Author name code: cattaneo
ADS astronomy entries on 2022-09-14
author:"Cattaneo, Fausto"
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Title: Research Opportunities in Plasma Astrophysics
Authors: Bale, Stuart; Bhattacharjee, Amitava; Cattaneo, Fausto; Drake,
Jemes; Ji, Hantao; Lee, Marty; Li, Hui; Liang, Edison; Pound, Marc;
Prager, Stewart; Quataert, Eliot; Remington, Bruce; Rosner, Robert;
Ryutov, Dmitri; Thomas, Edward, Jr; Zweibel, Ellen
Bibcode: 2022arXiv220302406B
Altcode:
Major scientific questions and research opportunities are described
on 10 unprioritized plasma astrophysics topics: (1) magnetic
reconnection, (2) collisionless shocks and particle acceleration, (3)
waves and turbulence, (4) magnetic dynamos, (5) interface and shear
instabilities, (6) angular momentum transport, (7) dusty plasmas,
(8) radiative hydrodynamics, (9) relativistic, pair-dominated and
strongly magnetized plasmas, (10) jets and outflows. Note that this
is a conference report from a Workshop on Opportunities in Plasma
Astrophysics (WOPA, https://w3.pppl.gov/conferences/2010/WOPA/) in
January 2010, that attracted broad representation from the community
and was supported by the U.S. Department of Energy, National Aeronautics
and Space Administration, National Science Foundation, American Physical
Society's Topical Group for Plasma Astrophysics and Division of Plasma
Physics, and Center for Magnetic Self-Organization in Laboratory and
Astrophysical Plasmas. Although there has been much planning and many
developments in both science and infrastructure since the report was
written, most of the motivation, priorities, problems and technical
challenges discussed therein remain unaddressed and are relevant at
the time of posting.
Title: Generation of coherent magnetic fields in periodic (closed)
and non-periodic (open) domains
Authors: Bhat, Pallavi; Tobias, Steven; Cattaneo, Fausto; Bodo,
Gianluigi
Bibcode: 2020APS..DFDE05005B
Altcode:
The origin of large-scale magnetic fields in most astrophysical
systems like the Sun, stars and galaxies remains a challenging open
problem. Dynamo action in the underlying turbulent fluid is thought
to be responsible for the emergence of coherent magnetic fields. Due
to the enormity of magnetic Reynolds numbers in these astrophysical
systems, current theoretical models of the turbulent dynamo struggle to
generate large-scale field on fast dynamic timescales. The conservation
properties of magnetic helicity can constrain the nonlinear evolution
of the dynamo. We have performed direct numerical simulations of the
turbulent dynamo to investigate if employing open boundaries relaxes
the constraint imposed by magnetic helicity conservation. We find
that in the open systems a net magnetic flux (or system-scale fields)
of significant strength arises. However, the type of open boundary we
employ does not alleviate the magnetic Reynolds number (in the range
explored) dependence in the nonlinear evolution of the large-scale
fields. Finally, simulations performed across different magnetic Prandtl
numbers indicate that the behavior of the magnetic helicity evolution
is affected by flow properties as well. European Research Council.
Title: Magnetorotational Turbulence, Dynamo Action and Transport in
Convective Disks
Authors: Bodo, G.; Cattaneo, F.; Mignone, A.; Rossi, P.
Bibcode: 2019ASSP...55....3B
Altcode:
No abstract at ADS
Title: Laboratory evidence of dynamo amplification of magnetic fields
in a turbulent plasma
Authors: Tzeferacos, P.; Rigby, A.; Bott, A. F. A.; Bell, A. R.;
Bingham, R.; Casner, A.; Cattaneo, F.; Churazov, E. M.; Emig, J.;
Fiuza, F.; Forest, C. B.; Foster, J.; Graziani, C.; Katz, J.; Koenig,
M.; Li, C. -K.; Meinecke, J.; Petrasso, R.; Park, H. -S.; Remington,
B. A.; Ross, J. S.; Ryu, D.; Ryutov, D.; White, T. G.; Reville,
B.; Miniati, F.; Schekochihin, A. A.; Lamb, D. Q.; Froula, D. H.;
Gregori, G.
Bibcode: 2018NatCo...9..591T
Altcode: 2017arXiv170203016T
Magnetic fields are ubiquitous in the Universe. The energy density of
these fields is typically comparable to the energy density of the fluid
motions of the plasma in which they are embedded, making magnetic fields
essential players in the dynamics of the luminous matter. The standard
theoretical model for the origin of these strong magnetic fields is
through the amplification of tiny seed fields via turbulent dynamo to
the level consistent with current observations. However, experimental
demonstration of the turbulent dynamo mechanism has remained elusive,
since it requires plasma conditions that are extremely hard to re-create
in terrestrial laboratories. Here we demonstrate, using laser-produced
colliding plasma flows, that turbulence is indeed capable of rapidly
amplifying seed fields to near equipartition with the turbulent fluid
motions. These results support the notion that turbulent dynamo is a
viable mechanism responsible for the observed present-day magnetization.
Title: Magnetic Helicities and Dynamo Action in Magneto-rotational
Turbulence
Authors: Bodo, G.; Cattaneo, F.; Mignone, A.; Rossi, P.
Bibcode: 2017ApJ...843...86B
Altcode: 2017arXiv170604492B
We examine the relationship between magnetic flux generation, taken
as an indicator of large-scale dynamo action, and magnetic helicity,
computed as an integral over the dynamo volume, in a simple dynamo. We
consider dynamo action driven by magneto-rotational turbulence (MRT)
within the shearing-box approximation. We consider magnetically open
boundary conditions that allow a flux of helicity in or out of the
computational domain. We circumvent the problem of the lack of gauge
invariance in open domains by choosing a particular gauge—the winding
gauge—that provides a natural interpretation in terms of the average
winding number of pairwise field lines. We use this gauge precisely
to define and measure the helicity and the helicity flux for several
realizations of dynamo action. We find in these cases that the system
as a whole does not break reflectional symmetry and that the total
helicity remains small even in cases when substantial magnetic flux
is generated. We find no particular connection between the generation
of magnetic flux and the helicity or the helicity flux through the
boundaries. We suggest that this result may be due to the essentially
nonlinear nature of the dynamo processes in MRT.
Title: Numerical modeling of laser-driven experiments aiming to
demonstrate magnetic field amplification via turbulent dynamo
Authors: Tzeferacos, P.; Rigby, A.; Bott, A.; Bell, A. R.; Bingham,
R.; Casner, A.; Cattaneo, F.; Churazov, E. M.; Emig, J.; Flocke,
N.; Fiuza, F.; Forest, C. B.; Foster, J.; Graziani, C.; Katz, J.;
Koenig, M.; Li, C. -K.; Meinecke, J.; Petrasso, R.; Park, H. -S.;
Remington, B. A.; Ross, J. S.; Ryu, D.; Ryutov, D.; Weide, K.; White,
T. G.; Reville, B.; Miniati, F.; Schekochihin, A. A.; Froula, D. H.;
Gregori, G.; Lamb, D. Q.
Bibcode: 2017PhPl...24d1404T
Altcode: 2017arXiv170203015T
The universe is permeated by magnetic fields, with strengths ranging
from a femtogauss in the voids between the filaments of galaxy clusters
to several teragauss in black holes and neutron stars. The standard
model behind cosmological magnetic fields is the nonlinear amplification
of seed fields via turbulent dynamo to the values observed. We have
conceived experiments that aim to demonstrate and study the turbulent
dynamo mechanism in the laboratory. Here, we describe the design of
these experiments through simulation campaigns using FLASH, a highly
capable radiation magnetohydrodynamics code that we have developed,
and large-scale three-dimensional simulations on the Mira supercomputer
at the Argonne National Laboratory. The simulation results indicate
that the experimental platform may be capable of reaching a turbulent
plasma state and determining the dynamo amplification. We validate and
compare our numerical results with a small subset of experimental data
using synthetic diagnostics.
Title: What is a large-scale dynamo?
Authors: Nigro, G.; Pongkitiwanichakul, P.; Cattaneo, F.; Tobias, S. M.
Bibcode: 2017MNRAS.464L.119N
Altcode:
We consider kinematic dynamo action in a sheared helical flow at
moderate to high values of the magnetic Reynolds number (Rm). We find
exponentially growing solutions which, for large enough shear, take
the form of a coherent part embedded in incoherent fluctuations. We
argue that at large Rm large-scale dynamo action should be identified
by the presence of structures coherent in time, rather than those at
large spatial scales. We further argue that although the growth rate
is determined by small-scale processes, the period of the coherent
structures is set by mean-field considerations.
Title: Shear-driven Dynamo Waves in the Fully Nonlinear Regime
Authors: Pongkitiwanichakul, P.; Nigro, G.; Cattaneo, F.; Tobias, S. M.
