd.book..329W Altcode:
Numerical experiments on three-dimensional convection in the presence
of an externally imposed magnetic field reveal a range of behaviour
that can be compared with that observed at the surface of the Sun
(and therefore expected to be present in other similar stars). In a
strongly stratified compressible layer small-scale convection gives
way to a regime with flux separation as the field strength is reduced;
with a weak mean field magnetic flux is concentrated into narrow
lanes enclosing vigorously convecting plumes. Small-scale dynamos,
generating disordered magnetic fields, have been found in Boussinesq
calculations with very high magnetic Reynolds numbers; there is a
gradual transition from dynamo action to magnetoconvection as the
strength of the imposed field is increased.

---------------------------------------------------------
Title: Modelling Stellar Magnetoconvection
Authors: Weiss, N. O.
2003IAUS..210..127W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Magnetic flux separation in photospheric convection
Authors: Weiss, N. O.; Proctor, M. R. E.; Brownjohn, D. P.
2002MNRAS.337..293W Altcode:
Three-dimensional non-linear magnetoconvection in a strongly stratified
compressible layer exhibits different patterns as the strength of
the imposed magnetic field is reduced. There is a transition from a
magnetically dominated regime, with small-scale convection in slender
hexagonal cells, to a convectively dominated regime, with clusters of
broad rising plumes that confine the magnetic flux to narrow lanes where
fields are locally intense. Both patterns can coexist for intermediate
field strengths, giving rise to flux separation: clumps of vigorously
convecting plumes, from which magnetic flux has been excluded, are
segregated from regions with strong fields and small-scale convection. A
systematic numerical investigation of these different states shows
that flux separation can occur over a significant parameter range and
that there is also hysteresis. The results are related to the fine
structure of magnetic fields in sunspots and in the quiet Sun.

---------------------------------------------------------
Title: Downward pumping of magnetic flux as the cause of filamentary
structures in sunspot penumbrae
Authors: Thomas, John H.; Weiss, Nigel O.; Tobias, Steven M.; Brummell,
Nicholas H.
2002Natur.420..390T Altcode:
The structure of a sunspot is determined by the local interaction
between magnetic fields and convection near the Sun's surface. The dark
central umbra is surrounded by a filamentary penumbra, whose complicated
fine structure has only recently been revealed by high-resolution
observations. The penumbral magnetic field has an intricate and
unexpected interlocking-comb structure and some field lines, with
associated outflows of gas, dive back down below the solar surface
at the outer edge of the spot. These field lines might be expected
to float quickly back to the surface because of magnetic buoyancy,
but they remain submerged. Here we show that the field lines are kept
submerged outside the spot by turbulent, compressible convection,
which is dominated by strong, coherent, descending plumes. Moreover,
this downward pumping of magnetic flux explains the origin of the
interlocking-comb structure of the penumbral magnetic field, and the
behaviour of other magnetic features near the sunspot.

---------------------------------------------------------
Title: Umbral and penumbral magnetoconvection
Authors: Weiss, N. O.
2002AN....323..371W Altcode:
Compressible convection in a strong vertical magnetic field can take two
forms: either there is a regular pattern of small plumes or else the
field separates from the motion giving regions of vigorous convection
and regions that are magnetically dominated. In an inclined field,
patterns are bound to travel. When the magnetic field is almost
horizontal, convection takes the form of rolls aligned with the
field. In the umbra of a sunspot convection will take the form of
spatially modulated oscillations, giving rise to umbral dots. The
penumbral field shows an interlocking-comb structure. In the bright
filaments the magnetic field is inclined to the horizontal and modulated
travelling waves, moving inwards or outwards, can give rise to the
migration of bright grains. In the dark filaments the field is nearly
horizontal, allowing only inefficient overturning convection.

---------------------------------------------------------
Title: Magnetic flux pumping and the structure of a sunspot penumbra
Authors: Thomas, J. H.; Weiss, N. O.; Tobias, S. M.; Brummell, N. H.
2002AN....323..383T Altcode:
We propose an overall scenario for the development and maintenance of
a sunspot penumbra, in which turbulent magnetic flux pumping plays a
key role. Recent high-resolution observations have revealed arched,
"returning" magnetic flux tubes that emerge in the inner or middle
penumbra, dive back down below the solar surface near the outer edge
of the penumbra, and carry much of the Evershed flow. Some mechanism
is required to keep the outer parts of the returning flux tubes
submerged in spite of their magnetic buoyancy. We have proposed that
the relevant mechanism is downward turbulent pumping of magnetic flux
by granular convection in the moat outside the sunspot. This mechanism
is demonstrated by means of an appropriate three-dimensional numerical
simulation of turbulent compressible convection in the strongly
superadiabatic granulation layer. We suggest that a penumbra first
forms through a convectively driven instability at the outer edge
of a growing pore. The nonlinear development of this instability
pUSA)roduces the filamentary penumbra with its interlocking-comb
magnetic field geometry. Downward flux pumping of some of the nearly
horizontal magnetic flux in the dark filaments produces the returning
flux tubes, with their associated Evershed flow, and also establishes
the subcritical nature of the bifurcation that produces the filamentary
penumbra, which explains why there are pores larger than the smallest
sunspots.

---------------------------------------------------------
Title: Presidential Address: Dynamos in planets, stars and galaxies
Authors: Weiss, Nigel
2002A&G....43c...9W Altcode:
Nigel Weiss discusses dynamos in settings as diverse as galaxies and
planets in this his 2000 Presidential Address to the Ordinary (A&amp;G)
Meeting of the Royal Astronomical Society. &lt;heading id="h10"
level="1"&lt;/heading&gt; Global magnetic fields in the Earth
and other major planets, in the Sun and other active stars, and also
in spiral galaxies like the Milky Way, are apparently maintained by
hydromagnetic dynamos. This lecture will contrast the various dynamo
models that have been put forward. Powerful supercomputers have now
made it possible to simulate the geodynamo in considerable detail. In
the case of the Sun, we have yet to explain its internal rotation
and models still have to rely on mean field dynamo theory. There are
many features that can be explained but extrapolation to other stars
remains uncertain. For galaxies, even the need for a dynamo is still
controversial.

---------------------------------------------------------
Title: On the Origin of the Solar Mesogranulation
Authors: Cattaneo, Fausto; Lenz, Dawn; Weiss, Nigel
2001ApJ...563L..91C Altcode:
The observed properties of mesogranules are related to structures found
in idealized numerical experiments on turbulent convection. We describe
results obtained for three-dimensional Boussinesq convection in a layer
with a very large aspect ratio. There are two distinct cellular patterns
at the surface. Energy-transporting convection cells (corresponding
to granules in the solar photosphere) have diameters comparable to
the layer depth, while macrocells (corresponding to mesogranules)
are several times larger. The motion acts as a small-scale turbulent
dynamo, generating a disordered magnetic field that is concentrated
at macrocellular corners and, to a lesser extent, in the lanes that
join them. These results imply that mesogranules owe their origin to
collective interactions between the granules.

---------------------------------------------------------
Title: Sustaining the Sun's Magnetic Network with Emerging Bipoles
Authors: Simon, G. W.; Title, A. M.; Weiss, N. O.
2001ApJ...561..427S Altcode:
The Michelson Doppler Imager experiment on SOHO has revealed a
“magnetic carpet” dominated by the emergence of bipolar magnetic flux
in ephemeral active regions, which subsequently split into small flux
elements that drift into the magnetic network. The effects of granular
and supergranular convection on these flux elements are represented
here by kinematic modeling: Elementary flux tubes are transported
passively by the supergranular flow, while experiencing small random
displacements produced by granulation. They end up in the magnetic
network that surrounds the supergranules, where they eventually meet
oppositely directed fields and are annihilated. The model calculations
show that the total unsigned magnetic flux will decay within a few
days unless it is continually replenished. A statistically steady
state with a total unsigned flux of 2-3×1023 Mx over the
whole solar surface can be maintained if bipolar flux emerges at a rate
of 7×1022 Mx day-1, as indicated by published
measurements of the rate at which ephemeral active regions appear.

---------------------------------------------------------
Title: Presidential Address: Turbulent magnetic fields in the Sun
Authors: Weiss, Nigel
2001A&G....42c..10W Altcode:
Nigel Weiss recounts his Presidential Address 2001, given to the RAS
A&amp;G Ordinary Meeting on 9 February 2001. Recent high-resolution
observations, from the ground and from space, have revealed the fine
structure of magnetic features at the surface of the Sun. At the same
time, advances in computing power have at last made it possible to
develop models of turbulent magnetoconvection that can be related to
these observations. The key features of flux emergence and annihilation,
as observed by the MDI experiment on SOHO, are reproduced in kinematic
calculations, while three-dimensional numerical experiments reveal the
dynamical processes that are involved. The pattern of convection depends
on the strength of the magnetic field: as the mean field decreases,
slender rising plumes give way to a regime where magnetic flux is
separated from the motion and then to one where locally intense magnetic
fields nestle between broad and vigorously convecting plumes. Moreover,
turbulent convection is itself able to act as a small-scale dynamo,
generating disordered fields near the solar surface.

---------------------------------------------------------
Title: How the Sun Maintains its Magnetic Network
Authors: Simon, G. W.; Title, A. M.; Weiss, N. O.
2001AAS...198.8601S Altcode: 2001BAAS...33..913S
The MDI experiment on SOHO has revealed a `magnetic carpet' dominated
by the emergence of bipolar magnetic flux in ephemeral active regions,
which subsequently split into small flux elements that drift into the
magnetic network. The effects of granular and supergranular convection
on these flux elements are represented here by kinematic modeling:
Elementary flux tubes are transported passively by the supergranular
flow, while experiencing small random displacements produced by
granulation. They end up in the magnetic network that surrounds the
supergranules, where they eventually meet oppositely directed fields and
are annihilated. The model calculations show that the total unsigned
magnetic flux will decay within a few days unless it is continually
replenished. A statistically steady state with a total unsigned
flux of 2-3 x 1023 Mx over the whole solar surface can be
maintained if bipolar flux emerges at a rate of 7 x 1022
Mx d-1, as indicated by published measurements of the rate
at which ephemeral active regions appear.

---------------------------------------------------------
Title: Flux Separation in Photospheric Magnetoconvection
Authors: Weiss, N. O.; Proctor, M. R. E.
2001IAUS..203..219W Altcode:
Numerical experiments on three-dimensional magnetoconvection in a
stratified compressible layer yield results that can now be compared
with the high resolution observations of granulation and intergranular
magnetic fields obtained at La Palma, and related to the slender
loops revealed by TRACE. As the imposed magnetic field strength
is decreased there is a transition from small-scale plumes, in the
magnetically dominated regime, to large-scale vigorous plumes when the
field is dominated by the motion. In the intermediate regime magnetic
flux separates from the motion, so that there are almost field-free
regions, with clusters of vigorous plumes, surrounded by regions where
the Lorentz force is strong enough to control the dynamics. There
is a range of field strengths where either small-scale plumes or
flux-separated solutions can persist, depending on initial conditions
for the computation. The patterns revealed in these calculations can
be related to convection in sunspot umbrae (where there is a strong
vertical field, and the appearance of umbral dots, to the formation
of plage regions and to the behaviour of intergranular fields in the
quiet Sun. In the weak field limit, turbulent convection is able to
act as a dynamo and to maintain a disordered field.

---------------------------------------------------------
Title: Generation of Coronal Currents by the Solar Convection Zone
Authors: Galloway, D. J.; Uchida, Y.; Weiss, N. O.
2001PASA...18..329G Altcode:
: Solar flares are thought to be caused by reconnection of magnetic
fields and their associated electric currents in the solar corona. The
currents have to be there to provide available energy over and above
the current-free minimum energy state, but what generates them has been
little discussed. This paper investigates the idea that twisting motions
in the turbulent convection zone below may provide a natural source for
the currents and explain some of their properties. The twists generate
upward-propagating Alfvén waves with a Poynting flux of the right order
of magnitude to power a flare. Depending on the depth it takes place,
the twisting event that initiates a particular flare may occur hours,
days or even months before the flare itself.

---------------------------------------------------------
Title: Physical Causes of Solar Activity
Authors: Weiss, N. O.; Tobias, S. M.
2000SSRv...94...99W Altcode:
The magnetic fields that dominate the structure of the Sun's atmosphere
are controlled by processes in the solar interior, which cannot be
directly observed. Magnetic activity is found in all stars with deep
convective envelopes: young and rapidly rotating stars are very active
but cyclic activity only appears in slow rotators. The Sun's 11-year
activity cycle corresponds to a 22-year magnetic cycle, since the
sunspot fields (which are antisymmetric about the equator) reverse
at each minimum. The record of magnetic activity is aperiodic and
is interrupted by episodes of reduced activity, such as the Maunder
Minimum in the seventeenth century, when sunspots almost completely
disappeared. The proxy record from cosmogenic isotopes shows that
similar grand minima recur at intervals of around 200 yr. The Sun's
large-scale field is generated by dynamo action rather than by an
oscillator. Systematic magnetic cycles are apparently produced by a
dynamo located in a region of weak convective overshoot at the base
of the convection zone, where there are strong radial gradients in
the angular velocity Ω. The crucial parameter (the dynamo number)
increases with increasing Ω and kinematic (linear) theory shows that
dynamo action can set in at an oscillatory (Hopf) bifurcation that is
probably subcritical. Although it has been demonstrated that the whole
process works in a self-consistent model, most calculations have relied
on mean-field dynamo theory. This approach is physically plausible
but can only be justified under conditions that do not apply in the
Sun. Still, mean-field dynamos do reproduce the butterfly diagram and
other key features of the solar cycle. An alternative approach is to
study generic behaviour in low-order models, which exhibit two forms
of modulation, associated with symmetry-breaking and with reduced
activity. Comparison with observed behaviour suggests that modulation
of the solar cycle is indeed chaotic, i.e. deterministically rather
than stochastically driven.

---------------------------------------------------------
Title: Sunspots
Authors: Weiss, N.
2000eaa..bookE2050W Altcode:
Sunspots are the sites of strong magnetic fields at the surface
of the Sun. They are visible as features that appear dark because
they are cooler than the surrounding SOLAR PHOTOSPHERE, owing to
partial suppression of convective energy transport by the magnetic
field. Sunspots are distinguished from SUNSPOT PORES by having a
filamentary SUNSPOT PENUMBRA surrounding a dark SUNSPOT UMBRA. Their
dia...

---------------------------------------------------------
Title: Resonance in a coupled solar-climate model
Authors: Tobias, S. M.; Weiss, N. O.
2000SSRv...94..153T Altcode:
The 11-year solar activity cycle is magnetic in origin and is
responsible for small changes in solar luminosity and the modulation
of the solar wind. The terrestrial climate exhibits much internal
variability supporting oscillations with many frequencies. The direct
effect of changing solar irradiance in driving climatic change is
believed to be small, and amplification mechanisms are needed to
enhance the role of solar variability. In this paper we demonstrate
that resonance may play a crucial role in the dynamics of the climate
system, by using the output from a nonlinear solar dynamo model as a
weak input to a simplified climate model. The climate is modelled as
oscillating about two fixed points (corresponding to a warm and cold
state) with the weak chaotically modulated solar forcing on average
pushing the solution towards the warm state. When a typical frequency
of the input is similar to that of the chaotic climate system then
a dramatic increase in the role of the solar forcing is apparent and
complicated intermittent behaviour is observed. The nonlinear effects
are subtle however, and forcing that on average pushes the solution
towards the warm state may lead to increased intervals of oscillation
about either state. Owing to the intermittent nature of the timeseries,
analysis of the relevant timeseries is shown to be non-trivial.

---------------------------------------------------------
Title: Turbulent Convection, Rotation, and the Solar Dynamo
Authors: Tobias, Steve; Toomre, Juri; Weiss, Nigel
2000astu.progE..30T Altcode:
No abstract at ADS

---------------------------------------------------------
Title: The Influence of Internal Heating on Nonlinear Compressible
Convection
Authors: Hurlburt, N. E.; Weiss, N. O.
2000SPD....31.0506H Altcode: 2000BAAS...32..837H
In the bulk of the solar convection zone we expect convection to be
efficient and therefore maintain an adiabatic temperature gradient. In
most numerical simulations of solar convection the total energy flux
within this region is due to the conduction down this gradient (which is
small) and the various contributions due to the convective motions. What
has often been neglected is the contribution that is transported by
radiation. The contribution of this flux decreases across the layer
and thereby deposits a significant amount of thermal energy in the
midst of the convection zone. This is in contrast to most simulations
of the convection where the input of energy is supplied exclusively
by conduction from the boundaries. Mixing length models predict that
approximately half of the total energy input to the solar convection
zone is deposited, more-or-less uniformly over the convection zone, with
the remaining half being conducted from the lower boundary. Thus the
study of the behavior of internally-heated compressible convection is
warranted. Previous studies of internally heated compressible convection
have been inconclusive due to the shearing instabilities that arise
in simple, periodic domains. Here we suppress these instabilities by
considering flows in axisymmetric geometries. We conduct surveys of
the structure and dynamics of the resulting flows and present possible
applications to observed solar and stellar phenomena.

---------------------------------------------------------
Title: Resonance in a Coupled Solar-Climate Model
Authors: Tobias, S. M.; Weiss, N. O.
2000svc..book..153T Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Physical Causes of Solar Activity
Authors: Weiss, N. O.; Tobias, S. M.
2000svc..book...99W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Symmetry Considerations in Stellar Dynamos
Authors: Tobias, S. M.; Knobloch, E.; Weiss, N. O.
1999ASPC..178..185T Altcode: 1999sdnc.conf..185T
No abstract at ADS

---------------------------------------------------------
Title: Modelling photospheric magnetoconvection
Authors: Blanchflower, S. M.; Rucklidge, A. M.; Weiss, N. O.
1998MNRAS.301..593B Altcode:
The increasing power of computers makes it possible to model the
non-linear interaction between magnetic fields and convection at
the surfaces of solar-type stars in ever greater detail. We present
the results of idealized numerical experiments on two-dimensional
magnetoconvection in a fully compressible perfect gas. We first vary
the aspect ratio lambda of the computational box and show that the
system runs through a sequence of convective patterns, and that it is
only for a sufficiently wide box (lambda&gt;=6) that the flow becomes
insensitive to further increases in lambda. Next, setting lambda=6,
we decrease the field strength from a value strong enough to halt
convection and find transitions to small-scale steady convection, next
to spatially modulated oscillations (first periodic, then chaotic)
and then to a new regime of flux separation, with regions of strong
field (where convection is almost completely suppressed) separated
by broad convective plumes. We also explore the effects of altering
the boundary conditions and show that this sequence of transitions
is robust. Finally, we relate these model calculations to recent
high-resolution observations of solar magnetoconvection, in plage
regions as well as in light bridges and the umbrae of sunspots.

---------------------------------------------------------
Title: Flux expulsion by inhomogeneous turbulence
Authors: Tao, L.; Proctor, M. R. E.; Weiss, N. O.
1998MNRAS.300..907T Altcode:
Flux expulsion is an important consequence of the interaction of
magnetic fields with fluid convection and has been well studied for
particular cases of steady, single-cell flows. Here we examine a
related phenomenon in inhomogeneous turbulence using direct numerical
simulations. To understand our numerical results, we analyse average
properties of our model, and obtain mean transport coefficients
which can be used to describe the approach of the system to its final
state. For the kinematic problem these transport coefficients give an
excellent prediction of the expulsion process; however, the enhanced
transport is suppressed by dynamical back-reaction of the Lorentz
force. Finally, we discuss the astrophysical implications for magnetic
fields in stellar convection zones. Segregation of magnetic fields from
turbulent motion not only allows strong toroidal fields to accumulate
in regions of convective overshoot but also permits significant poloidal
fields to be maintained by dynamo action in stars like the Sun.

---------------------------------------------------------
Title: Modulation and symmetry changes in stellar dynamos
Authors: Knobloch, E.; Tobias, S. M.; Weiss, N. O.
1998MNRAS.297.1123K Altcode:
Stellar dynamos are governed by non-linear partial differential
equations (PDEs) which admit solutions with dipole, quadrupole or mixed
symmetry (i.e. with different parities). These PDEs possess periodic
solutions that describe magnetic cycles, and numerical studies reveal
two different types of modulation. For modulations of Type 1 there
are parity changes without significant changes of amplitude, while
for Type 2 there are amplitude changes without significant changes in
parity. In stars like the Sun, cyclic magnetic activity is interrupted
by grand minima that correspond to Type 2 modulation. Although the
Sun's magnetic field has maintained dipole symmetry for almost 300
yr, there was a significant parity change at the end of the Maunder
Minimum. We infer that the solar field may have flipped from dipole
to quadrupole polarity (and back) after deep minima in the past and
may do so again in the future. Other stars, with different masses or
rotation rates, may exhibit cyclic activity with dipole, quadrupole
or mixed parity. The origins of such behaviour can be understood
by relating the PDE results to solutions of appropriate low-order
systems of ordinary differential equations (ODEs). Type 1 modulation
is reproduced in a fourth-order system while Type 2 modulation occurs
in a third-order system. Here we construct a new sixth-order system
that describes both types of modulation and clarifies the interactions
between symmetry-breaking and modulation of activity. Solutions of these
non-linear ODEs reproduce the qualitative behaviour found for the PDEs,
including flipping of polarity after a prolonged grand minimum. Thus
we can be confident that these patterns of behaviour are robust,
and will apply to stars that are similar to the Sun.

---------------------------------------------------------
Title: An Active Sun Throughout the Maunder Minimum
Authors: Beer, Jürg; Tobias, Steven; Weiss, Nigel
1998SoPh..181..237B Altcode:
Measurements of 10Be concentration in the Dye 3 ice core
show that magnetic cycles persisted throughout the Maunder Minimum,
although the Sun's overall activity was drastically reduced and sunspots
virtually disappeared. Thus the dates of maxima and minima can now be
reliably estimated. Similar behaviour is shown by a nonlinear dynamo
model, which predicts that, after a grand minimum, the Sun's toroidal
field may switch from being antisymmetric to being symmetric about the
equator. The presence of cyclic activity during the Maunder Minimum
limits estimates of the solar contribution to climatic change.

---------------------------------------------------------
Title: Flux Separation in Stellar Magnetoconvection
Authors: Tao, L.; Weiss, N. O.; Brownjohn, D. P.; Proctor, M. R. E.
1998ApJ...496L..39T Altcode:
The effect of a strong magnetic field on photospheric convection in a
cool star like the Sun can be established by relating high-resolution
solar observations to results from nonlinear models that rely on
computation. The patterns of motion in numerical experiments on
three-dimensional, compressible magnetoconvection depend not only on
the strength of the imposed vertical magnetic field but also on the
aspect ratio λ of the computational box. In a wide box (λ=8) with a
moderately strong field, the flow organizes itself so that magnetic flux
is separated from the motion. There are regions with strong fields and
small-scale oscillatory convection next to almost field-free regions
with clusters of broad and vigorous convective plumes. In the solar
photosphere, this corresponds to the difference between the patterns
of granulation in plage regions (with fields greater than 100 G)
and in the adjacent quiet Sun.

---------------------------------------------------------
Title: Kinematic Modeling of Vortices in the Solar Photosphere
Authors: Simon, G. W.; Weiss, N. O.
1997ApJ...489..960S Altcode:
The application of local correlation tracking to the proper motions of
granules yields the horizontal velocity field at the solar surface. The
divergence of the velocity reveals a pattern of sources and sinks. The
vorticity is concentrated at sinks to form local swirls (with either
sense of motion). A simple kinematic model of such a vortex, in
which the radial inflow is balanced by an eddy viscosity, predicts
that the vorticity should have a Gaussian profile. This prediction is
confirmed by comparison with three sets of high-resolution observations,
obtained from Spacelab 2 and from the Swedish Vacuum Solar Telescope
on La Palma. Finally, we develop a more precise version of the model
and provide an estimate of the eddy viscosity due to small-scale
granulation.

---------------------------------------------------------
Title: Physics of the solar dynamo
Authors: Weiss, N. O.
1997ppvs.conf..325W Altcode:
Introduction Stellar magnetic cycles Solar magnetic activity Stellar
activity Origins of the Sun's magnetic field Dynamo theory The
kinematic dynamo problem Nonlinear equilibration Mean-field dynamo
theory Modulation of activity cycles Toy models Global models Solar
activity and climatic change Observational correlations Mechanisms
and speculations

---------------------------------------------------------
Title: Modulation of Solar and Stellar Activity Cycles
Authors: Weiss, N. O.; Tobias, S. M.
1997LNP...489...25W Altcode: 1997shpp.conf...25W
Cyclic magnetic activity in the Sun and other similar stars is
interrupted by episodes of reduced activity such as the Maunder
Minimum. This pattern is reproduced in mean field (αθ) dynamo models,
where growth of the field is limited by the nonlinear action of the
Lorentz force on differential rotation. The observed aperiodicity
can be ascribed to deterministic rather than stochastic processes,
and chaotic modulation is demonstrated for a low-order system, for
two-dimensional dynamo waves and for a simple global model. Amplitude
modulation that leads to grand minima is distinct from modulation
associated with changes in the symmetry of the field.

---------------------------------------------------------
Title: Magnetoconvection
Authors: Weiss, N. O.
1997ASPC..118...21W Altcode: 1997fasp.conf...21W
Two recent computational treatments of the nonlinear interaction
between convection and magnetic fields are described and contrasted. The
first is a sequence of numerical experiments on an idealized model of
three-dimensional compressible magnetoconvection, with an emphasis
on changes in the magnetic field structure and the velocity pattern
as the strength of the imposed field is reduced. The second is a
two-dimensional simulation of the formation and evolution of a highly
dynamical magnetic flux sheet, in a realistic model of the solar
photosphere. The results are related to high-resolution observations
of fine structure in sunspots and to the behaviour of intergranular
magnetic fields.