Bibcode: 2016ApJ...825...23P
Altcode:
Large-scale dynamo action is well understood when the magnetic Reynolds
number (Rm) is small, but becomes problematic in the astrophysically
relevant large Rm limit since the fluctuations may control the
operation of the dynamo, obscuring the large-scale behavior. Recent
works by Tobias & Cattaneo demonstrated numerically the existence of
large-scale dynamo action in the form of dynamo waves driven by strongly
helical turbulence and shear. Their calculations were carried out in
the kinematic regime in which the back-reaction of the Lorentz force on
the flow is neglected. Here, we have undertaken a systematic extension
of their work to the fully nonlinear regime. Helical turbulence and
large-scale shear are produced self-consistently by prescribing body
forces that, in the kinematic regime, drive flows that resemble the
original velocity used by Tobias & Cattaneo. We have found four
different solution types in the nonlinear regime for various ratios
of the fluctuating velocity to the shear and Reynolds numbers. Some
of the solutions are in the form of propagating waves. Some solutions
show large-scale helical magnetic structure. Both waves and structures
are permanent only when the kinetic helicity is non-zero on average.
Title: Strong-field dynamo action in rapidly rotating convection
with no inertia
Authors: Hughes, David W.; Cattaneo, Fausto
Bibcode: 2016PhRvE..93f1101H
Altcode: 2015arXiv151006220H
The earth's magnetic field is generated by dynamo action driven by
convection in the outer core. For numerical reasons, inertial and
viscous forces play an important role in geodynamo models; however,
the primary dynamical balance in the earth's core is believed to be
between buoyancy, Coriolis, and magnetic forces. The hope has been
that by setting the Ekman number to be as small as computationally
feasible, an asymptotic regime would be reached in which the correct
force balance is achieved. However, recent analyses of geodynamo models
suggest that the desired balance has still not yet been attained. Here
we adopt a complementary approach consisting of a model of rapidly
rotating convection in which inertial forces are neglected from the
outset. Within this framework we are able to construct a branch of
solutions in which the dynamo generates a strong magnetic field that
satisfies the expected force balance. The resulting strongly magnetized
convection is dramatically different from the corresponding solutions
in which the field is weak.
Title: The electromotive force in multi-scale flows at high magnetic
Reynolds number
Authors: Tobias, Steven M.; Cattaneo, Fausto
Bibcode: 2015JPlPh..81f3901T
Altcode:
> Recent advances in dynamo theory have been made by examining the
competition between small- and large-scale dynamos at high magnetic
Reynolds number . Small-scale dynamos rely on the presence of chaotic
stretching whilst the generation of large-scale fields occurs in
flows lacking reflectional symmetry via a systematic electromotive
force (EMF). In this paper we discuss how the statistics of the EMF
(at high ) depend on the properties of the multi-scale velocity that
is generating it. In particular, we determine that different scales
of flow have different contributions to the statistics of the EMF,
with smaller scales contributing to the mean without increasing
the variance. Moreover, we determine when scales in such a flow act
independently in their contribution to the EMF. We further examine the
role of large-scale shear in modifying the EMF. We conjecture that the
distribution of the EMF, and not simply the mean, largely determines
the dominant scale of the magnetic field generated by the flow.
Title: A model of plasma heating by large-scale flow
Authors: Pongkitiwanichakul, P.; Cattaneo, F.; Boldyrev, S.; Mason,
J.; Perez, J. C.
Bibcode: 2015MNRAS.454.1503P
Altcode: 2015arXiv150908848P
In this work, we study the process of energy dissipation triggered
by a slow large-scale motion of a magnetized conducting fluid. Our
consideration is motivated by the problem of heating the solar corona,
which is believed to be governed by fast reconnection events set off by
the slow motion of magnetic field lines anchored in the photospheric
plasma. To elucidate the physics governing the disruption of the
imposed laminar motion and the energy transfer to small scales, we
propose a simplified model where the large-scale motion of magnetic
field lines is prescribed not at the footpoints but rather imposed
volumetrically. As a result, the problem can be treated numerically
with an efficient, highly accurate spectral method, allowing us to use
a resolution and statistical ensemble exceeding those of the previous
work. We find that, even though the large-scale deformations are slow,
they eventually lead to reconnection events that drive a turbulent
state at smaller scales. The small-scale turbulence displays many of the
universal features of field-guided magnetohydrodynamic turbulence like
a well-developed inertial range spectrum. Based on these observations,
we construct a phenomenological model that gives the scalings of
the amplitude of the fluctuations and the energy-dissipation rate as
functions of the input parameters. We find good agreement between the
numerical results and the predictions of the model.
Title: Global Properties of Fully Convective Accretion Disks from
Local Simulations
Authors: Bodo, G.; Cattaneo, F.; Mignone, A.; Ponzo, F.; Rossi, P.
Bibcode: 2015ApJ...808..141B
Altcode: 2016arXiv160207334B
We present an approach to deriving global properties of accretion disks
from the knowledge of local solutions derived from numerical simulations
based on the shearing box approximation. The approach consists of a
two-step procedure. First, a local solution valid for all values of
the disk height is constructed by piecing together an interior solution
obtained numerically with an analytical exterior radiative solution. The
matching is obtained by assuming hydrostatic balance and radiative
equilibrium. Although in principle the procedure can be carried out
in general, it simplifies considerably when the interior solution is
fully convective. In these cases, the construction is analogous to
the derivation of the Hayashi tracks for protostars. The second step
consists of piecing together the local solutions at different radii
to obtain a global solution. Here we use the symmetry of the solutions
with respect to the defining dimensionless numbers—in a way similar
to the use of homology relations in stellar structure theory—to obtain
the scaling properties of the various disk quantities with radius.
Title: Energy dynamics and current sheet structure in fluid and
kinetic simulations of decaying magnetohydrodynamic turbulence
Authors: Makwana, K. D.; Zhdankin, V.; Li, H.; Daughton, W.;
Cattaneo, F.
Bibcode: 2015PhPl...22d2902M
Altcode: 2014arXiv1412.4723M
Simulations of decaying magnetohydrodynamic (MHD) turbulence
are performed with a fluid and a kinetic code. The initial
condition is an ensemble of long-wavelength, counter-propagating,
shear-Alfvén waves, which interact and rapidly generate strong
MHD turbulence. The total energy is conserved and the rate of
turbulent energy decay is very similar in both codes, although
the fluid code has numerical dissipation, whereas the kinetic code
has kinetic dissipation. The inertial range power spectrum index
is similar in both the codes. The fluid code shows a perpendicular
wavenumber spectral slope of k⊥-1.3 . The kinetic code
shows a spectral slope of k⊥-1.5 for smaller simulation
domain, and k⊥-1.3 for larger domain. We estimate that
collisionless damping mechanisms in the kinetic code can account for
the dissipation of the observed nonlinear energy cascade. Current
sheets are geometrically characterized. Their lengths and widths are
in good agreement between the two codes. The length scales linearly
with the driving scale of the turbulence. In the fluid code, their
thickness is determined by the grid resolution as there is no explicit
diffusivity. In the kinetic code, their thickness is very close to the
skin-depth, irrespective of the grid resolution. This work shows that
kinetic codes can reproduce the MHD inertial range dynamics at large
scales, while at the same time capturing important kinetic physics at
small scales.
Title: Fully Convective Magneto-rotational Turbulence in Large
Aspect-ratio Shearing Boxes
Authors: Bodo, G.; Cattaneo, F.; Mignone, A.; Rossi, P.
Bibcode: 2015ApJ...799...20B
Altcode:
We present a numerical study of turbulence and dynamo action in
stratified shearing boxes with both finite and zero net magnetic
flux. We assume that the fluid obeys the perfect gas law and has finite
thermal diffusivity. The latter is chosen to be small enough so that
vigorous convective states develop. The properties of these convective
solutions are analyzed as the aspect ratio of the computational domain
is varied and as the value of the mean field is increased. For the
cases with zero net flux, we find that a well-defined converged state
is obtained for large enough aspect ratios. In the converged state,
the dynamo can be extremely efficient and can generate substantial
toroidal flux. We identify solutions in which the toroidal field is
mostly symmetric about the mid-plane and solutions in which it is mostly
anti-symmetric. The symmetric solutions are found to be more efficient
at transporting angular momentum and can give rise to a luminosity that
is up to an order of magnitude larger than the corresponding value
for the anti-symmetric states. In the cases with a finite net flux,
the system appears to spend most of the time in the symmetric states.
Title: Plasma Heating by Volumetric Large-scale Flows
Authors: Pongkitiwanichakul, P.; Cattaneo, F.; Boldyrev, S.; Mason,
J.; Perez, J. C.
Bibcode: 2014AGUFMSH13C4136P
Altcode:
We solve an incompressible magnetohydrodynamo system.We simulate a
series of high-resolution numerical simulations and aim at clarifying
the mechanisms that lead to heating of the solar corona. The model
consists of an initially uniform magnetic field that is slowly deformed
by a volumetric prescribed flow.The response of the system is to
re-adjust the magnetic configuration by a series of non-ideal events
that lead to the heating of the plasma. Our simulations show that the
system develops an MHD turbulent state. The heating is intermittent
and independent of Lundquist number. The time averaged magnetic and
kinetic energies also are independent of Lundquist number.Thereafter,
we propose a phenomenological model to explain our finding. Our model
provides the scaling laws that fairly describe the heating rate,
the time averaged magnetic energy, and the time averaged kinetic energy.