---------------------------------------------------------
Title: Photospheric Convection in Strong Magnetic Fields
Authors: Weiss, N. O.; Brownjohn, D. P.; Matthews, P. C.; Proctor,
M. R. E.
1996MNRAS.283.1153W Altcode:
The effect of magnetic fields on convection at the surfaces of
cool stars can be explored by comparing the results of detailed
numerical experiments with high-resolution solar observations. We
have investigated non-linear three-dimensional magnetoconvection in
a fully compressible perfect gas. In this paper we study the effect
of an imposed magnetic field on the pattern of convection in a deep
stratified layer. When the field is strong enough to dominate the
motion we find steady convection with rising plumes on a deformed
hexagonal lattice, and a magnetic network at the upper boundary. This
gives way to spatially modulated oscillations for weaker fields. As the
field strength is further reduced the oscillations become more violent
and irregular, and their horizontal scale increases. Magnetic flux
moves rapidly along the network that encloses the ephemeral plumes;
when the imposed field is relatively weak, intense fields appear at
junctions in the network, where the magnetic pressure is comparable to
the gas pressure and an order of magnitude greater than the dynamic
pressure. This behaviour is related to convection in sunspots and
plages and to the structure of intergranular magnetic fields on the Sun.

---------------------------------------------------------
Title: Dynamos in Different Types of Stars
Authors: Weiss, N. O.
1996mpsa.conf..387W Altcode: 1996IAUCo.153..387W
No abstract at ADS

---------------------------------------------------------
Title: Double-diffusive convection with two stabilizing gradients:
strange consequences of magnetic buoyancy.
Authors: Hughes, D. W.; Weiss, N. O.
1995JFM...301..383H Altcode:
Instabilities due to a vertically stratified horizontal magnetic field
(magnetic buoyancy instabilities) are believed to play a key role in the
escape of the Sun's internal magnetic field and the formation of active
regions and sunspots. In a star the magnetic diffusivity is much smaller
than the thermal diffusivity and magnetic buoyancy instabilities are
double-diffusive in character. The authors have studied the nonlinear
development of these instabilities, in an idealized two-dimensional
model, by exploiting a non-trivial transformation between the governing
equations of magnetic buoyancy and those of classical thermosolutal
convection. The main result is extremely surprising. They have
demonstrated the existence of finite-amplitude steady convection
when both the influential gradients (magnetic and convective) are
stabilizing. This strange behaviour is caused by the appearance of
narrow magnetic boundary layers, which distort the mean pressure
gradient so as to produce a convectively unstable stratification.

---------------------------------------------------------
Title: Chaotically modulated stellar dynamos
Authors: Tobias, S. M.; Weiss, N. O.; Kirk, V.
1995MNRAS.273.1150T Altcode:
Slowly rotating, late-type stars show intermittent cyclic magnetic
activity, interrupted by grand minima. The record of the solar cycle
is apparently chaotic. We construct a simple third-order model of a
stellar dynamo following two different procedures. The first uses simple
physical arguments based on the processes that occur in a dynamo. The
second relies on bifurcation theory, with no explicit reference to the
dynamo equations, and displays the essential mathematical structure
of the model. Modulation of the basic cycle and chaos are found to be
a natural consequence of the transition from a non-magnetic state to
one with periodically reversing fields. The model is related to more
general normal forms and it is shown that the behaviour described is
generic and therefore robust.

---------------------------------------------------------
Title: Kinematic Models of Supergranular Diffusion on the Sun
Authors: Simon, G. W.; Title, A. M.; Weiss, N. O.
1995ApJ...442..886S Altcode:
We develop kinematic models of diffusion generated by supergranulation
at the solar surface. These models use current observations for the
size, horizontal velocity, and lifetime of supergranules. Because there
is no observational description of the appearance and disappearance of
supergranules, we investigate models using several plausible evolution
processes, including the effect of different lifetime distribution
functions for the cells. The results are quite insensitive to the
methods chosen to replace old supergranules, the distribution of cell
lifetimes, and even the cell lifetime itself, for mean lifetimes between
15 to 30 hr. Calculated diffusion coefficients range between 500 and 700
sq km/s, in agreement with the best fit diffusion coefficients used by
Sheeley and his collaborators to model the large-scale distribution
of magnetic fields over the solar surface. However, our models do
not explain the field distribution in plage, and they predict that
virtually all the strong field in quiet Sun exists in relatively
isolated clumps. We suggest possible mechanisms for the creation of
plage and the bright network seen in quiet Sun.

---------------------------------------------------------
Title: The Structure of Sunspots
Authors: Weiss, N. O.
1995SPD....26..301W Altcode: 1995BAAS...27..952W
No abstract at ADS

---------------------------------------------------------
Title: The abrupt development of penumbrae in sunspots
Authors: Rucklidge, A. M.; Schmidt, H. U.; Weiss, N. O.
1995MNRAS.273..491R Altcode:
A sunspot is distinguished from a pore by having a filamentary penumbra,
corresponding to convective motions that carry energy into the spot
from the surrounding field-free plasma. A simplified model of energy
transport in sunspots is developed in order to model the transition
from pores to spots as the magnetic flux is varied. The observed
overlap between the radii of large pores and small spots implies that
the filamentary convective mode sets in suddenly and rapidly, as in
the idealized case where pore solutions lose stability at a bifurcation.

---------------------------------------------------------
Title: Kinematic modelling of magnetoconvection
Authors: Simon, G. W.; Title, A. M.; Weiss, N. O.; Ginet, G. P.
1994smf..conf..276S Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Solar and Stellar Dynamos
Authors: Weiss, N. O.
1994lspd.conf...59W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Modeling Solar Magnetoconvection
Authors: Weiss, N. O.
1994ASPC...68...45W Altcode: 1994sare.conf...45W
No abstract at ADS

---------------------------------------------------------
Title: Magnetoconvective patterns
Authors: Weiss, N. O.
1994ASIC..433..287W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Kinematic Modeling of Magnetic Field Diffusion at the Solar
Surface
Authors: Title, Alan M.; Simon, George W.; Weiss, Nigel O.
1994ASPC...68...87T Altcode: 1994sare.conf...87T
No abstract at ADS

---------------------------------------------------------
Title: Nonlinear three-dimensional magnetoconvection in a compressible
atmosphere
Authors: Matthews, P. C.; Proctor, M. R. E.; Rucklidge, A. M.; Weiss,
N. O.
1994smf..conf..279M Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Nonlinear stellar dynamos.
Authors: Tobias, S. M.; Weiss, N. O.
1994cmcp.conf...46T Altcode:
Slowly rotating late-type stars show intermittent cyclic activity,
interrupted by grand minima. A simple third-order dynamo model
describes the transition from a non-magnetic state to one with
periodically reversing fields. As the rate of rotation is increased,
subsequent bifurcations lead to periodically modulated cycles and then
to chaotically modulated oscillations.

---------------------------------------------------------
Title: Diffusion of "Corks" Over the Solar Surface
Authors: Title, A. M.; Simon, G. W.; Weiss, N. O.
1993BAAS...25Q1183T Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Book-Review - Sunspots - Theory and Observations
Authors: Thomas, J. H.; Weiss, N. O.; Parkinson, J. H.
1993Obs...113..145T Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Diffusion of “Corks” Over the Solar Surface
Authors: Title, A. M.; Simon, G. W.; Weiss, N. O.
1993AAS...182.4804T Altcode: 1993BAAS...25Q.880T
Test particles in flow fields generated by correlation tracking of
movies of the solar surface and kinematic models of the solar surface
quickly collect in stagnation points of the flow fields and remain
there. Test particles do not form a quasi-stable network pattern. The
diffusion coefficients generated from a net of kinematic models with a
range of cell sizes and lifetimes are not proportional to the cell size
squared divided by the cell lifetime as commonally assumed. Reasonable
estimates of cell sizes and lifetimes yield diffusiion coefficients that
are lower than the 600 km(2) /s used by Sheeley and his collaborators in
their surface diffusion models. We conclude that: 1) The appearance of
plages and enhanced network can not be explained by adjustment of the
cell sizes or surface velocities; and 2) diffusion is not sufficient
to explain the appearance of plages and enhanced network.

---------------------------------------------------------
Title: Magnetic geometry of sunspots
Authors: Weiss, Nigel
1993Natur.362..208W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Solar and Stellar Dynamos
Authors: Weiss, N. O.
1993ASSL..183..541W Altcode: 1993pssc.symp..541W
No abstract at ADS

---------------------------------------------------------
Title: Oscillations and secondary bifurcations in nonlinear
magnetoconvection
Authors: Rucklidge, A. M.; Weiss, N. O.; Brownjohn, D. P.; Proctor,
M. R. E.
1993GApFD..68..133R Altcode:
Complicated bifurcation structures that appear in nonlinear
systems governed by partial differential equations (PDEs) can be
explained by studying appropriate low-order amplitude equations. We
demonstrate the power of this approach by considering compressible
magnetoconvection. Numerical experiments reveal a transition from a
regime with a subcritical Hopf bifurcation from the static solution,
to one where finite-amplitude oscillations persist although there
is no Hopf bifurcation from the static solution. This transition is
associated with a codimension-two bifurcation with a pair of zero
eigenvalues. We show that the bifurcation pattern found for the
PDEs is indeed predicted by the second-order normal form equation
(with cubic nonlinearities) for a Takens - Bogdanov bifurcation
with Z2 symmetry. We then extend this equation by adding quintic
nonlinearities and analyse the resulting system. Its predictions provide
a qualitatively accurate description of solutions of the full PDEs
over a wider range of parameter values. Replacing the reflecting (Z2)
lateral boundary conditions with periodic [O(2)] boundaries allows
stable travelling wave and modulated wave solutions to appear; they
could be described by a third-order system.

---------------------------------------------------------
Title: Bifurcations and Symmetry-Breaking in Simple Models of
Nonlinear Dynamos
Authors: Weiss, N. O.
1993IAUS..157..219W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Symmetries of time-dependent magnetoconvection
Authors: Proctor, M. R. E.; Weiss, N. O.
1993GApFD..70..137P Altcode:
In the presence of a magnetic field, convection may set in at a
stationary or an oscillatory bifurcation, giving rise to branches
of steady, standing wave and travelling wave solutions. Numerical
experiments provide examples of nonlinear solutions with a variety
of different spatiotemporal symmetries, which can be classified by
establishing an appropriate group structure. For the idealized problem
of two-dimensional convection in a stratified layer the system has
left-right spatial symmetry and a continuous symmetry with respect
to translations in time. For solutions of period P the latter can be
reduced to Z2 symmetry by sampling solutions at intervals of ½P. Then
the fundamental steady solution has the spatiotemporal symmetry D2 = Z2
Z2 and symmetry-breaking yields solutions with Z2 symmetry corresponding
to travelling waves, standing waves and pulsating waves. A further
loss of symmetry leads to modulated waves. Interactions between the
fundamental and its first harmonic are described by the group D2h =
D2 ⊗ Z2 and its invariant subgroups, which describe solutions that
are either steady or periodic in a uniformly moving frame. For a
Boussinesq fluid in a layer with identical top and bottom boundary
conditions there is also an up-down symmetry. With fixed lateral
boundaries the spatiotemporal symmetries, again described by D2h
and its invariant subgroups, can be related to results obtained in
numerical experiments and analysed by Nagata et al. (1990). With
periodic boundary conditions, the full symmetry group, D2h⊗Z2,
is of order 16. Its invariant subgroups describe pure and mixed-mode
solutions, which may be steady states, standing waves, travelling waves,
pulsating waves or modulated waves.

---------------------------------------------------------
Title: X-Ray Observations of Sunspot Penumbral Structure
Authors: Sams, B. J., III; Golub, L.; Weiss, N. O.
1992ApJ...399..313S Altcode:
High-resolution coronal observations with the Normal Incidence X-ray
Telescope (NIXT) reveal previously unobserved structure in the magnetic
fields above a sunspot. The X-ray images are precisely aligned with
a continuum photospheric image taken at the same time. The X-ray
brightness traces magnetic field lines and shows: (1) that none of
the bright loops originate in the spot umbra and (2) that some field
lines emerging from the inner penumbra connect to regions far away
from the spot. Such large-scale structures must remain distinct from
the shallowly inclined fields in the outer penumbra. In particular,
they cannot be involved in any interchange between the bright and dark
filaments. This imposes constraints on models of penumbral convection.