Title: The statistics of a passive scalar in field-guided
magnetohydrodynamic turbulence
Authors: Mason, J.; Boldyrev, S.; Cattaneo, F.; Perez, J. C.
Bibcode: 2014GApFD.108..686M
Altcode: 2014arXiv1409.7196M
A variety of studies of magnetised plasma turbulence invoke theories for
the advection of a passive scalar by turbulent fluctuations. Examples
include modelling the electron density fluctuations in the interstellar
medium, understanding the chemical composition of galaxy clusters and
the intergalactic medium, and testing the prevailing phenomenological
theories of magnetohydrodynamic turbulence. While passive scalar
turbulence has been extensively studied in the hydrodynamic case,
its counterpart in MHD turbulence is significantly less well
understood. Herein we conduct a series of high-resolution direct
numerical simulations of incompressible, field-guided, MHD turbulence
in order to establish the fundamental properties of passive scalar
evolution. We study the scalar anisotropy, establish the scaling
relation analogous to Yaglom's law, and measure the intermittency
of the passive scalar statistics. We also assess to what extent the
pseudo Alfvén fluctuations in strong MHD turbulence can be modelled as
a passive scalar. The results suggest that the dynamics of a passive
scalar in MHD turbulence is considerably more complicated than in the
hydrodynamic case.
Title: Scaling Properties of Small-scale Fluctuations in
Magnetohydrodynamic Turbulence
Authors: Perez, Jean Carlos; Mason, Joanne; Boldyrev, Stanislav;
Cattaneo, Fausto
Bibcode: 2014ApJ...793L..13P
Altcode: 2014arXiv1409.2728P
Magnetohydrodynamic (MHD) turbulence in the majority of natural systems,
including the interstellar medium, the solar corona, and the solar wind,
has Reynolds numbers far exceeding the Reynolds numbers achievable
in numerical experiments. Much attention is therefore drawn to the
universal scaling properties of small-scale fluctuations, which
can be reliably measured in the simulations and then extrapolated
to astrophysical scales. However, in contrast with hydrodynamic
turbulence, where the universal structure of the inertial and
dissipation intervals is described by the Kolmogorov self-similarity,
the scaling for MHD turbulence cannot be established based solely on
dimensional arguments due to the presence of an intrinsic velocity
scale—the Alfvén velocity. In this Letter, we demonstrate that the
Kolmogorov first self-similarity hypothesis cannot be formulated for
MHD turbulence in the same way it is formulated for the hydrodynamic
case. Besides profound consequences for the analytical consideration,
this also imposes stringent conditions on numerical studies of MHD
turbulence. In contrast with the hydrodynamic case, the discretization
scale in numerical simulations of MHD turbulence should decrease
faster than the dissipation scale, in order for the simulations to
remain resolved as the Reynolds number increases.
Title: Comment on the numerical measurements of the
magnetohydrodynamic turbulence spectrum by A. Beresnyak
(Phys. Rev. Lett. 106 (2011) 075001; MNRAS 422 (2012) 3495; ApJ 784
(2014) L20)
Authors: Perez, J. C.; Mason, J.; Boldyrev, S.; Cattaneo, F.
Bibcode: 2014arXiv1409.8106P
Altcode:
The inertial-interval energy spectrum of strong magnetohydrodynamic
(MHD) turbulence with a uniform background magnetic field was observed
numerically to be close to $k^{-3/2}$ by a number of independent
groups. A dissenting opinion has been voiced by Beresnyak, A. 2011,
PRL, 106, 075001-. 2012, MNRAS, 422, 3495-. 2014, ApJ, 784, L20 that
the spectral scaling is close to $k^{-5/3}$. The conclusions of these
papers are however incorrect as they are based on numerical simulations
that are drastically unresolved, so that the discrete numerical scheme
does not approximate the physical solution at the scales where the
measurements are performed. These results have been rebutted in our
more detailed papers Perez, J. C., Mason, J., Boldyrev, S., &
Cattaneo, F. 2012, PRX, 2, 041005-. 2014, ApJL, 793, L13; here, by
popular demand, we present a brief and simple explanation of our major
criticism of Beresnyak's work.
Title: On Large-scale Dynamo Action at High Magnetic Reynolds Number
Authors: Cattaneo, F.; Tobias, S. M.
Bibcode: 2014ApJ...789...70C
Altcode: 2014arXiv1405.3071C
We consider the generation of magnetic activity—dynamo waves—in
the astrophysical limit of very large magnetic Reynolds number. We
consider kinematic dynamo action for a system consisting of helical
flow and large-scale shear. We demonstrate that large-scale dynamo
waves persist at high Rm if the helical flow is characterized by a
narrow band of spatial scales and the shear is large enough. However,
for a wide band of scales the dynamo becomes small scale with a further
increase of Rm, with dynamo waves re-emerging only if the shear is then
increased. We show that at high Rm, the key effect of the shear is to
suppress small-scale dynamo action, allowing large-scale dynamo action
to be observed. We conjecture that this supports a general "suppression
principle"—large-scale dynamo action can only be observed if there
is a mechanism that suppresses the small-scale fluctuations.
Title: On the Convergence of Magnetorotational Turbulence in
Stratified Isothermal Shearing Boxes
Authors: Bodo, G.; Cattaneo, F.; Mignone, A.; Rossi, P.
Bibcode: 2014ApJ...787L..13B
Altcode: 2014arXiv1404.6079B
We consider the problem of convergence in stratified isothermal
shearing boxes with zero net magnetic flux. We present results with
the highest resolution to date—up to 200 grid points per pressure
scale height—that show no clear evidence of convergence. Rather, the
Maxwell stresses continue to decrease with increasing resolution. We
propose some possible scenarios to explain the lack of convergence
based on multi-layer dynamo systems.
Title: Fully Convective Magnetorotational Turbulence in Stratified
Shearing Boxes
Authors: Bodo, G.; Cattaneo, F.; Mignone, A.; Rossi, P.
Bibcode: 2013ApJ...771L..23B
Altcode: 2013arXiv1306.3386B
We present a numerical study of turbulence and dynamo action in
stratified shearing boxes with zero magnetic flux. We assume that
the fluid obeys the perfect gas law and has finite (constant) thermal
diffusivity. We choose radiative boundary conditions at the vertical
boundaries in which the heat flux is proportional to the fourth power
of the temperature. We compare the results with the corresponding cases
in which fixed temperature boundary conditions are applied. The most
notable result is that the formation of a fully convective state in
which the density is nearly constant as a function of height and the
heat is transported to the upper and lower boundaries by overturning
motions is robust and persists even in cases with radiative boundary
conditions. Interestingly, in the convective regime, although the
diffusive transport is negligible, the mean stratification does not
relax to an adiabatic state.
Title: Computation as a Bridge between the Laboratory and Astrophysics
Authors: Rosner, Robert; Cattaneo, F.
Bibcode: 2013AAS...22221201R
Altcode:
Over the past decade, the many deep connections between terrestrial
laboratory studies and astrophysics have been powerfully supported
by modern numerical simulation: These calculations are able to make
contact with modeling of both physically complex astrophysical phenomena
and related phenomena observed in far greater detail in terrestrial
laboratories. We will describe several examples that illustrate the
power of numerical simulations to bridge laboratory and astrophysical
studies.
Title: Recent results on magnetic plasma turbulence
Authors: Boldyrev, Stanislav; Perez, Jean Carlos; Mason, Joanne;
Cattaneo, Fausto
Bibcode: 2013AIPC.1539..135B
Altcode:
Magnetic plasma turbulence is observed over a broad range of scales
in the solar wind. We discuss the results of high-resolution numerical
simulations of magnetohydrodynamic (MHD) turbulence that models plasma
motion at large scales and the results of numerical simulations
of kinetic-Alfvén turbulence that models plasma motion at small,
sub-proton scales. The simulations, with numerical resolutions up to
20483 mesh points in the MHD case and 5123 points in kinetic-Alfvén
case and statistics accumulated over 30 to 150 eddy turnover times,
constitute, to the best of our knowledge, the largest statistical
sample of steadily driven three dimensional MHD and kinetic-Alfvén
turbulence to date.
Title: Shear-driven dynamo waves at high magnetic Reynolds number
Authors: Tobias, S. M.; Cattaneo, F.
Bibcode: 2013Natur.497..463T
Altcode:
Astrophysical magnetic fields often display remarkable organization,
despite being generated by dynamo action driven by turbulent flows at
high conductivity. An example is the eleven-year solar cycle, which
shows spatial coherence over the entire solar surface. The difficulty
in understanding the emergence of this large-scale organization is that
whereas at low conductivity (measured by the magnetic Reynolds number,
Rm) dynamo fields are well organized, at high Rm their structure is
dominated by rapidly varying small-scale fluctuations. This arises
because the smallest scales have the highest rate of strain, and can
amplify magnetic field most efficiently. Therefore most of the effort
to find flows whose large-scale dynamo properties persist at high
Rm has been frustrated. Here we report high-resolution simulations
of a dynamo that can generate organized fields at high Rm; indeed,
the generation mechanism, which involves the interaction between
helical flows and shear, only becomes effective at large Rm. The shear
does not enhance generation at large scales, as is commonly thought;
instead it reduces generation at small scales. The solution consists
of propagating dynamo waves, whose existence was postulated more than
60 years ago and which have since been used to model the solar cycle.
Title: Magnetorotational Turbulence in Stratified Shearing Boxes
with Perfect Gas Equation of State and Finite Thermal Diffusivity
Authors: Bodo, G.; Cattaneo, F.; Mignone, A.; Rossi, P.
Bibcode: 2012ApJ...761..116B
Altcode: 2012arXiv1210.6443B
We present a numerical study of turbulence and dynamo action in
stratified shearing boxes with zero mean magnetic flux. We assume
that the fluid obeys the perfect gas law and has finite (constant)
thermal diffusivity. The calculations begin from an isothermal state
spanning three scale heights above and below the mid-plane. After a
long transient the layers settle to a stationary state in which thermal
losses out of the boundaries are balanced by dissipative heating. We
identify two regimes. The first is a conductive regime in which the
heat is transported mostly by conduction and the density decreases with
height. In the limit of large thermal diffusivity this regime resembles
the more familiar isothermal case. The second is the convective regime,
observed at smaller values of the thermal diffusivity, in which the
layer becomes unstable to overturning motions, the heat is carried
mostly by advection, and the density becomes nearly constant throughout
the layer. In this latter constant-density regime we observe evidence
for large-scale dynamo action leading to a substantial increase in
transport efficiency relative to the conductive case.
Title: On the Energy Spectrum of Strong Magnetohydrodynamic Turbulence
Authors: Perez, Jean Carlos; Mason, Joanne; Boldyrev, Stanislav;
Cattaneo, Fausto
Bibcode: 2012PhRvX...2d1005P
Altcode: 2012arXiv1209.2011P
The energy spectrum of magnetohydrodynamic turbulence attracts
interest due to its fundamental importance and its relevance for
interpreting astrophysical data. Here we present measurements of
the energy spectra from a series of high-resolution direct numerical
simulations of magnetohydrodynamics turbulence with a strong guide
field and for increasing Reynolds number. The presented simulations,
with numerical resolutions up to 20483 mesh points
and statistics accumulated over 30 to 150 eddy turnover times,
constitute, to the best of our knowledge, the largest statistical
sample of steady state magnetohydrodynamics turbulence to date. We
study both the balanced case, where the energies associated with
Alfvén modes propagating in opposite directions along the guide field,
E+(k⊥) and E-(k⊥), are
equal, and the imbalanced case where the energies are different. In
the balanced case, we find that the energy spectrum converges to a
power law with exponent -3/2 as the Reynolds number is increased,
which is consistent with phenomenological models that include
scale-dependent dynamic alignment. For the imbalanced case,
with E+>E-, the simulations show that
E-∝k⊥-3/2 for all Reynolds
numbers considered, while E+ has a slightly steeper
spectrum at small Re. As the Reynolds number increases, E+
flattens. Since E± are pinned at the dissipation scale and
anchored at the driving scales, we postulate that at sufficiently high
Re the spectra will become parallel in the inertial range and scale
as E+∝E-∝k⊥-3/2.
Questions regarding the universality of the spectrum and the value of
the “Kolmogorov constant” are discussed.
Title: Numerical simulations of strong incompressible
magnetohydrodynamic turbulence
Authors: Mason, J.; Perez, J. C.; Boldyrev, S.; Cattaneo, F.
Bibcode: 2012PhPl...19e5902M
Altcode: 2012arXiv1202.3474M
Magnetised plasma turbulence pervades the universe and is
likely to play an important role in a variety of astrophysical
settings. Magnetohydrodynamics (MHD) provides the simplest theoretical
framework in which phenomenological models for the turbulent dynamics
can be built. Numerical simulations of MHD turbulence are widely used
to guide and test the theoretical predictions; however, simulating
MHD turbulence and accurately measuring its scaling properties is far
from straightforward. Computational power limits the calculations to
moderate Reynolds numbers and often simplifying assumptions are made in
order that a wider range of scales can be accessed. After describing
the theoretical predictions and the numerical approaches that are
often employed in studying strong incompressible MHD turbulence, we
present the findings of a series of high-resolution direct numerical
simulations. We discuss the effects that insufficiencies in the
computational approach can have on the solution and its physical
interpretation.
Title: Symmetries, Scaling Laws, and Convergence in Shearing-box
Simulations of Magneto-rotational Instability Driven Turbulence
Authors: Bodo, G.; Cattaneo, F.; Ferrari, A.; Mignone, A.; Rossi, P.
Bibcode: 2011ApJ...739...82B
Altcode: 2011arXiv1106.5727B
We consider the problem of convergence in homogeneous shearing-box
simulations of magneto-rotationally driven turbulence. When there is
no mean magnetic flux, if the equations are non-dimensionalized with
respect to the diffusive scale, the only free parameter in the problem
is the size of the computational domain. The problem of convergence then
relates to the asymptotic form of the solutions as the computational
box size becomes large. By using a numerical code with a high order of
accuracy we show that the solutions become asymptotically independent
of domain size. We also show that cases with weak magnetic flux join
smoothly to the zero-flux cases as the flux vanishes. These results
are consistent with the operation of a subcritical small-scale dynamo
driving the turbulence. We conclude that for this type of turbulence
the angular momentum transport is proportional to the diffusive flux
and therefore has limited relevance in astrophysical situations.
Title: Extended Scaling Laws in Numerical Simulations of
Magnetohydrodynamic Turbulence
Authors: Mason, Joanne; Perez, Jean Carlos; Cattaneo, Fausto;
Boldyrev, Stanislav
Bibcode: 2011ApJ...735L..26M
Altcode: 2011arXiv1104.1437M
Magnetized turbulence is ubiquitous in astrophysical systems, where it
notoriously spans a broad range of spatial scales. Phenomenological
theories of MHD turbulence describe the self-similar dynamics of
turbulent fluctuations in the inertial range of scales. Numerical
simulations serve to guide and test these theories. However,
the computational power that is currently available restricts the
simulations to Reynolds numbers that are significantly smaller than
those in astrophysical settings. In order to increase computational
efficiency and, therefore, probe a larger range of scales, one often
takes into account the fundamental anisotropy of field-guided MHD
turbulence, with gradients being much slower in the field-parallel
direction. The simulations are then optimized by employing the
reduced MHD equations and relaxing the field-parallel numerical
resolution. In this work we explore a different possibility. We propose
that there exist certain quantities that are remarkably stable with
respect to the Reynolds number. As an illustration, we study the
alignment angle between the magnetic and velocity fluctuations in
MHD turbulence, measured as the ratio of two specially constructed
structure functions. We find that the scaling of this ratio can be
extended surprisingly well into the regime of relatively low Reynolds
number. However, the extended scaling easily becomes spoiled when the
dissipation range in the simulations is underresolved. Thus, taking the
numerical optimization methods too far can lead to spurious numerical
effects and erroneous representation of the physics of MHD turbulence,
which in turn can affect our ability to identify correctly the physical
mechanisms that are operating in astrophysical systems.
Title: The α-effect in rotating convection: a comparison of numerical
simulations
Authors: Hughes, D. W.; Proctor, M. R. E.; Cattaneo, F.
Bibcode: 2011MNRAS.414L..45H
Altcode: 2011arXiv1103.0754H
Numerical simulations are an important tool in furthering our
understanding of turbulent dynamo action, a process that occurs
in a vast range of astrophysical bodies. It is important in all
computational work that comparisons are made between different codes
and, if non-trivial differences arise, that these are explained. In a
recent paper, Käpylä, Korpi & Brandenburg describe an attempt
to reproduce some of our results and, by employing a different
methodology, they arrive at very different conclusions concerning the
mean electromotive force and the generation of large-scale fields. Here
we describe why the simulations of Käpylä et al. are simply not
suitable for a meaningful comparison, since they solve different
equations, at different parameter values and with different boundary
conditions. Furthermore, we describe why the 'resetting' method adopted
by Käpylä et al. to calculate the α-effect is inappropriate, since
the resulting value of α cannot be related to the evolution of any
large-scale magnetic field.