---------------------------------------------------------
Title: Kinematic Modeling of Active Region Decay
Authors: Simon, G. W.; Title, A. M.; Weiss, N. O.
1992AAS...180.1101S Altcode: 1992BAAS...24..746S
No abstract at ADS

---------------------------------------------------------
Title: Convective motion on the Sun
Authors: Weiss, Nigel
1992Natur.356..287W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: The Theory of Sunspots
Authors: Thomas, John H.; Weiss, Nigel O.
1992ASIC..375....3T Altcode: 1992sto..work....3T
This review covers the present state of our theoretical understanding
of the physics of sunspots, along with the principal observational
results that need to be explained. The topics covered range from the
detailed structure of an individual sunspot to the broad connection
between sunspots and the global solar magnetic field and the solar
cycle. Our aim is to give a critical discussion of the theoretical ideas
and models without presenting mathematical details. After outlining
the historical development of the basic concepts associated with the
magnetohydrodynamic theory of sunspots, we discuss recent treatments of
their properties and structure, placing special emphasis on developments
that have occurred within the last ten years. There have been remarkable
improvements in the theoretical modelling of sunspots, led by new
ideas and by more elaborate and realistic numerical simulations. At
the same time, new observations have raised new theoretical questions
or caused old ones to be reconsidered. In particular, measurements
of oscillations in and around sunspots have opened up the new field
of sunspot seismology, while recent high-resolution observations have
forced us to rethink the structure of a sunspot penumbra.

---------------------------------------------------------
Title: Sunspots - Theory &amp; Observations: NATO Cambridge, 1992
Authors: Thomas, John H.; Weiss, Nigel O.
1992ASIC..375.....T Altcode: 1992sto..work.....T
The papers contained in this volume focus on theoretical problems
associated with sunspots and present results of recent high-resolution
observations of sunspots. In particular, attention is given to the
evolution of sunspots, overall structure and fine structure of sunspots,
waves and oscillations in sunspots, and the relation of sunspots to the
global solar magnetic field. Specific topics discussed include continuum
observations and empirical models of the thermal structure of sunspots,
fine structure of umbrae and penumbrae, magnetohydrodynamic waves in
structural magnetic fields, and the motion of magnetic flux tubes in
the convection zone and the surface origin of active regions.

---------------------------------------------------------
Title: The Origin of the Solar Cycle
Authors: Rosner, R.; Weiss, N. O.
1992ASPC...27..511R Altcode: 1992socy.work..511R
No abstract at ADS

---------------------------------------------------------
Title: What is a stellar dynamo?
Authors: Cattaneo, F.; Hughes, D. W.; Weiss, N. O.
1991MNRAS.253..479C Altcode:
Numerical simulations of turbulent stellar dynamos are now feasible. The
characteristic time-scale for kinematic behavior is related to the
turnover time of the turbulent eddies. Results from idealized 2D
models show that the Lorentz force alters the velocity field, allowing
transient magnetic activity to persist for intervals much longer than
the expected turbulent decay time. For 3D flows a characteristic time
Te is defined for turbulent diffusion to act, based on the rate at which
magnetic energy is dissipated, and it is asserted that there is a dynamo
only if the field survives for times much longer than Te. This criterion
is then applied to cyclic magnetic activity in late-type stars.

---------------------------------------------------------
Title: Convective structures in the sun
Authors: Simon, G. W.; Weiss, N. O.
1991MNRAS.252P...1S Altcode:
Observed patterns of motion at the solar surface reflect the structure
of subphotospheric convection, which controls the distribution of
angular momentum and magnetic fields. Mesogranules are interpreted
as secondary features associated with supergranular circulation,
and that coupling between mesogranules and granulation triggers the
spasmodic formation of exploding granules. Supergranules are expected
to generate isolated sinking plumes. It is argued that these plumes
can penetrate to the base of the convective zone, and that there is
no organized structure on larger scales.

---------------------------------------------------------
Title: Symmetry breaking in stellar dynamos
Authors: Jennings, R. L.; Weiss, N. O.
1991MNRAS.252..249J Altcode:
The generation of magnetic fields in stars like the sun can be
described by an azimuthally averaged dynamo model. Solutions of the
linear (kinematic) problem have pure dipole or quadrupole symmetry,
i.e., toroidal fields that are antisymmetric or symmetric about the
equator. These symmetries can be broken only at bifurcations in the
nonlinear regime, which lead to the appearance of spatially asymmetric
mixed-mode solutions. The symmetries of dipole, quadrupole and
mixed-mode solutions, whether steady or periodic, form the same group
for any axisymmetric dynamo. To establish the bifurcation structure it
is necessary to follow unstable as well as stable solutions. This is
feasible only for simple systems and a minimal nonlinear alpha(omega)
dynamo is studied in detail in order to illustrate the formation
of mixed-mode periodic solutions and to distinguish between their
symmetries. The results are applied to the sun (where there are
persistent deviations from dipole symmetry) and to other late-type
stars.

---------------------------------------------------------
Title: Modeling Mesogranules and Exploders on the Solar Surface
Authors: Simon, G. W.; Title, A. M.; Weiss, N. O.
1991ApJ...375..775S Altcode:
Radial outflows in exploders and mesogranules can be modeled by
superposing Gaussian source functions. This model is used to explore
the relationship between mesogranules and exploders. Although it
is demonstarted that there is a mathematical equivalence between
mesogranules and exploders distributed normally about the mesogranule
centers, the results indicate that the observed mesogranular velocity
pattern is not consistent with a flow pattern generated by exploders
dropped randomly on the solar surface. Detailed comparisons with
observations suggest that the averaged mesogranular velocity is produced
by a combination of a persistent outflow from a source together with
exploders distributed randomly about its center. Similar analysis
also shows supergranules are not the result of random occurrences
of mesogranules.

---------------------------------------------------------
Title: Magnetoconvection
Authors: Weiss, N. O.
1991GApFD..62..229W Altcode:
Cowling investigated the effect of an imposed magnetic field on
convection in order to explain the origin of sunspots. After summarizing
the classical linear theory of Boussinesq magnetoconvection, this review
proceeds to more recent nonlinear results. Weakly nonlinear theory is
used to establish the relevant bifurcation structure, which involves
steady, oscillatory and chaotic solutions. Behaviour found in numerical
experiments can then be related to these analytical results. Thereafter,
attention is focused on the astrophysically relevant problem of fully
compressible magnetoconvection. Steady two-dimensional nonlinear
solutions show two important effects: stratification introduces an
asymmetry between rising and falling fluid, while compressibility
leads to evacuated magnetic flux sheets. Time-dependent behaviour
includes transitions between standing waves and travelling waves,
as well as changes in horizontal scale, leading to the development of
more complicated spatial structures. Work on three-dimensional models,
which is now in progress, will lead to a better understanding of the
structure of a sunspot.

---------------------------------------------------------
Title: Simulating exploding granules and mesogranular flows
Authors: Simon, G. W.; Title, A. M.; Weiss, N. O.
1991AdSpR..11e.259S Altcode: 1991AdSpR..11..259S
Cellular convective motion at the solar surface can be simulated by a
suitable distribution of axisymmetric sources /1/. With this model we
represent randomly distributed exploding granules or mesogranules. The
effect of a given velocity field on the magnetic field is modelled
by inserting test particles (“corks”) and following their resultant
motions. An important question raised by the observations is whether
mesogranular flows are generated entirely by exploding granules
which recur in approximately the same location or whether there is a
persistent underlying circulation. Our model calculations suggest
that a combination of systematic cellular motion on a mesogranular scale
and recurrent exploding granules located near the mesogranular centers
is compatible with observed magnetic structures. We also generate
randomly-distributed exploders not tethered to mesogranular sites, and
the resulting cork patterns do not resemble those observed on the solar
surface. Finally we introduce a large-scale persistent supergranular
flow which transports the mesogranules and exploders towards the
supergranular network and obtain patterns not unlike those seen on
the Sun. Operated by the National Optical Astronomy Observatories
for the Association of Universities for Research in Astronomy, Inc.,
under contract with the National Science Foundation. Partial Support
for the National Solar Observatory is provided by the USAF under a
Memorandum of Understanding with the NSF.

---------------------------------------------------------
Title: Momentum boundary conditions and Euclidean field theory
Authors: Unruh, W. G.; Weiss, N.
1990CQGra...7.2331U Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Kinematic Modeling of the Relations Among Exploders,
Mesogranules, and Supergranules
Authors: Simon, G. W.; Title, A. M.; Weiss, N. O.
1990BAAS...22R1225S Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Oscillatory convection in sunspot umbrae
Authors: Weiss, N. O.; Brownjohn, D. P.; Hurlburt, N. E.; Proctor,
M. R. E.
1990MNRAS.245..434W Altcode:
Subphotospheric convection is partially inhibited by the strong
vertical magnetic field at the centre of a sunspot. We investigate
the effects of stratification on non-linear magnetoconvection in a
fully compressible perfect gas by means of two-dimensional numerical
experiments. Behaviour depends critically on the ratio ξ of the
magnetic to the thermal diffusivity, which increases with depth. If
ξ &gt; 1 throughout the layer we find steady overturning convection
with an asymmetry between rising and falling plumes. For ξ &gt; 1
we obtain oscillatory convection with reversals of the flow. When ξ
&gt; 1 at the top of the layer but ξ &gt; 1 at its base, convection
sets in as steady motion but there is a transition (involving several
bifurcations) to mixed-mode periodic solutions as the Rayleigh number
is increased. The flow at the bottom of the layer does not reverse
but adjacent rising plumes alternate between active and quiescent
states. In the umbral photosphere t, &gt; 1 but ξ &gt; 1 at depths
below 1500 km owing to the increase in opacity. Our results imply that
time-dependent convection immediately below the photosphere is coupled
to motion at levels where ξ &gt; 1. They also explain the existence
of umbral dots with a lifetime corresponding to the Alfven time for
the converting layer.

---------------------------------------------------------
Title: Solar and stellar convection zones.
Authors: Weiss, N. O.
1990CoPhR..12..233W Altcode:
There are several important astrophysical questions that might be
answered by numerical modelling. These involve the kinematic effects
of motion on magnetic fields, the dynamics of magnetoconvection, the
structure and scale of convection and the global dynamo problem. This
review focuses on detailed modelling of nonlinear compressible
convection in a strong vertical magnetic field. Techniques range
from heuristic models, which may be relatively primitive, through
idealized experiments to large scale simulations and each approach
has its proponents. There have been systematic investigations of
fully compressible two- and three-dimensional convection as well as
ambitious simulations. Detailed studies of two-dimensional behaviour
reveal complicated bifurcation structures, involving changes of scale
and transitions from steady to oscillatory solutions and from standing
waves to travelling waves. Models of large-scale behaviour throughout
the convection zone of a star like the sun show that dynamo action
can occur but are still far from being able to reproduce the observed
patterns of differential rotation or magnetic activity.

---------------------------------------------------------
Title: Fine structure on the Sun
Authors: Weiss, Nigel
1990Natur.344..815W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Periodicity and Aperiodicity in Solar Magnetic Activity
Authors: Weiss, N. O.
1990RSPTA.330..617W Altcode:
Solar activity varies irregularly with an 11-year period whereas the
magnetic cycle has a period of 22 years. Similar cycles of activity
are seen in other slowly rotating late-type stars. The only plausible
theory for their origin ascribes them to a hydromagnetic dynamo
operating at, or just below, the base of the convective zone. Linear
(kinematic) dynamo models yield strictly periodic solutions with
dynamo waves propagating towards or away from the equator. Nonlinear
(magneto-hydrodynamic) dynamo models allow transitions from periodic to
quasi-periodic to chaotic behaviour, as well as loss of spatial symmetry
followed by the development of complex spatial structure. Results from
simple models can be compared with the observed sunspot record over
the past 380 years and with proxy records extending over 9000 years,
which show aperiodic modulation of the 11-year cycle.

---------------------------------------------------------
Title: Symmetry Breaking in the Solar Dynamo: Nonlinear Solutions
Authors: Jennings, R. L.; Weiss, N. O.
1990IAUS..138..355J Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Magnetohydrodynamics of Sunspots
Authors: Weiss, N. O.
1990IAUS..142..139W Altcode:
Recent numerical investigations of fully compressible nonlinear
magnetoconvection have clarified the nature of convection in sunspot
umbrae. In a shallow layer with a strong vertical magnetic field
oscillations give way to traveling waves as the Rayleigh number is
increased but in a deep stratified layer oscillatory behavior only
appears after secondary bifurcations. This behavior leads to a model
that explains the formation of umbral dots. Penumbral structure is
more difficult to explain owing to the apparent presence of adjacent
horizontal and inclined fields in dark and bright filaments. The inner
penumbra lies above a transition zone where volume currents are needed
to maintain an overall static equilibrium; instabilities in this region
may be responsible for filamentary structure in the penumbra as well
as for fine structure at the umbral-penumbral boundary.

---------------------------------------------------------
Title: Transitions to asymmetry in magnetoconvection
Authors: Nagata, M.; Proctor, M. R. E.; Weiss, N. O.
1990GApFD..51..211N Altcode:
In two-dimensional Boussinesq magnetoconvection with symmetrical
boundary conditions upward and downward motion are equivalent. Hence
there exist symmetric solutions with equivalent flux sheets on either
side of each convection roll. Numerical experiments show that this
symmetry can be broken for both steady and oscillatory solutions. The
underlying bifurcation structure is established by studying a truncated
seventeenth-order model system. Steady solutions of this relatively
low-order system can be obtained explicitly and their stability can be
investigated. Primary bifurcations from the trivial static solution lead
to pure single-roll and two-roll solutions, both steady and oscillatory;
secondary bifurcations give mixed-mode steady and oscillatory branches
while tertiary bifurcations allow behaviour that is more complicated but
less robust. Properly interpreted, this detailed study of a particular
system provides a better understanding of the behaviour of nonlinear
solutions of the full partial differential equations.

---------------------------------------------------------
Title: Periodicity and aperiodicity in solar magnetic activity.
Authors: Weiss, N. O.
1990ecvs.conf..617W Altcode:
Solar activity varies irregularly with an 11-year period whereas the
magnetic cycle has a period of 22 years. Similar cycles of activity
are seen in other slowly rotating late-type stars. The only plausible
theory for their origin ascribes them to a hydromagnetic dynamo
operating at, or just below, the base of the convective zone. Linear
(kinematic) dynamo models yield strictly periodic solutions with
dynamo waves propagating towards or away from the equator. Nonlinear
(magnetohydrodynamic) dynamo models allow transitions from periodic to
quasi-periodic to chaotic behaviour, as well as loss of spatial symmetry
followed by the development of complex spatial structure. Results from
simple models can be compared with the observed sunspot record over
the past 380 years and with proxy records extending over 9000 years,
which show aperiodic modulation of the 11-year cycle.

---------------------------------------------------------
Title: Nonlinear compressible magnetoconvection. I - Travelling
waves and oscillations
Authors: Hurlburt, N. E.; Proctor, M. R. E.; Weiss, N. O.; Brownjohn,
D. P.
1989JFM...207..587H Altcode:
Two-dimensional compressible convection in a polytropic layer with an
imposed vertical magnetic field is studied in a series of numerical
experiments which consider a shallow layer, spanning only a fraction
of a scale height in density, and increase the ratio (1/beta) of the
magnetic to the thermal pressure in a regime where convection sets in
at an oscillatory bifurcation. Initially, there are stable periodic
oscillations (standing wave solutions). For moderate values of beta
the only deviations from Boussinesq behavior are where the field is
locally intense but as beta is decreased magnetic pressure fluctuations
become increasingly important. When beta is of order unity at the top
of the layer standing waves become unstable at higher Rayleigh numbers
and traveling waves are preferred. This is an essentially compressible
effect in which magnetic pressure plays a crucial role. The associated
bifurcation structure is investigated in some detail.

---------------------------------------------------------
Title: Simulation of Large-Scale Flows at the Solar Surface
Authors: Simon, G. W.; Weiss, N. O.
1989ApJ...345.1060S Altcode:
A simple analytic axisymmetric function is used to represent the radial
outflow associated with an isolated convection plume at the solar
surface. The vertical velocity can be deduced from the continuity
equation. A regular cellular pattern of convection can be created
by superposing a number of such sources. The function is applied
to the large-scale horizontal motions observed by the Solar Optical
Universal Polarimeter (SOUP) instrument on Spacelab 2. The flow pattern
visible in three different regions covered by the SOUP observations
is simulated. In each case a superposition of the plume functions
mimics the observed mesogranular and supergranular motions well. The
model flows are used to compute the motion of passive test particles
(corks) which accumulate in a network that outlines mesogranular
cells. Detailed comparisons suggest that magnetic flux tubes are
affected more by outflow from sources at the centers of mesogranules
than by flow into sinks within the network.

---------------------------------------------------------
Title: Simulating plumes and sinks observed at the solar surface
Authors: Simon, G. W.; Weiss, N. O.
1989hsrs.conf..529S Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Modeling the Flow in Solar Vortices
Authors: Simon, G. W.; Weiss, N. O.; Scharmer, G. B.
1989BAAS...21Q.829S Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Time Dependent Compressible Magnetoconvection
Authors: Weiss, N. O.
1989ASIC..263..471W Altcode: 1989ssg..conf..471W
No abstract at ADS

---------------------------------------------------------
Title: Compressible Magnetoconvection
Authors: Weiss, N. O.
1989gmca.conf....1W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: A Simple Model of Mesogranular and Supergranular Flows
Authors: Simon, G. W.; Weiss, N. O.
1989ASIC..263..595S Altcode: 1989ssg..conf..595S
No abstract at ADS

---------------------------------------------------------
Title: Dynamo Processes in Stars
Authors: Weiss, N. O.
1989ASSL..156...11W Altcode: 1989admf.proc...11W
Present understanding of stellar dynamo processes is reviewed. The
observational constraints are described, and the basic physical
processes of helicity and differential rotation that lead to
dynamo action are outlined, stressing the importance of recent
helioseismological results. Mean field dynamo theory and nonlinear
dynamo waves are discussed.

---------------------------------------------------------
Title: Simulation of Large-Scale Flows at the Solar Surface
Authors: Simon, G. W.; Weiss, N. O.
1988BAAS...20.1008S Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Is the solar cycle an example of deterministic chaos?
Authors: Weiss, N. O.
1988ssgv.conf...69W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: The relation between convection flows and magnetic structure
at the solar surface
Authors: Simon, G. W.; November, L. J.; Acton, L. W.; Title, A. M.;
Tarbell, T. D.; Topka, K. P.; Shine, R. A.; Ferguson, S. H.; Weiss,
N. O.; Zirin, H.
1988AdSpR...8k.133S Altcode: 1988AdSpR...8..133S
We describe recent results from the comparison of data from the Solar
Optical Universal Polarimeter instrument on Spacelab 2 and magnetograms
from Big Bear Solar Observatory. We show that the Sun's surface velocity
field governs the structure of the observed magnetic field over the
entire solar surface outside sunspots and pores. We attempt to describe
the observed flows by a simple axisymmetric plume model. Finally,
we suggest that these observations may have important implications
for the prediction of solar flares, mass ejections, and coronal heating.

---------------------------------------------------------
Title: Dynamics of Convection
Authors: Weiss, N. O.
1987RSPSA.413...71W Altcode:
Thermal convection in a fluid layer is an example of a dynamical system
governed by partial differential equations. As the relevant control
parameter (the Rayleigh number) is increased, successive bifurcations
may lead to chaos and the nature of the transition depends on the
spatial structure of the flow. Numerical experiments with idealized
symmetry and boundary conditions make it possible to explore nonlinear
behaviour in some detail and to relate bifurcation structures to
those found in appropriate low-order systems. Two examples are used
to illustrate transitions to chaos. In two-dimensional thermosolutal
convection, where the spatial structure is essentially trivial,
chaos is caused by a heteroclinic bifurcation involving a symmetric
pair of saddle foci. When convection is driven by internal heating
several competing spatial structures are involved and the transition
to chaos is more complicated in both two-and three-dimensional
configurations. Although the first few bifurcations can be isolated a
statistical treatment is needed for behaviour at high Rayleigh numbers.

---------------------------------------------------------
Title: Magnetic fields and non-uniform rotation in stellar radiatives
zones.
Authors: Mestel, L.; Weiss, N. O.
1987MNRAS.226..123M Altcode:
This paper examines the effects of dynamical and resistive instabilities
on magnetic redistribution of angular momentum within a star. It is
tentatively concluded that if significant differential rotation survives
in a stably stratified radiative zone over a stellar evolution time,
then the poloidal field, Bp, cannot exceed an upper limit of
order 3×10-2G and is probably less than 10-3G. In
the radiative core of the Sun Bp is estimated to be at
least of order 5×10-2G and probably 100 G or more. Values
greater than 0.1 G cannot easily be reconciled with the rotational
shear inferred from frequency splitting of solar oscillations.

---------------------------------------------------------
Title: Rotation and magnetic fields in the Sun.
Authors: Weiss, N. O.
1987ppcs.work...46W Altcode:
Stellar magnetic fields exert torques which alter the distribution of
angular momentum in a star. In the radiative interior of the sun, these
torques tend to enforce uniform rotation and the existence of a rapidly
rotating core would imply a poloidal field of less than 0.01 G. In
the convective envelope, magnetic fields generated by dynamo action
produce torques which lead to torsional oscillations. A simple nonlinear
model allows both multiply periodic and chaotic behavior. This system
demonstrates that both aperiodic magnetic cycles and the irregular
modulation responsible for grand minima can be regarded as examples of
deterministic chaos. This picture is consistent with the C-14 record
but implies that the multiply periodic lamination of some Precambrian
varves is not associated with the solar cycle.

---------------------------------------------------------
Title: What can the sun tell us about stellar activity?
Authors: Weiss, N. O.
1987LNP...292....1W Altcode:
The solar-stellar connection relates high-resolution synoptic solar
observations to observations of magnetic activity in stars with
different rotation rates and internal structures. Our knowledge of
magnetic fields in stellar convection zones is based on detailed
observations of field structures in the Sun but recent measurements
of magnetic activity in other late-type stars have extended
our understanding of the solar dynamo. These observations have
stimulated detailed modelling of processes associated with magnetic
activity. Modulation of activity cycles in slowly rotating stars can
be inferred from terrestrial data extending over the last 104 years,
while the evolution of the Sun's magnetic field can be inferred from
the behaviour of younger stars.

---------------------------------------------------------
Title: What Can the Sun Tell Us About Stellar Activity?
Authors: Weiss, N. O.
1987LNP...292....3W Altcode: 1987ssp..conf....3W
The solar-stellar connection relates high-resolution synoptic
solar observations to observations of magnetic activity in stars
with different rotation rates and internal structures. Modulation
of activity cycles in slowly rotating stars can be inferred from
terrestrial data extending over the last 104years, while
the evolution of the Sun's magnetic field can be inferred from the
behaviour of younger stars.

---------------------------------------------------------
Title: Dynamical chaos. Proceedings of a Royal Society discussion
meeting held in London, UK, 4 - 5 February 1987.
Authors: Berry, M. V.; Percival, I. C.; Weiss, N. O.; Zeeman, E. C.
1987dcpr.book.....B Altcode:
The individual contributions within the subject scope of Astronomy and
Astrophysics Abstracts are included in their corresponding categories -
see abstracts 015.003, 021.002, 021.003, 022.002 - 022.005, 062.006 -
062.009, 091.002.

---------------------------------------------------------
Title: Interaction between Magnetic Fields and Convection
Authors: Hurlburt, N. E.; Weiss, N. O.
1987rfsm.conf...35H Altcode:
The authors discuss nonlinear convection in the presence of an imposed
vertical magnetic field and its influence on the fine structure of the
resulting field. They contrast recent results of numerical experiments
on steady and oscillatory magnetoconvection with those obtained in the
Boussinesq approximation. An attempt is also made to relate idealized
model calculations to the structure of observed magnetic fields in
the solar photosphere.

---------------------------------------------------------
Title: Simulation of Surface Flows in Supergranulation
Authors: Simon, G. W.; Weiss, N. O.
1986BAAS...18R.990S Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Energy transport in sunspot penumbrae.
Authors: Schmidt, H. U.; Spruit, H. C.; Weiss, N. O.
1986A&A...158..351S Altcode:
It is proposed that the magnetic field in the outer penumbra of a
sunspot is almost horizontal and that the penumbra itself is very
shallow, with a sharp lower boundary. A simple model of energy transport
in the outer penumbra predicts that there is a Wilson depression
of about 100 km, below which the penumbra extends for only 80 km. A
two-component model with bright and dark filaments suggests that the
associated differences in observed field strength and corrugations
of the visible surface of the penumbra will be small. The authors
argue that flows along the field are needed to explain the existence
of bright and dark filaments while the Evershed flow is driven by
pressure differences along flux tubes.

---------------------------------------------------------
Title: Magnetic torques and differential rotation.
Authors: Weiss, N. O.
1986ASIC..169..253W Altcode: 1986ssds.proc..253W
The rotation profile deduced from the measured splitting of solar
oscillations raises several problems. The slight decrease in angular
velocity within the convective zone can be explained and the transition
from differential to uniform rotation on spherical surfaces must cause
a further reduction in the radiative zone. The bump, associated with
harmonics of degree 11, seems implausible and it is hard to reconcile
a rapidly rotating core with the presence of a significant magnetic
field. A possible explanation is that this core has been magnetically
decoupled from outer regions since the Sun evolved on to the Hayashi
track.

---------------------------------------------------------
Title: Stellar dynamo characteristics
Authors: Weiss, N. O.
1986HiA.....7..385W Altcode:
Recent discoveries have shown that magnetic activity is typical of
cool stars with deep convective zones and magnetic cycles are found in
slowly rotating stars like the sun. The current state of hydromagnetic
dynamo theory is reviewed, and simplified models are used in an attempt
to isolate the dominant nonlinear processes in stellar dynamos.