Title: Magnetic Dynamo Action in Random Flows with Zero and Finite
Correlation Times
Authors: Mason, Joanne; Malyshkin, Leonid; Boldyrev, Stanislav;
Cattaneo, Fausto
Bibcode: 2011ApJ...730...86M
Altcode: 2011arXiv1101.5181M
Hydromagnetic dynamo theory provides the prevailing theoretical
description for the origin of magnetic fields in the universe. Here,
we consider the problem of kinematic, small-scale dynamo action driven
by a random, incompressible, non-helical, homogeneous, and isotropic
flow. In the Kazantsev dynamo model, the statistics of the driving flow
are assumed to be instantaneously correlated in time. Here, we compare
the results of the model with the dynamo properties of a simulated
flow that has similar spatial characteristics as the Kazantsev flow but
different temporal statistics. In particular, the simulated flow is a
solution of the forced Navier-Stokes equations and hence has a finite
correlation time. We find that the Kazantsev model typically predicts
a larger magnetic growth rate and a magnetic spectrum that peaks at
smaller scales. However, we show that by filtering the diffusivity
spectrum at small scales it is possible to bring the growth rates into
agreement and simultaneously align the magnetic spectra.
Title: MHD Dynamos and Turbulence
Authors: Tobias, Steven M.; Cattaneo, Fausto; Boldyrev, Stanislav
Bibcode: 2011arXiv1103.3138T
Altcode:
A review of MHD dynamos and turbulence.
Title: On the Generation of Organized Magnetic Fields
Authors: Tobias, S. M.; Cattaneo, F.; Brummell, N. H.
Bibcode: 2011ApJ...728..153T
Altcode:
Motivated by the problem of the origin of astrophysical magnetic fields,
we introduce two concepts. The first is that of a "system-scale dynamo",
i.e., a dynamo that can organize magnetic fields on the scale of the
astrophysical object. The second is that of an "essentially nonlinear
dynamo". This is a dynamo which relies on a velocity driven by magnetic
forces and/or magnetic instabilities. We construct a simple framework
that can be used to study such dynamos and give examples in which
the evolution is such to generate a system-scale field. We argue that
this framework provides a valuable complementary approach to the more
conventional studies based on kinematic mean-field dynamo theory.
Title: An Experimental Plasma Dynamo Program for Investigations of
Fundamental Processes in Heliophysics
Authors: Brown, Benjamin; Forest, Cary; Nornberg, Mark; Zweibel,
Ellen; Cattaneo, Fausto; Cowley, Steven
Bibcode: 2011arXiv1101.0176B
Altcode:
Plasma experiments in laboratory settings offer unique opportunities
to address fundamental aspects of the solar dynamo and magnetism
in the solar atmosphere. We argue here that ground-based laboratory
experiments have direct connections to NASA based missions and NSF
programs, and that a small investment in laboratory heliophysics may
have a high payoff. We advocate for broad involvement in community-scale
plasma experiments.
Title: Dynamo efficiency in compressible convective dynamos with
and without penetration
Authors: Brummell, Nicholas; Tobias, Steven; Cattaneo, Fausto
Bibcode: 2010GApFD.104..565B
Altcode:
We investigate dynamo action in compressible convection via numerical
simulations in a Cartesian domain. We directly compare the dynamo
properties of a fully convective domain with the same domain extended
to include an underlying stable region. These simulations extend models
of fully convective domains with open lower boundary conditions to
a more self-consistent model. We examine whether the extremely slow
recirculation of the lower region affects the dynamo properties in
the convection zone. We find that the dynamo properties of the upper
convective region are essentially unchanged by the addition of the
lower stable region. After a transient period, dynamo action in the
convective region not only proceeds as normal, but also extends into
the region of overshooting flow in the stable region. Downward magnetic
pumping, long recirculation times and the low percentage of rising
elements that transit the vertical extent of the domain all fail to
eliminate the dynamo. Sufficient magnetic field is recirculated or
remains in the convective region to fuel the local dynamo there. The
independence of the convective layer from the conditions of the lower
layer makes the dynamo truly local.
Title: Dynamic Alignment and Exact Scaling Laws in Magnetohydrodynamic
Turbulence
Authors: Boldyrev, Stanislav; Mason, Joanne; Cattaneo, Fausto
Bibcode: 2009ApJ...699L..39B
Altcode:
Magnetohydrodynamic (MHD) turbulence is pervasive in astrophysical
systems. Recent high-resolution numerical simulations suggest that
the energy spectrum of strong incompressible MHD turbulence is E(k
bottom) vprop k -3/2 bottom. So
far, there has been no phenomenological theory that simultaneously
explains this spectrum and satisfies the exact analytic relations
for MHD turbulence due to Politano & Pouquet. Indeed, the
Politano-Pouquet relations are often invoked to suggest that
the spectrum of MHD turbulence instead has the Kolmogorov scaling
-5/3. Using geometrical arguments and numerical tests, here we analyze
this seeming contradiction and demonstrate that the -3/2 scaling and
the Politano-Pouquet relations are reconciled by the phenomenon of
scale-dependent dynamic alignment that was recently discovered in
MHD turbulence.
Title: Problems with kinematic mean field electrodynamics at high
magnetic Reynolds numbers
Authors: Cattaneo, F.; Hughes, D. W.
Bibcode: 2009MNRAS.395L..48C
Altcode: 2009MNRAS.tmpL.213C; 2008arXiv0805.2138C
We discuss the applicability of the kinematic α-effect formalism at
high magnetic Reynolds numbers. In this regime, the underlying flow is
likely to be a small-scale dynamo, leading to the exponential growth
of fluctuations. Difficulties arise with both the actual calculation of
the α coefficients and their interpretation. We argue that although the
former may be circumvented - and we outline several procedures by which
the α coefficients can be computed in principle - the interpretation
of these quantities in terms of the evolution of the large-scale field
may be fundamentally flawed.
Title: Aspect Ratio Dependence in Magnetorotational Instability
Shearing Box Simulations
Authors: Mignone, Andrea; Ferrari, Attilio; Bodo, Gianluigi; Rossi,
Paola; Cattaneo, Fausto
Bibcode: 2009ASSP...13...77M
Altcode: 2009pjc..book...77M
Three-dimensional numerical simulations of the magnetorotational
instability in the shearing box approximation with a nonzero net flux
are presented. By changing the size of the computational domain in
the radial direction relative to the vertical box height, we find, in
agreement with previous studies, that transport of angular momentum
(associated with the so-called "channel solution") is strongly
intermittent and maximized for boxes of unit aspect ratio. On the
other hand, in boxes with larger aspect ratio the intermittent behavior
disappears and angular momentum transport is inhibited.
Title: The influence of horizontal boundaries on Ekman circulation
and angular momentum transport in a cylindrical annulus
Authors: Obabko, Aleksandr V.; Cattaneo, Fausto; F Fischer, Paul
Bibcode: 2008PhST..132a4029O
Altcode: 2008arXiv0806.4630O
We present numerical simulations of circular Couette flow in
axisymmetric and fully three-dimensional geometry of a cylindrical
annulus inspired by Princeton magnetorotational instability (MRI) liquid
gallium experiment. The incompressible Navier-Stokes equations are
solved with the spectral element code Nek5000 incorporating realistic
horizontal boundary conditions of differentially rotating rings. We
investigate the effect of changing rotation rates (Reynolds number)
and of the horizontal boundary conditions on flow structure, Ekman
circulation and associated transport of angular momentum through the
onset of unsteadiness and three-dimensionality. A mechanism for the
explanation of the dependence of the Ekman flows and circulation on
horizontal boundary conditions is proposed. First International
Conference 'Turbulent Mixing and Beyond' held on 18-26 August 2007
at the Abdus Salam International Centre for Theoretical Physics,
Trieste, Italy.
Title: Convective Dynamos with Penetration, Rotation, and Shear
Authors: Tobias, Steven M.; Cattaneo, Fausto; Brummell, Nicholas H.
Bibcode: 2008ApJ...685..596T
Altcode:
We investigate the dynamo properties of Boussinesq, penetrative
convection in the presence of rotation and large-scale velocity shear
flows. Several numerical experiments are conducted in a local Cartesian
computational domain in which the relative stability of the lower stable
layer, the rotation rate, the supercriticality of the convection, and
the strength of the imposed shear flow are varied. Once a statistically
steady hydrodynamic state is achieved for any set of parameters, a
weak seed magnetic field is added and the subsequent dynamo evolution
is followed. In all cases studied, the weak seed field is initially
amplified exponentially and then eventually saturates in a stationary
magnetohydrodynamic (MHD) state. Even in the presence of penetration,
rotation, and shear, the field is predominantly small-scale. We
analyze the reasons for this and make suggestions as to possible
further mechanisms that may lead to large-scale field generation.
Title: Limited Role of Spectra in Dynamo Theory: Coherent versus
Random Dynamos
Authors: Tobias, Steven M.; Cattaneo, Fausto
Bibcode: 2008PhRvL.101l5003T
Altcode:
We discuss the importance of phase information and coherence times
in determining the dynamo properties of turbulent flows. We compare
the kinematic dynamo properties of three flows with the same energy
spectrum. The first flow is dominated by coherent structures with
nontrivial phase information and long eddy coherence times, the second
has random phases and long-coherence time, the third has nontrivial
phase information, but short coherence time. We demonstrate that
the first flow is the most efficient kinematic dynamo, owing to the
presence of sustained stretching and constructive folding. We argue
that these results place limitations on the possible inferences of
the dynamo properties of flows from the use of spectra alone, and that
the role of coherent structures must always be accounted for.
Title: Aspect ratio dependence in magnetorotational instability
shearing box simulations
Authors: Bodo, G.; Mignone, A.; Cattaneo, F.; Rossi, P.; Ferrari, A.
Bibcode: 2008A&A...487....1B
Altcode: 2008arXiv0805.1172B
Aims: We study the changes in the properties of turbulence driven
by the magnetorotational instability in a shearing box, as the
computational domain size in the radial direction is varied relative
to the height.
Methods: We perform 3D simulations in the
shearing box approximation, with a net magnetic flux, and we consider
computational domains with different aspect ratios.
Results:
We find that in boxes of aspect ratio unity the transport of angular
momentum is strongly intermittent and dominated by channel solutions in
agreement with previous work. In contrast, in boxes with larger aspect
ratios, the channel solutions and the associated intermittent behavior
disappear.
Conclusions: There is strong evidence that, as the
aspect ratio becomes larger, the characteristics of the solution become
aspect ratio independent. We conclude that shearing box calculations
with an aspect ratio of unity or near unity may introduce spurious
effects.
Title: Numerical measurements of the spectrum in magnetohydrodynamic
turbulence
Authors: Mason, Joanne; Cattaneo, Fausto; Boldyrev, Stanislav
Bibcode: 2008PhRvE..77c6403M
Altcode: 2007arXiv0706.2003M
We report the results of an extensive set of direct numerical
simulations of forced, incompressible, magnetohydrodynamic
(MHD) turbulence with a strong guide field. The aim is to
resolve the controversy regarding the power-law exponent
( α , say) of the field-perpendicular energy spectrum
E(k⊥)∝k⊥α . The two main
theoretical predictions α=-3/2 and α=-5/3 have both received
some support from differently designed numerical simulations. Our
calculations have a resolution of 5123 mesh points, a strong
guide field, and an anisotropic simulation domain and implement a broad
range of large-scale forcing routines, including those previously
reported in the literature. Our findings indicate that the spectrum
of well-developed, strong incompressible MHD turbulence with a strong
guide field is E(k⊥)∝k⊥-3/2 .
Title: Numerical Simulations of Strong MHD Turbulence
Authors: Mason, J.; Cattaneo, F.; Boldyrev, S.
Bibcode: 2007APS..DPPGP8028M
Altcode:
Magnetohydrodynamic turbulence plays an important role in many
astrophysical phenomena, including the solar wind, angular momentum
transport in accretion disks and interstellar scintillation. Despite
more than 40 years of investigations much within the subject remains
controversial. Recently a new theory has been developed [1, 2]. It
predicts a scale-dependent dynamic alignment between the velocity and
magnetic fluctuations and leads to the field-perpendicular energy
spectrum E(k)k-3/2. Here we discuss this new theory and
present the results of a series of numerical tests. Quantities measured
include the alignment angle, the spectrum and the third order structure
functions for which the exact relations due to Politano & Pouquet
[3] hold.
[1] Boldyrev, S. (2005) Astrophys. J. 626, L37.
[2] Boldyrev, S. (2006) Phys. Rev. Lett. 96, 115002.
[3]
Politano, H. & Pouquet, A. (1998) Geophys. Res. Lett. 25, 273.
Title: New directions in the theory of hydromagnetic dynamos
Authors: Cattaneo, Fausto
Bibcode: 2007APS..DPPUT2001C
Altcode:
In dynamo theory a distinction is made between small- and large-scale
dynamo action. The former refers to the generation of magnetic fields
on scales smaller than or comparable with the characteristic scale of
the velocity. It is now widely believed that in a turbulent fluid,
small-scale dynamo action is always possible provided the magnetic
Reynolds number is sufficiently high. Large-scale dynamo action, on
the other hand, refers to the generation of large-scale fields, i.e
the generation of magnetic flux which is of considerable importance in
many astrophysical situations. The traditional view is that large-scale
generation occurs via an inverse cascade of magnetic helicity driven
by turbulence lacking reflectional symmetry. This view, however, is
becoming increasingly at odds with numerical simulations that show that
the cascade is either absent or ineffective. The question then arises
of what are the alternative mechanisms that can leads to the generation
of large-scale fields. I will discuss two possible resolutions: one
based on the role of boundary conditions in releasing the constraints
of helicity conservation, the other based on the existence of special
classes of velocity fields that are generated by magnetic instabilities
and that are particularly suited to dynamo action. In both cases I
will discuss important analogies between the astrophysical and the
laboratory situations.
Title: Spectra and structure of MHD turbulence
Authors: Boldyrev, S.; Perez, J. C.; Mason, J.; Cattaneo, F.
Bibcode: 2007APS..DPPPO7001B
Altcode:
We present recent results on magnetohydrodynamic (MHD) turbulent
cascades. We concentrate on the physical processes that determine
the structure of MHD turbulence in the regimes of weak and strong
turbulence, and discuss the corresponding turbulent spectra. The results
are compared with numerical simulations and geophysical (solar wind)
and astrophysical (interstellar scintillation) observations.
Title: The Spectrum and Small-Scale Structures of Magnetohydrodynamic
Turbulence
Authors: Mason, J.; Boldyrev, S.; Cattaneo, F.
Bibcode: 2007ASPC..365..315M
Altcode:
A theory of incompressible MHD turbulence in the presence of a strong
guiding magnetic field is described. Numerical results that show
good agreement with the theory are also presented. The theory was
developed in tet{boldyrev,boldyrev2} and predicts that in the plane
perpendicular to the guiding field, the velocity and magnetic field
fluctuations align within a scale dependent angle θλ∝
λ1/4. The phenomena is known as dynamic alignment and leads
to the field-perpendicular energy spectrum E(k⊥)∝
k⊥-3/2. The results are of interest in
understanding turbulence in the interstellar medium and may provide
a natural explanation for the recent observations of interstellar
scintillations of PSR 0329+54 and PSR J0437-4715 tep{shishov,smirnova}.
Title: Challenges to the theory of solar convection
Authors: Cattaneo, F.
Bibcode: 2007IAUS..239...35C
Altcode:
No abstract at ADS
Title: Dynamic Alignment in Driven Magnetohydrodynamic Turbulence
Authors: Mason, Joanne; Cattaneo, Fausto; Boldyrev, Stanislav
Bibcode: 2006PhRvL..97y5002M
Altcode: 2006astro.ph..2382M
Motivated by recent analytic predictions, we report numerical
evidence showing that in driven incompressible magnetohydrodynamic
turbulence the magnetic- and velocity-field fluctuations locally
tend to align the directions of their polarizations. This dynamic
alignment is stronger at smaller scales with the angular mismatch
between the polarizations decreasing with the scale λ approximately
as θλ∝λ1/4. This can naturally lead to a
weakening of the nonlinear interactions and provide an explanation
for the energy spectrum E(k)∝k-3/2 that is observed in
numerical experiments of strongly magnetized turbulence.
Title: What is a flux tube? On the magnetic field topology of buoyant
flux structures
Authors: Cattaneo, Fausto; Brummell, Nicholas H.; Cline, Kelly S.
Bibcode: 2006MNRAS.365..727C
Altcode: 2005MNRAS.tmp.1117C
We study the topology of field lines threading buoyant magnetic flux
structures. The magnetic structures, visually resembling idealized
magnetic flux tubes, are generated self-consistently by numerical
simulation of the interaction of magnetic buoyancy and a localized
velocity shear in a stably stratified atmosphere. Depending on the
parameters, the system exhibits varying degrees of symmetry. By
integrating along magnetic field lines and constructing return maps,
we show that, depending on the type of underlying behaviour, the
stages of the evolution, and therefore the degree of symmetry, the
resulting magnetic structures can have field lines with one of three
distinct topologies. When the x-translational and y-reflectional
symmetries remain intact, magnetic field lines lie on surfaces but
individual lines do not cover the surface. When the y symmetry is
broken, magnetic field lines lie on surfaces and individual lines do
cover the surface. When both x and y symmetries are broken, magnetic
field lines wander chaotically over a large volume of the magnetically
active region. We discuss how these results impact our simple ideas
of a magnetic flux tube as an object with an inside and an outside,
and introduce the concept of `leaky' tubes.
Title: Magnetic-Field Generation in Helical Turbulence
Authors: Boldyrev, Stanislav; Cattaneo, Fausto; Rosner, Robert
Bibcode: 2005PhRvL..95y5001B
Altcode: 2005astro.ph..4588B
We investigate analytically the amplification of a weak magnetic
field in a homogeneous and isotropic turbulent flow lacking
reflectional symmetry (helical turbulence). We propose that the
spectral distributions of magnetic energy and magnetic helicity can
be found as eigenmodes of a self-adjoint, Schrödinger-type system of
evolution equations. We argue that large-scale and small-scale magnetic
fluctuations cannot be effectively separated, and that the conventional
α model is, in general, not an adequate description of the large-scale
dynamo mechanism. As a consequence, the correct numerical modeling of
such processes should resolve magnetic fluctuations down to the very
small, resistive scales.