---------------------------------------------------------
Title: Differential rotation and magnetic torques in the interior
of the Sun
Authors: Rosner, R.; Weiss, N. O.
1985Natur.317..790R Altcode:
The frequencies of solar oscillations can be measured with extreme
precision and 5-min oscillations reveal the internal structure of
the Sun1-5. In particular, measurements of rotational
splitting4 have provided the first reliable indications of
the variation of angular velocity with radius6, while recent
observations5 have yielded information on the variation
with depth of latitudinal differential rotation. These results confirm
theoretical predictions that the angular velocity decreases inwards in
the convective zone7,8 but raise problems for dynamo models
of the solar cycle. The suggestion that the core rotates with roughly
twice the surface angular velocity has important implications both
for the rotational history of the Sun and for other late-type stars,
whose magnetic activity is closely correlated with rotation. Such a
rapidly rotating core is hard to reconcile with the presence of any
significant magnetic field pervading the entire radiative interior. We
can only explain it by suggesting that the core contains a fossil
field, unaffected by turbulence in the pre-main sequence Hayashi phase,
that is decoupled from the rest of the star.

---------------------------------------------------------
Title: Oscillatory Convection in Flux Tubes Pores and Sunspots
Authors: Hurlburt, N.; Weiss, N. O.
1985tphr.conf..198H Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Buoyant magnetic flux tubes. II - Three-dimensional behaviour
in granules and supergranules
Authors: Schmidt, H. U.; Simon, G. W.; Weiss, N. O.
1985A&A...148..191S Altcode:
A simple model is used to study the interaction of isolated magnetic
flux tubes with convection in the sun. Convective motion in granules and
supergranules is represented by prescribed flows in three-dimensional
cells with square cross-sections and thin flux tubes move under the
action of magnetic buoyancy, Lorentz curvature forces and aerodynamic
drag. Inflow at the base of a cell competes with outflow at its upper
surface; small flux tubes tend to be swept to the cell boundaries while
larger, more buoyant tubes are dragged to the axis of the cell. These
results are compared with recent observations of small-scale granular
and intergranular magnetic fields.

---------------------------------------------------------
Title: Chaotic behavior in stellar dynamos
Authors: Weiss, N. O.
1985JSP....39..477W Altcode:
Slowly rotating main-sequence stars with deep convective zones have
activity cycles like the sun's. The solar cycle is aperiodic and
modulated to give intervals of reduced activity. A simple sixth-order
system, obtained by truncating the dynamo equations, has solutions
that mimic this behavior. The transition to chaos is analyzed and the
astrophysical significance of these results is discussed.

---------------------------------------------------------
Title: Book-Review - the Solar Granulation
Authors: Bray, R. J.; Loughhead, R. E.; Durrant, C. J.; Weiss, N. O.
1985SoPh...96..423B Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Book review
Authors: Weiss, N. O.
1985SoPh...96..423W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: 3-D Behavior of Buoyant Magnetic Flux Tubes in Granules and
Supergranules
Authors: Simon, G. W.; Schmidt, H. U.; Weiss, N. O.
1985BAAS...17Q.642S Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Oscillatory convection in flux tubes, pores and sunspots.
Authors: Hurlburt, N. E.; Weiss, N. O.
1985MPARp.212..198H Altcode:
High-resolution images of the solar surface provide a means for probing
sub-photospheric structures. The authors combine simple conceptual
arguments with numerical models to consider the different flow regimes
possible within flux tubes, pores and sunspots which should be found
in detailed observations. In the presence of a strong magnetic field
convection near the photosphere is likely to be oscillatory. The
authors have carried out a series of numerical experiments involving
simple atmospheres (polytropic in the absence of convection).

---------------------------------------------------------
Title: Nonlinear dynamos: A complex generalization of the Lorenz
equations
Authors: Jones, C. A.; Weiss, N. O.; Cattaneo, F.
1985PhyD...14..161J Altcode:
Plane nonlinear dynamo waves can be described by a sixth order system
of nonlinear ordinary differential equations which is a complex
generalization of the Lorenz system. In the regime of interest
for modelling magnetic activity in stars there is a sequence of
bifurcations, ending in chaos, as a stability parameter D (the
dynamo number) is increased. We show that solutions undergo three
successive Hopf bifurcations, followed by a transition to chaos. The
system possesses a symmetry and can therefore be reduced to a fifth
order system, with trajectories that lie on a 2-torus after the
third bifurcation. As D is then increased, frequency locking occurs,
followed by a sequence of period-doubling bifurcations that leads to
chaos. This behaviour is probably caused by the Shil'nikov mechanism,
with a (conjectured) homoclinic orbit when D is infinite.

---------------------------------------------------------
Title: Energy transport in sunspot penumbrae.
Authors: Schmidt, H. U.; Spruit, H. C.; Weiss, N. O.
1985MPARp.182.....S Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Theoretical Interpretation of Small-Scale Solar Features
Authors: Weiss, N. O.
1985LNP...233..217W Altcode: 1985hrsp.proc..217W
The structure of photospheric magnetic fields is dominated by the
interaction between granular convection and isolated flux tubes. The
current understanding of compressible convection, and of both kinematic
and dynamical aspects of magnetoconvection is summarized. These theories
are related to the formation and location of intense magnetic fields
within the photospheric network. The overall structure of sunspots is
reconsidered and related to umbral and penumbral features.

---------------------------------------------------------
Title: Magnetoconvection.
Authors: Weiss, N. O.
1985ssmf.conf..156W Altcode:
The author focuses on three topics. These are, first, the formation of
small flux tubes; second, the nature of convection in a strong magnetic
field; and, third, the structure of the large-scale magnetic field in
the sun.

---------------------------------------------------------
Title: The relation between stellar rotation rate and activity
cycle periods.
Authors: Noyes, R. W.; Weiss, N. O.; Vaughan, A. H.
1984ApJ...287..769N Altcode:
The empirical relation between rotation period, spectral type, and
cycle activity period in 13 slowly rotating main-sequence stars is
investigated, on the basis of available spectrometric data. It is
shown that for slowly rotating stars with similar spectral types, the
cycle period P(cyc), and rotation period P(rot) were related such that
P(cyc) varies as P(rot) to the nth, where n equals 1.25. In a group of
stars with individual spectral types from G2 to K7, the cycle periods
were consistent with the relation P(cyc) is approximately equal to (P
rot/tauc) exp n, where tauc is the convective
turnover time near the bottom of the convection zone. On the basis
of the above relations, it is suggested that an increase of P(cyc)
with increasing P(rot) does not agree with conventional estimates from
nonlinear dynamo models, and is limited by two factors: the quenching
of the alpha effect; and differential rotation.

---------------------------------------------------------
Title: Amplification and maintenance of thin magnetic flux tubes by
compressible convection.
Authors: Proctor, M. R. E.; Weiss, N. O.
1984ESASP.220...77P Altcode: 1984ESPM....4...77P
The authors present a model that includes both the effects of diffusion
and proper treatment of the Lorentz forces, for a thin tube whose depth
is of the order of a scale height. The model includes both magnetic
pressure (leading to evacuation of the tube) and curvature forces. It
is found that while small tubes are limited principally by pressure
effects, tubes with fluxes ≡1018mx exert an important
retarding force on the convection that causes them.

---------------------------------------------------------
Title: Convection in sunspots and the origin of umbral dots
Authors: Knobloch, E.; Weiss, N. O.
1984MNRAS.207..203K Altcode:
Recent studies of non-linear magnetoconvection are used to show that
the observed properties of umbral dots can be explained if they are
produced by oscillatory convection in the umbrae of sunspots. The
overall magnetic field is assumed to be coherent within the flux tube
underneath the sunspot. Individual convection cells are about 1500 km
deep and 300 km in diameter. The oscillations are highly non-linear,
with periods of around 6 hr, but the relatively vigorous upward motion
that is responsible for umbral dots lasts for only a fraction of this
lifetime. This model is compared with various alternative hypotheses.

---------------------------------------------------------
Title: Periodic and aperiodic dynamo waves
Authors: Weiss, N. O.; Cattaneo, F.; Jones, C. A.
1984GApFD..30..305W Altcode:
In order to show that aperiodic magnetic cycles, with Maunder
minima, can occur naturally in nonlinear hydromagnetic dynamos, we
have investigated a simple nonlinear model of an oscillatory stellar
dynamo. The parametrized mean field equations in plane geometry have a
Hopf bifurcation when the dynamo number D=1, leading to Parker's dynamo
waves. Including the nonlinear interaction between the magnetic field
and the velocity shear results in a system of seven coupled nonlinear
differential equations. For D&gt;1 there is an exact nonlinear
solution, corresponding to periodic dynamo waves. In the regime
described by a fifth order system of equations this solution remains
stable for all D and the velocity shear is progressively reduced by
the Lorentz force. In a regime described by a sixth order system, the
solution becomes unstable and successive transitions lead to chaotic
behaviour. Oscillations are aperiodic and modulated to give episodes
of reduced activity.

---------------------------------------------------------
Title: Problems of Flux Tube Formation
Authors: Weiss, N. O.
1984ssdp.conf..287W Altcode:
Recent theoretical studies of magnetoconvection predict that strong
fields will be formed between granules but also suggest that much of
the magnetic flux may remain near the center of a granule.

---------------------------------------------------------
Title: Solar and stellar magnetic fields
Authors: Priest, E. R.; Weiss, N. O.
1983Obs...103..239P Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Simple models for magnetic flux tubes.
Authors: Simon, G. W.; Weiss, N. O.; Nye, A. H.
1983SoPh...87...65S Altcode:
Known potential field solutions can be used to model the structure of
magnetic fields in the solar photosphere. Several two-dimensional and
axisymmetric solutions are compared. In the most satisfactory model
the vertical component of the field is prescribed on a horizontal
plane so as to be uniform within a finite disc and zero outside it. The
resulting flux distribution provides a good description of small scale
intergranular magnetic fields and of the observed field structure in
a pore, but is inadequate for sunspots.

---------------------------------------------------------
Title: A review of: "Finite-difference techniques for vectorized
fluid dynamics calculations"
Authors: Weiss, N. O.
1983GApFD..23..344W Altcode:
Edited by D. L. Book. Springer-Verlag, New York, 1981. 226 pp., DM 72,
- , $33.60. (ISBN 0 387 104828)

---------------------------------------------------------
Title: Solar magnetism
Authors: Weiss, N. O.
1983spm..conf..115W Altcode:
Magnetic fields in the Sun and other late-type stars follow cycles of
activity, which are more vigorous in rapidly rotating stars. Mean-field
dynamo theory provides a good qualitative description of these magnetic
cycles, though it cannot be justified in detail. Future progress will
require more elaborate models, related to observations and relying
heavily on computation.

---------------------------------------------------------
Title: Simple models for magnetic flux tubes.
Authors: Simon, G. W.; Weiss, N. O.; Nye, A. H.
1983BAAS...15R.874S Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Future research directions - Theoretical approach and
perspective
Authors: Weiss, N. O.
1983ASSL..102..639W Altcode: 1983IAUCo..71..639W; 1983ards.proc..639W
Theoretical aspects of magnetic activity in red dwarfs are
surveyed. Some general remarks about the role of theory in astrophysics
are made, and a phenomenological description of red dwarf magnetic
fields is briefly presented. Numerical simulation of nonlinear processes
in magnetic fields is illustrated with examples of stellar dynamos,
turbulent magnetic fields, and the interaction of magnetic fields
with granular convection. Examples of simplified problems that can
be solved by some combination of analytical or numerical techniques
as an alternative to large scale simulations are given, including
problems involving alpha-omega dynamo models, formation of flux ropes
by magnetic buoyancy, and isolated flux tubes.

---------------------------------------------------------
Title: Periodic and aperiodic behaviour in stellar dynamos
Authors: Cattaneo, F.; Weiss, N. O.; Jones, C. A.
1983IAUS..102..307C Altcode:
A simple parameterized mean field dynamo model has been constructed
that includes the dynamical interaction between the magnetic field and
differential rotation. This system of seven coupled nonlinear ordinary
differential equations has finite amplitude oscillatory solutions
(corresponding to Parker's dynamo waves) when the dynamo number (D)
is greater than one. Two regimes were studied. In the first, the
velocity shear is reduced by the Lorentz force and there are stable
periodic solutions for all dynamo numbers greater than one. In the
second there is a transition from strictly periodic oscillations to
aperiodic (chaotic) behavior as D is increased. This simple example
shows that nonlinear hydromagnetic dynamos can produce aperiodic cycles,
with Maunder minima, as observed in the sun and other late-type stars.

---------------------------------------------------------
Title: Magnetic buoyancy and the Boussinesq approximation
Authors: Spiegel, E. A.; Weiss, N. O.
1982GApFD..22..219S Altcode:
The full Boussinesq equations for hydromagnetic convection are derived
and shown to include the effects of magnetic buoyancy. Instabilities
caused by magnetic buoyancy are analyzed and their roles in double
convection are brought out.