Title: Simulations of magneto-convection in the solar photosphere.
Equations, methods, and results of the MURaM code
Authors: Vögler, A.; Shelyag, S.; Schüssler, M.; Cattaneo, F.;
Emonet, T.; Linde, T.
Bibcode: 2005A&A...429..335V
Altcode:
We have developed a 3D magnetohydrodynamics simulation code for
applications in the solar convection zone and photosphere. The code
includes a non-local and non-grey radiative transfer module and takes
into account the effects of partial ionization. Its parallel design
is based on domain decomposition, which makes it suited for use on
parallel computers with distributed memory architecture. We give a
description of the equations and numerical methods and present the
results of the simulation of a solar plage region. Starting with
a uniform vertical field of 200 G, the processes of flux expulsion
and convective field amplification lead to a dichotomy of strong,
mainly vertical fields embedded in the granular downflow network and
weak, randomly oriented fields filling the hot granular upflows. The
strong fields form a magnetic network with thin, sheet-like structures
extending along downflow lanes and micropores with diameters of up to
1000 km which form occasionally at vertices where several downflow
lanes merge. At the visible surface around optical depth unity,
the strong field concentrations are in pressure balance with their
weakly magnetized surroundings and reach field strengths of up to 2
kG, strongly exceeding the values corresponding to equipartition with
the kinetic energy density of the convective motions. As a result of
the channelling of radiation, small flux concentrations stand out as
bright features, while the larger micropores appear dark in brightness
maps owing to the suppression of the convective energy transport. The
overall shape of the magnetic network changes slowly on a timescale
much larger than the convective turnover time, while the magnetic flux
is constantly redistributed within the network leading to continuous
formation and dissolution of flux concentrations. Appendices A-D
are only available in electronic form at http://www.edpsciences.org
Title: Magnetic field generation in Kolmogorov turbulence
Authors: Boldyrev, Stanislav; Cattaneo, Fausto
Bibcode: 2004AIPC..733..137B
Altcode:
We analyze the initial, kinematic stage of magnetic field evolution
in an isotropic and homogeneous turbulent conducting fluid with a
``rough'' velocity field, v(l) ~ lα, α < 1. This
regime is relevant to the problem of magnetic field generation in
turbulent fluids with small magnetic Prandtl number, i.e. with ohmic
resistivity much larger than viscosity. Our interest in motivated by
the following question: suppose that smooth fluctuations of velocity
field are able to amplify a weak magnetic field, would the magnetic
field be still amplified if the fluid motion becomes strongly turbulent,
i.e. non-smooth? Quite paradoxically, turbulence can be dangerous for
magnetic field generation. We propose that the smaller the magnetic
Prandtl number, the larger the magnetic Reynolds number that is
needed to excite magnetic fluctuations. This implies that numerical
or experimental investigations of magnetohydrodynamical turbulence
with small Prandtl numbers need to achieve extremely high resolution
in order to describe magnetic phenomena adequately.
Title: Magnetic-Field Generation in Kolmogorov Turbulence
Authors: Boldyrev, Stanislav; Cattaneo, Fausto
Bibcode: 2004PhRvL..92n4501B
Altcode: 2003astro.ph.10780B
We analyze the initial, kinematic stage of magnetic field evolution
in an isotropic and homogeneous turbulent conducting fluid with a
rough velocity field, v(l)∼lα, α<1. This regime is
relevant to the problem of magnetic field generation in fluids with
small magnetic Prandtl number, i.e., with Ohmic resistivity much larger
than viscosity. We propose that the smaller the roughness exponent
α, the larger the magnetic Reynolds number that is needed to excite
magnetic fluctuations. This implies that numerical or experimental
investigations of magnetohydrodynamic turbulence with small Prandtl
numbers need to achieve extremely high resolution in order to describe
magnetic phenomena adequately.
Title: The Generation of Surface Magnetic Fields
Authors: Cattaneo, F.; Emonet, T.
Bibcode: 2004cosp...35.4443C
Altcode: 2004cosp.meet.4443C
The most readily observable manifestation of convection at the solar
surface is the granulation. Granules with a characteristic size of
1,000 km and a lifetime of 5 min are too small and too short-lived
to be significantly affected by the solar rotation. Thus, the upper
layers of the convective zone are in a state of strongly turbulent,
non-helical convection. Because of the high electrical conductivity
of the solar plasma, the magnetic Reynmolds number of the granulation
is large (> 10^5). These considerations, suggest that the granular
flows can act as local small-scale dynamos, generating disordered
small-scale magnetic fields with lifetimes comparable to that of the
granulation. Numerical simulations support this conclusion showing
that intense highly intermittent fields can readily be generated
provided the magnetic Reynolds number is large enough. One interesting
aspect of the solar small-scale dynamo problem is related to the
extremely small value of the plasma viscosity; much smaller than the
magnetic diffusivity. In this regime (small magnetic Prandtl number)
the velocity has strong fluctuations at the magnetic diffusion scale
with profound consequences for the operation of the dynamo. In this
talk I will address how our ideas of dynamo action, mostly based on
smooth velocity fields, must be modified to account for this fact
Title: Dynamo Action Driven by Shear and Magnetic Buoyancy
Authors: Cline, Kelly S.; Brummell, Nicholas H.; Cattaneo, Fausto
Bibcode: 2003ApJ...599.1449C
Altcode:
We present direct numerical simulations based on the full MHD
equations of dynamo action in a nonrotating, convectively stable layer
containing a forced, localized velocity shear. The dynamo operates
by the interaction of two MHD processes: the production of toroidal
magnetic field from poloidal field by the shear, and the regeneration
of poloidal loops from toroidal field due to the combined action
of magnetic buoyancy and Kelvin-Helmholtz instabilities. The nature
of the dynamo process is such that it can occur only if the initial
magnetic fields exceed a critical value that typically depends on the
magnetic Reynolds number. As such, this dynamo does not operate in the
kinematic limit. Several different behaviors are observed, including
steady dynamo production and cyclic as well as chaotic activity. In
the cyclic regimes, the dynamo process exhibits polarity reversals
and periods of reduced activity.
Title: Dynamos in small magnetic Prandtl number fluids
Authors: Cattaneo, Fausto
Bibcode: 2003APS..DPPKM1003C
Altcode:
In liquid metals and dense stellar plasmas, the magnetic Prandtl
number Pm--the ratio between viscosity and magnetic diffusivity--is
a very small number (10-5-10-9). Consequently
the scales of dissipation of velocity and magnetic field are widely
separated, and dynamo processes must operate in the inertial range
of the turbulence. Two questions naturally arise. First, can the
dynamo operate in such a strongly turbulent environment? Second, if
it operates, what is the typical strength of the resulting magnetic
field? I will argue that dynamo action is possible even at moderate
magnetic Reynolds numbers, provided that either the turbulence
spectrum is not too flat, or that favorable coherent structures are
present. Concerning the strength of the generated dynamo field, I will
present numerical results suggesting that a magnetic Prandtl number
independent regime is reached even for values of Pm only slightly
smaller than unity. If this result were valid in general it would
imply that numerical models with Pm near unity could be adequate to
describe many aspects of the dynamics of fluids with Pm very small.
Title: Future Perspectives of Laboratory Plasma Astrophysics II:
Liquid Metal and Basic Plasma Experiments
Authors: Ji, H.; Cattaneo, F.; Colgate, S.; Cowley, S.; Forest, C.;
Lathrop, D.; Gekelman, W.
Bibcode: 2003APS..DPPKM1007J
Altcode:
This is for a panel discussion slot for mini- conference on laboratory
plasma astrophysics II: Liquid Metal and Basic Plasma Experiments
Title: On the Formation of Magnetic Structures by the Combined Action
of Velocity Shear and Magnetic Buoyancy
Authors: Cline, Kelly S.; Brummell, Nicholas H.; Cattaneo, Fausto
Bibcode: 2003ApJ...588..630C
Altcode:
Using numerical simulations of a compressible, stably stratified,
magnetohydrodynamical (MHD) flow, we investigate a mechanism for
producing a series of rising tubelike magnetic structures. In this
process, a steadily forced shear flow stretches a weak poloidal
background magnetic field to create a strong toroidal field that is
magnetically buoyant. The subsequent evolution of this system depends on
the parameters: At moderate magnetic Reynolds numbers (Rm),
the system reaches a stable nonstatic equilibrium. At larger values
of Rm, this equilibrium becomes unstable to a shear-buoyant
instability, involving a modification of the background velocity shear
by the magnetically induced buoyant poloidal flow. The system then
produces a series of buoyant magnetic structures at regular intervals
that are expelled from the region of strong velocity shear. Even
higher Rm causes the magnetic intensity of the structures
to strengthen and the intervals between expulsion events to become
irregular. For large enough kinetic Reynolds numbers (Re),
the magnetic modification of the background shear can trigger a
secondary three-dimensional Kelvin-Helmholtz instability that can
twist the magnetic structures into a helical shape.