---------------------------------------------------------
Title: REVIEW ARTICLE: Magnetoconvection
Authors: Proctor, M. R. E.; Weiss, N. O.
1982RPPh...45.1317P Altcode:
The interaction between convection and an externally imposed magnetic
field in a Boussinesq fluid is discussed. The equations that govern
Boussinesq magnetoconvection are derived and boundary conditions
and simplified geometries are discussed. The kinematic effects
of prescribed velocity fields on magnetic fields, including flux
expulsion and the formation of isolated sheets or tubes of flux, are
treated. Dynamical effects are introduced by considering the simpler
Oberbeck problem and demonstrating the exclusion of motion from the
flux sheets. Linear stability theory for the Rayleigh-Benard problem is
summarized. Two-dimensional magnetoconvection is discussed in detail;
results obtained by perturbation methods are described and extended
into the nonlinear regime by adopting a truncated model system, and
numerical results for the full problem are presented. Axisymmetric
magnetoconvection is described, and the transition from the
kinematic regime to one in which the field is dynamically active is
discussed. Extensions of the theory to more exotic effects are briefly
reviewed, and astrophysical implications are briefly commented on.

---------------------------------------------------------
Title: Magnetic fields in late-type stars
Authors: Knobloch, E.; Rosner, R.; Weiss, N. O.
1981MNRAS.197P..45K Altcode:
Observations show that magnetic activity in late-type stars is
correlated with rotation rates and that there is a discontinuous change
in behavior at a critical rotation period. This can be explained as
a consequence of a transition from convection in rolls parallel to
the rotation axis to normal convection cells as the angular velocity
is decreased.

---------------------------------------------------------
Title: The interplay between magnetic fields and convection
Authors: Weiss, N. O.
1981JGR....8611689W Altcode:
The development of hydrodynamic dynamo theory is considered, taking into
account investigations related to the solar cycle. Before constructing
any detailed models of the solar cycle it is necessary to understand
both the kinematic effect of convection on the magnetic field and the
dynamical effect of the distorted field on the motion. The effect of a
convective eddy on the magnetic field can be explored by studying an
isolated sphere or cylinder rotating as a solid body in an otherwise
uniform field. It is shown that reconnection of the lines of force leads
to flux expulsion. A summary is provided of the relevant aspects of
magnetoconvection, and a description is presented of some new results,
obtained from numerical experiments at fairly high Rayleigh numbers. The
computations illustrate the complexity of the nonlinear interaction
between magnetic fields and convection.

---------------------------------------------------------
Title: Convection and magnetic fields in late-type stars.
Authors: Weiss, N. O.
1981Obs...101...37W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Convection and magnetic fields in stars
Authors: Galloway, D. J.; Weiss, N. O.
1981ApJ...243..945G Altcode:
Recent observations have demonstrated the unity of the study of stellar
and solar magnetic fields. Results from numerical experiments on
magnetoconvection are presented and used to discuss the concentration
of magnetic flux into isolated ropes in the turbulent convective
zones of the sun or other late-type stars. Arguments are given for
siting the solar dynamo at the base of the convective zone. Magnetic
buoyancy leads to the emergence of magnetic flux in active regions, but
weaker flux ropes are shredded and dispersed throughout the convective
zone. The observed maximum field strengths in late-type stars should
be comparable with the field that balances the photospheric pressure.

---------------------------------------------------------
Title: Stellar magnetic structure and activity (theory).
Authors: Weiss, N. O.
1981ASIC...68..449W Altcode: 1981spss.conf..449W
Both the overall behavior of the solar cycle and the underlying
fine structure of magnetic fields in the sun have been studied
mathematically in some detail. These theories are summarized and
different phenomenological models of the solar cycle are reviewed. In
order to provide a description of the magnetic fields in late-type
stars it is necessary to extrapolate boldly from what is known about the
sun. In this way field strengths and configurations can be estimated.

---------------------------------------------------------
Title: Solar magnetic fields - The generation of emerging flux
Authors: Golub, L.; Rosner, R.; Vaiana, G. S.; Weiss, N. O.
1981ApJ...243..309G Altcode:
X-ray observations have provided information about magnetic fields on
the sun, and the implications of these observations are discussed. The
pattern of small-scale flux emergence is quite different from that of
active regions. It is inferred that the small-scale fields originate
fairly high in the convective zone, while the fields in active regions
have a deeper origin. The small-scale turbulent fields are only loosely
related to the fields that define the normal solar cycle. The way in
which dynamo models must be modified in the light of these results
is indicated.

---------------------------------------------------------
Title: Large aspect ratio cells in two-dimensional thermal convection
Authors: Hewitt, J. M.; McKenzie, D. P.; Weiss, N. O.
1980E&PSL..51..370H Altcode:
Numerical experiments have been carried out on two-dimensional thermal
convection, in a Boussinesq fluid with infinite Prandtl number,
at high Rayleigh numbers. With stress free boundary conditions
and fixed heat flux on upper and lower boundaries, convection
cells develop with aspect ratios (width/depth) λ≿ 5, if heat
is supplied either entirely from within or entirely from below the
fluid layer. The preferred aspect ratio is affected by the lateral
boundary conditions. If the temperature, rather than the heat flux,
is fixed on the upper boundary the cells haveλ ≈ 1. At Rayleigh
numbers of 2.4 × 10 5 and greater, small sinking sheets
are superimposed on the large aspect ratio cells, though they do not
disrupt the circulation. Similar two-scale flows have been proposed
for convection in the earth's mantle. The existence of two scales of
flow in two-dimensional numerical experiments when the viscosity is
constant will allow a variety of geophysically important effects to
be investigated.

---------------------------------------------------------
Title: Magnetic activity and variations in solar luminosity
Authors: Spiegel, E. A.; Weiss, N. O.
1980Natur.287..616S Altcode:
Attempts to detect changes in the solar luminosity suggest that the
solar constant has been misnamed1-4. Although the Nimbus
satellite data4 show no significant fractional variations
above 5 × 10-3 during the period 1975-78, results from
recent balloon5 and rocket6 flights show changes
of 4 × 10-3. Intense magnetic fields in sunspots hamper
convection locally7 but active regions are believed not
to be directly responsible for long term variations in luminosity of
the Sun8 or of RS CVn and BY Dra stars9. The
cause of luminosity variations over spot cycles should be sought
in more deep-seated global features. Here we indicate how strong
magnetic fields at the base of the convective zone can alter the local
convection. The resulting changes in thermal energy are large enough
to produce variations of order 0.1% in the solar luminosity over the
11-yr sunspot cycle.

---------------------------------------------------------
Title: Problems on Interior Structure, the Solar Dynamo and the Role
of SCADM in Providing Interior Diagnostics
Authors: Weiss, N. O.
1980NASCP2098...55W Altcode: 1980sscs.nasa...55W
What is already known about the structure of the Sun, the motion
of its convective zone, and the solar cycle is reviewed. Topics
discussed include solar variability, solar 'seismology', velocity
patterns, magnetic fields, and the dynamo theory. Observations are
needed to determine global properties (solar luminosity and radius),
oscillations (p and g models), velocities (variation of rotation with
time and depth), and magnetic fields.

---------------------------------------------------------
Title: The nature of solar behaviour
Authors: Weiss, N. O.
1980asfr.symp....1W Altcode:
Current knowledge of the present state of the sun and of its evolution
since formation as a main sequence star 4.7 billion years ago is
reviewed as an astrophysical background to studies of the fossil record
of solar behavior. Attention is given to the internal structure of the
sun as a reflection of the thermonuclear energy generation processes
and convective energy dissipation processes occurring there, and to
the magnetic fields caused by motions in the convective zone, which
are responsible for solar activity. The long-term variability of the
periodic changes in solar magnetic fields explained by kinematic
dynamo theory is then considered in light of the sunspot record,
terrestrial records, and the relationship between magnetic activity,
solar luminosity and terrestrial climate. The evident magnetic
properties of the sun are compared with those observed in other stars,
and it is concluded that solar activity may have been 10 to 100 times
more vigorous than at present when the sun reached the main sequence,
and even more violent before then.

---------------------------------------------------------
Title: Andrew Marvell and the Maunder Minimum
Authors: Weiss, J. E.; Weiss, N. O.
1979QJRAS..20..115W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Buoyant magnetic flux tubes in supergranules.
Authors: Meyer, F.; Schmidt, H. U.; Simon, G. W.; Weiss, N. O.
1979A&A....76...35M Altcode:
The motion of filamentary flux tubes is described by a simplified
model. Relative to the prescribed supergranular flow, the tubes drift at
a rate determined by magnetic buoyancy, Lorentz forces and aerodynamic
drag. The effect of buoyancy is most pronounced near the surface:
small flux tubes are swept towards the network at the edge of a cell
but those with larger fluxes float vertically at the center. New flux
emerges at the center of the cell. These results are related to the
emergence of active regions and ephemeral active regions, and to the
slow decay of sunspots.

---------------------------------------------------------
Title: The pattern of convection in the sun.
Authors: Weiss, N. O.
1979psa..conf..121W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: The nature of solar behavior
Authors: Weiss, N. O.
1979LPICo.390..106W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Magnetic flux ropes and convection
Authors: Galloway, D. J.; Proctor, M. R. E.; Weiss, N. O.
1978JFM....87..243G Altcode:
Three-dimensional cellular convection concentrates magnetic flux into
ropes when the magnetic Reynolds number is large. Amplification of
the magnetic field is limited by the Lorentz force and the maximum
field in a flux rope can be estimated. Boundary-layer analysis yields
a completely self-consistent solution for a model of convection driven
by imposed horizontal temperature gradients, and the transition from a
kinematic to a dynamic regime can be followed in detail. The maximum
value of the amplified field is proportional to the square root of
the ratio of the viscous to the magnetic diffusivity.

---------------------------------------------------------
Title: Small-scale magnetic fields and convection in the solar
photosphere.
Authors: Weiss, N. O.
1978MNRAS.183P..63W Altcode:
The detection of solar magnetic structures with diameters less
than 300 km, as reported by Ramsey et al. (1977), is related to
theoretical studies of the nonlinear interaction between magnetic
fields and convection. In particular, it is shown that the location
of the small-scale magnetic fields at the centers of granules cannot
be readily explained on the basis of theoretical investigations of
vigorous Boussinesq convection in a magnetic field.

---------------------------------------------------------
Title: On the dynamic interaction between magnetic fields and
convection.
Authors: Peckover, R. S.; Weiss, N. O.
1978MNRAS.182..189P Altcode:
A simple two-dimensional model of convection in an electrically
conducting Boussinesq fluid with an externally imposed magnetic field
has been investigated in a series of numerical experiments. Convection
is driven by horizontal gradients in an imposed temperature field
which is unaffected by the motion. The transition from a kinematic to
a dynamic regime is studied: magnetic flux is concentrated into ropes
and the maximum field strength depends on the ratio of the viscous
and magnetic diffusivities. The magnetic energy density in the ropes
is unrelated to, and may be much greater than, the kinetic energy
density outside. These results are relevant to the interaction between
small-scale magnetic fields and photospheric granulation in the sun.

---------------------------------------------------------
Title: The stability of sunspots.
Authors: Meyer, F.; Schmidt, H. U.; Weiss, N. O.
1977MNRAS.179..741M Altcode:
The energy principle of Bernstein et al. (1958) is used to demonstrate
that a magnetic flux tube in equilibrium with an external stratified
field-free gas is stable to interchanges, provided the magnitude of the
radial field component decreases upward on the tube boundary. Stability
conditions on the external pressure in the case where a vacuum field is
inside the flux tube are investigated, and it is found that both stable
and unstable vacuum-field configurations can exist. A vacuum-field
model is employed to show that tubes with fluxes greater than about
10 to the 19th power Mx are stable in the sun, and this result is
applied to observations of small-scale solar magnetic fields as well
as to sunspot groups. Analysis of a simple sunspot model indicates
that a sunspot can be stable in and immediately below the photosphere,
that this stability is related to the potential energy associated with
the Wilson depression, and that twisted fields need not be invoked.

---------------------------------------------------------
Title: Formation of intense magnetic fields near the surface of
the sun
Authors: Galloway, D. J.; Proctor, M. R. E.; Weiss, N. O.
1977Natur.266..686G Altcode:
Possible mechanisms for the concentration of magnetic flux in the solar
photosphere in the form of ropes of average magnetic field strengths
of about 1500 gauss are discussed. Some upper limits to amplification
of magnetic fields by convection are obtained on the assumption that
the field strength cannot exceed the value for which the power needed
to contain the flux rope is equal to the rate of turbulent energy
dissipation. It is shown that the maximum field strength produced by
flux concentration is typically an order of magnitude higher than the
equipartition limit.

---------------------------------------------------------
Title: Small scale solar magnetic fields: theory.
Authors: Weiss, N. O.
1977IAUS...62..241W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Numerical methods in convection theory
Authors: Weiss, N. O.
1977LNP....71..142W Altcode: 1977stco.coll..142W; 1977IAUCo..38..142W; 1977psc..conf..142W
Nonlinear astrophysical convection is analyzed numerically, with
attention to the relationship between convective heat transport and
the super-adiabatic temperature gradient. Cellular patterns revealed
by direct solar observations are modeled by two and three dimensional
methods. The stability of the models is then evaluated on the basis
of axisymmetric flow subjected to nonaxisymmetric perturbations.

---------------------------------------------------------
Title: Magnetic fields and convection
Authors: Weiss, N. O.
1977LNP....71..176W Altcode: 1977IAUCo..38..176W; 1977stco.coll..176W; 1977psc..conf..176W
In a highly conducting plasma convection is hindered by the imposition
of a magnetic field. Convection may set in as direct or overstable modes
and behavior near the onset of instability depends on the ratio of the
magnetic to the thermal diffusivity. Vigorous convection produces local
flux concentrations with magnetic fields that may be much greater than
the equipartition value. The interaction between magnetic fields and
convection can be observed in detail on the sun and is essential to
any stellar dynamo.

---------------------------------------------------------
Title: The calibration of stellar convection theories.
Authors: Gough, D. O.; Weiss, N. O.
1976MNRAS.176..589G Altcode:
Any formula used to calculate the temperature gradient in a stellar
convection zone must be calibrated, for example, by evolving
1-solar-mass stellar models to fit the present age, luminosity, and
effective temperature of the sun. When this procedure is followed
for various convection theories, including those of Opik (1950)
and Boehm-Vitense (1958), the corresponding models become almost
indistinguishable. In particular, they predict the same depth, around
150,000 km, for the solar convective zone.

---------------------------------------------------------
Title: Convective Instability in a Compressible Atmosphere. II
Authors: Gough, D. O.; Moore, D. R.; Spiegel, E. A.; Weiss, N. O.
1976ApJ...206..536G Altcode:
The onset of steady convection in polytropic atmosphere with constant
viscosity is studied numencally. Subject headings: convection :
atmospheres

---------------------------------------------------------
Title: Magnetohydrodynamics (Book Review)
Authors: Mestel, L.; Weiss, N. O.
1976ApL....17..152M Altcode:
No abstract at ADS

---------------------------------------------------------
Title: The Solar Magnetic Field - Observation and Theory
Authors: Weiss, N. O.
1976IAUTB..16..240W Altcode: 1976IAUT...16B.240W
No abstract at ADS

---------------------------------------------------------
Title: Stability of sunspots
Authors: Meyer, F.; Schmidt, H. U.; Weiss, N. O.
1976MitAG..40..160M Altcode:
No abstract at ADS

---------------------------------------------------------
Title: The Pattern of Convection in the Sun
Authors: Weiss, N. O.
1976IAUS...71..229W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Axisymmetric convection in a cylinder
Authors: Jones, C. A.; Moore, D. R.; Weiss, N. O.
1976JFM....73..353J Altcode:
The geometrical properties of axisymmetric convection in a Boussinesq
fluid contained in a cylindrical cell with free boundaries
are investigated. The range of unsteady behavior requiring a
full three-dimensional solution of the governing equations is not
considered. The solution near the critical Reynolds number is obtained
from a perturbation expansion. For values of the Nusselt number not
greater than 2, solutions are obtained from an expansion in a finite
number of vertical modes. For Prandtl numbers less than unity the
solution becomes independent of the Prandtl number at large Reynolds
numbers. As the Prandtl number approaches 0 the Nusselt number is
a function of the Rayleigh number only and there is an effective
critical Rayleigh number equal to 1.32 times the critical Rayleigh
number. Numerical results obtained for Rayleigh numbers up to 100 times
the critical Rayleigh number and Prandtl numbers not in excess of 0.01
are similar to those for two-dimensional rolls. For Prandtl numbers
greater than unity there is a viscous regime. At high Rayleigh numbers
a large isothermal region develops in which the ratio of vorticity to
distance from the axis is almost constant.

---------------------------------------------------------
Title: What drives the solar cycle?
Authors: Weiss, Nigel
1975Natur.258..197W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: The growth and decay of sunspots.
Authors: Meyer, F.; Schmidt, H. U.; Weiss, N. O.; Wilson, P. R.
1974MNRAS.169...35M Altcode:
Sunspots are formed between supergranules, at junctions in the
chromospheric network. Many spots disappear rapidly. However, some large
spots enter a phase of slow decay: an annular cell develops, centered
on the spot and with a systematic outward velocity directed from the
penumbra toward the nearest faculae. This flow forms a moat around
the spot swept clear of magnetic field except for magnetic features
which migrate from the penumbra to the surrounding network. This
phase may persist for several months before the spot is finally
destroyed. Throughout this period the sunspot area, and hence its flux,
decrease at a constant rate. The evolution of a sunspot is related
to subphotospheric convection, with particular emphasis on a model of
the slow decay phase which explains the steady decay of magnetic flux.

---------------------------------------------------------
Title: A Theoretical Model for the Convection of Magnetic Flux in
and Near Sunspots
Authors: Meyer, F.; Schmidt, H. U.; Weiss, N. O.; Wilson, P. R.
1974IAUS...56..235M Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Introduction to Magnetohydrodynamics
Authors: Weiss, N. O.
1974magn.conf....2W Altcode: 1974SAAS....4....2W
Field in conducting fluids Maxwell's equations and the
magnetohydrodynamic approximation Kinematic magnetohydrodynamics
and the magnetic Reynolds number Perfectly conducting fluids
Flux conservation: Alfvén's theorem Consequences of flux-freezing
Hydromagnetic waves Alfvén waves Magneto-sonic waves Equilibria and
stability Magnetohydrostatic equilibria Force-free fields The Virial
theorem Stability problems Effects of finite resistivity Static
diffusion Effects of motion Currents in ionized gases Fully ionized
gas: two-fluid model Slightly ionized gas: three-fluid model Other
dissipative processes References

---------------------------------------------------------
Title: Convection in the earth's mantle: towards a numerical
simulation
Authors: McKenzie, D. P.; Roberts, J. M.; Weiss, N. O.
1974JFM....62..465M Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Dynamo Maintenance of Magnetic Fields in Stars
Authors: Weiss, N. O.
1974magn.conf..185W Altcode: 1974SAAS....4..185W
Astrophysical magnetic fields Introduction Observed magnetic fields
Hydromagnetic dynamos The solar cycle Observations Phenomenological
model Kinematic dynamo theory Cowling's theorem Simple dynamo models
Computational techniques Finite differences Expansion in toroidal
and poloidal spherical harmonics Macroscopic dynamos Mean field
electrodynamics The dynamo equations Mean field electrodynamics Dynamo
models Constant α α2 dynamos αω dynamos Oblique rotators
Magnetohydrodynamic dynamos Mean field dynamos Macroscopic motions
Convective models Dynamo action in the sun and stars Astrophysical
dynamos Convection and magnetic fields in the sun Problems of the
solar dynamo Stellar dynamos References

---------------------------------------------------------
Title: Magnetohydrodynamics
Authors: Mestel, L.; Weiss, N. O.
1974magn.conf.....M Altcode: 1974mssa.book.....M; 1974QB353.M47......; 1974SAAS....4.....M
No abstract at ADS

---------------------------------------------------------
Title: Two-dimensional Rayleigh-Benard convection
Authors: Moore, D. R.; Weiss, N. O.
1973JFM....58..289M Altcode:
No abstract at ADS

---------------------------------------------------------
Title: The Dynamo Problem
Authors: Weiss, N. O.
1971QJRAS..12..432W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Theories of Large Scale Fields and the Magnetic Active Cycle
Authors: Weiss, N. O.
1971IAUS...43..757W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: On the Magnetic Field in Pores
Authors: Simon, G. W.; Weiss, N. O.
1970SoPh...13...85S Altcode:
The magnetic field in an axisymmetric pore is current free and
can be represented by a flux tube with a magnetic potential of the
formAJ0(kr)e-kz. For a given magnetic flux the
field in this pore model is uniquely defined if the magnetic pressure
balances the gas pressure at two levels. For models with fluxes of
0.5-3.0 × 1020 mx the surface radius varies from 1100-2700
km (diameters of 3-8 arc-sec) and the Wilson depression is estimated
at 200 km. As the flux increases, the field becomes nearly horizontal
at the edge of the pore and eventually a penumbra is formed. The
distinction between pores and sunspots is investigated; the critical
flux is about 1020 Mx, corresponding to a radius of 1500 km.

---------------------------------------------------------
Title: On the Magnetic Field in Pores
Authors: Weiss, N. O.; Simon, G. W.
1969BAAS....1S.295W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Sunspots and photospheric convection
Authors: Weiss, N. O.
1969pia..conf..153W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Supergranules and the Hydrogen Convection Zone
Authors: Simon, G. W.; Weiss, N. O.
1968ZA.....69..435S Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Supergranules and the Hydrogen Convection Zone.
Authors: Simon, G. W.; Weiss, N. O.
1968AJS....73S..77S Altcode:
The strong magnetic fields observed between supergranules indicate
that there must be subphotospheric convection in cells with a
preferred diameter of about 30 000 km. Orthodox mixing length theory
assumes that the dimensions of cells are limited by the density scale
height. This is adequate fot explaining granules but cannot account
for supergranulation. A model is therefore proposed in which cellular
motions extend over several scale heights. In addition to granules
~nd supergranules, this model predicts a third characteristic scale
of motion, with giant cells around 300 000 km in diameter, These cells
may produce a pattern of magnetic fields like that suggested by Bumba
and Howard for complexes of activity.

---------------------------------------------------------
Title: Concentration of Magnetic Fields in the Deep Convection Zone
Authors: Simon, G. W.; Weiss, N. O.
1968IAUS...35..108S Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Convection in the Earth's mantle
Authors: Allan, D. W.; Thompson, W. B.; Weiss, N. O.
1967metp.conf..507A Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Concentration of magnetic fields by convection in the Sun
Authors: Weiss, N. O.
1967maco.conf..262W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: The Expulsion of Magnetic Flux by Eddies
Authors: Weiss, N. O.
1966RSPSA.293..310W Altcode: 1966RSLPS.293..310W
A convective eddy imposed on an initially uniform magnetic field in a
highly conducting fluid distorts the lines of force and amplifies the
field. Flux is concentrated outside the eddy; within it, the field grows
and its scale of variation decreases until resistive effects become
important. Closed lines of force are then formed by reconnexion. The
central field decays and a steady state is reached. Within a period,
small compared with the characteristic time for resistive decay,
magnetic flux is almost entirely expelled from regions of rapid motion
and concentrated at the edges of convection cells. This process is
demonstrated from numerical experiments. The results are applied to
the sun, where the concentrated fields are strong enough to inhibit
convection locally.

---------------------------------------------------------
Title: Convection and the differential rotation of the Sun
Authors: Weiss, N. O.
1965Obs....85...37W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Magnetic flux tubes and convection in the sun
Authors: Weiss, N. O.
1965IAUS...22..330W Altcode:
No abstract at ADS

---------------------------------------------------------
Title: Convection in the Presence of Restraints
Authors: Weiss, N. O.
1964RSPTA.256...99W Altcode:
In the presence of rotation or a magnetic field, the linearized
convection problem reduces to a cubic characteristic equation. In part
I, general methods are given for determining the onset of convection;
in particular, the transition from oscillatory to steady modes is
considered. The importance of this transition arises from evidence that
oscillatory modes are inefficient at transporting heat. These methods
are then applied to a rotating system where the critical Rayleigh
number can be expressed in terms of a Taylor number. It is found that
overstable modes develop into steady unstable modes before the exchange
of stabilities for Prandtl numbers less than one-third. The nature
of the motions is discussed and a similar treatment is provided for
convection in a magnetic field. In part II, criteria for the onset
of instability are derived from physical arguments. Convection can
be treated by balancing the work done by buoyancy forces against the
energy dissipated. In a rotating system, the effect of the Coriolis
forces is to restrict the cell width and thus to enhance dissipation
and promote stability. A magnetic field similarly attenuates the cells
and prevents steady convection until the liberated kinetic energy
exceeds the energy in the field. In part III, a cellular model is
proposed for turbulent convection in a fluid of negligible viscosity,
where the motion is limited by the non-linear transfer of energy to
smaller-scale motions. If the Rayleigh number R3 = gα β
d4/π 4kappa 2&gt;&gt; 1 the convective
transport varies as R31/2, while it varies as
R32 when R3&lt;&lt; 1. The discussion
is extended to convection in the presence of rotation or a magnetic
field; it is shown that overstable perturbations cannot develop into
steady turbulent convection unless the system is already unstable to
non-oscillatory modes. The transition from overstable to steady modes
should therefore correspond to a sharp increase in convective transport.

---------------------------------------------------------
Title: Magnetic flux tubes and convection in the Sun
Authors: Weiss, N. O.
1964MNRAS.128..225W Altcode:
Convection in the Sun is apparently cellular and the convective
velocities can be estimated. The interaction of cellular convection
with a weak magnetic field leads to concentrated ropes of flux in the
convective zone with fields of about 5000 gauss and fluxes of 1021
maxwells in agreement with observation. These flux tubes tend to float
outwards from the centre of the Sun. The magnetic pressure associated
with the fields required to halt photospheric convection is comparable
with the gas pressure and so fields will generally be diffuse as in
bipolar magnetic regions. Occasionally the flux is concentrated to
form a sunspot but the cooling is insignificant at more than 1000 km
below the surface of the Sun.

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Title: Nouvelles de la Science. - Varietes. La prochaine comete.
Authors: Weiss
1886LAstr...5..109W Altcode:
No abstract at ADS