Title: On the Interaction between Convection and Magnetic Fields
Authors: Cattaneo, Fausto; Emonet, Thierry; Weiss, Nigel
Bibcode: 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: Magnetic Dynamos: Numerical Simulations and Experimental Statu
Authors: Cattaneo, Fausto
Bibcode: 2003APS..APR.U4004C
Altcode:
Dynamo action--the process of magnetic field generation by the motions
of an electrically conducting fluids--is often invoked to explain the
origin of magnetic fields in stars and planets. In many situations
of astrophysical interest, the plasma motions that drive the dynamos
are characterised by a large magnetic Reynolds number--the ratio of
diffusive to convective timescales-- and a small magnetic Prandtl
number--the ratio of viscosity to magnetic diffusivity, implying that
that the dynamos operate in highly turbulent environments, where
the velocity fluctuates on scales much smalled than the lentgth at
which the magnetic diffusion becomes important. These constraint pose
significant challenges to the numerical and experimental attempts to
model astrophysical dynamos. In this talk I will review the present
state of numerical and laboratory dynamo experiments as well as the
efforts to extend it towards more realistic astrophysical regimes.
Title: Polarization of Photospheric Lines from Turbulent Dynamo
Simulations
Authors: Sánchez Almeida, J.; Emonet, T.; Cattaneo, F.
Bibcode: 2003ApJ...585..536S
Altcode: 2002astro.ph.11175S; 2002astro.ph.11175A
We employ the magnetic and velocity fields from turbulent dynamo
simulations to synthesize the polarization of a typical photospheric
line. The synthetic Stokes profiles have properties in common with
those observed in the quiet Sun. The simulated magnetograms present a
level of signal similar to that of the Inter-Network regions. Asymmetric
Stokes V profiles with two, three, and more lobes appear in a natural
way. The intensity profiles are broadened by the magnetic fields
in fair agreement with observational limits. Furthermore, the Hanle
depolarization signals of the Sr I λ4607 Å line turn out to be within
the solar values. Differences between synthetic and observed polarized
spectra can also be found. There is a shortage of Stokes V asymmetries,
which we attribute to a deficit of structuring in the magnetic and
velocity fields from the simulations as compared to the Sun. This
deficit may reflect the fact that the Reynolds numbers of the numerical
data are still far from solar values. We consider the possibility that
intense and tangled magnetic fields, like those in the simulations,
exist in the Sun. This scenario has several important consequences. For
example, less than 10% of the existing unsigned magnetic flux would
be detected in present magnetograms. The existing flux would exceed
by far that carried by active regions during the maximum of the solar
cycle. Detecting these magnetic fields would involve improving the
angular resolution, the techniques to interpret the polarization
signals, and to a lesser extent, the polarimetric sensitivity.
Title: The Polarized Spectrum Emerging from Fast Dynamo Simulations
Authors: Sánchez Almeida, J.; Emonet, T.; Cattaneo, F.
Bibcode: 2003ASPC..307..293S
Altcode:
No abstract at ADS
Title: Simulation of Solar Magnetoconvection
Authors: Vögler, A.; Shelyag, S.; Schüssler, M.; Cattaneo, F.;
Emonet, T.; Linde, T.
Bibcode: 2003IAUS..210..157V
Altcode:
No abstract at ADS
Title: Formation of buoyant magnetic structures by a localized
velocity shear
Authors: Brummell, N.; Cline, K.; Cattaneo, F.
Bibcode: 2002MNRAS.329L..73B
Altcode:
Motivated by considerations of the solar tachocline, we study the
generation of strong buoyant magnetic structures by a sheared velocity
field localized in a convectively stable background, using non-linear
three-dimensional (3D) magnetohydrodynamic (MHD) simulations. The shear
flow can spontaneously create strong tube-like toroidal (streamwise)
magnetic structures from an imposed weak uniform poloidal (cross-stream)
magnetic field. The structures are magnetically buoyant and therefore
rise, and may evolve further to a rich variety of geometries, including
kinked or arched shapes. The emergence process can repeat indefinitely
with a characteristic period. These mechanisms may be relevant to the
MHD processes in the solar tachocline and the creation and emergence
of solar active regions.
Title: On the nonlinear nature of the turbulent α-effect
Authors: Cattaneo, Fausto; Hughes, David W.; Thelen, Jean-Claude
Bibcode: 2002HiA....12..733C
Altcode:
Galactic magnetic fields are, typically, modelled by mean-field dynamos
involving the α-effect. Here we consider, very briefly, some of the
issues involving the nonlinear dependence of α on the mean field.
Title: On the Origin of the Solar Mesogranulation
Authors: Cattaneo, Fausto; Lenz, Dawn; Weiss, Nigel
Bibcode: 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: Small-Scale Photospheric Fields: Observational Evidence and
Numerical Simulations
Authors: Emonet, Thierry; Cattaneo, Fausto
Bibcode: 2001ApJ...560L.197E
Altcode:
Observations suggest that magnetic fields at the solar photosphere
may be structured below the limit of the present resolution. We
argue that numerical simulations could be used in a complementary
way to observations in order to study the small-scale structure of
photospheric fields. We present a number of illustrative examples.
Title: Solar dynamo theory : Solar dynamo theory: a new look at the
origin of small-scale magnetic fields
Authors: Cattaneo, Fausto; Hughes, David W.
Bibcode: 2001A&G....42c..18C
Altcode:
Fausto Cattaneo and David W Hughes delve beneath the surface of the
Sun with numerical models of turbulent convection. Although
magnetic dynamo action is traditionally associated with rotation,
fast dynamo theory shows that chaotic flows, even without rotation,
can act as efficient small-scale dynamos. Indeed, numerical simulations
suggest that granular and supergranular convection may generate locally
a substantial part of the field in the quiet photosphere.
Title: Numerical simulations of self-excited dynamos
Authors: Cattaneo, F.; Brummell, N.; Cline, K.
Bibcode: 2001sps..proc..122C
Altcode:
We present results of numerical simulations of self-consistent dynamo
action in electrically conducting fluids. Two cases are discussed in
details. In the first, dynamo action is driven by turbulent convection;
in the second, it is driven by a combination of velocity shear and
magnetic buoyancy instabilities. In both cases the magnetic field is
generated by fluid motions with no net helicity and in the absence of
rotational effects.
Title: Effects of Limited Resolution on the Inferred Structure of
Photospheric Magnetic Fields
Authors: Emonet, T.; Cattaneo, F.
Bibcode: 2001ASPC..236..355E
Altcode: 2001aspt.conf..355E
No abstract at ADS
Title: Magnetohydrodynamics: Magnetoconvection
Authors: Cattaneo, F.
Bibcode: 2000eaa..bookE2223C
Altcode:
Convective motions occur naturally in layers of fluid heated from
below. In the Sun turbulent convection carries most of the luminosity
over the outer 30% by radius of the star. Because of the high electrical
conductivity of the solar plasma convective motions interact with
magnetic fields. The modified form of convection that occurs in a
conducting fluid when externally imposed magnetic fields...
Title: Dynamo action driven by convection: the influence of magnetic
boundary conditions
Authors: Thelen, J. -C.; Cattaneo, F.
Bibcode: 2000MNRAS.315L..13T
Altcode:
We study the influence of different magnetic boundary conditions
on the generation of magnetic fields by turbulent convection. It is
found that the structure and strength of the generated field in the
vicinity of the boundary is strongly dependent on the choice of boundary
conditions. In the convective interior, however, the solutions remain
largely insensitive to the boundary conditions. In all cases the overall
efficiency of the dynamo process remains high with a steady state
magnetic energy density between 12 and 25per cent of the turbulent
kinetic energy, and peak field values exceeding the equipartition
level. These results support the idea that the solar granulation may
constitute a dynamo source for magnetic fields in the quiet photosphere.
Title: The Solar Dynamos
Authors: Cattaneo, F.
Bibcode: 2000SPD....31.0402C
Altcode: 2000BAAS...32Q.835C
Magnetic activity on the Sun presents us with an interesting
dichotomy. On large spatial and temporal scales the solar magnetic field
displays a remarkable degree of organization. The 11 years cadence of
the solar cycle, Hales' polarity law, and the systematic drift of the
regions of emergence of active regions towards the equator throughout
the solar cycle are all indicative of a powerful organizing process. On
small spatial and temporal scales, the Solar magnetic field appears
random and chaotic. It is interesting that recent advances in dynamo
theory provide us with a unified approach to solar magnetic activity
whereby both large and small scales emerge naturally as dynamo processes
associated with rotationally constrained and unconstrained scales of
motions in the convection zone (or directly below it). According to
this view all coherent scales of motions produce magnetic structures of
comparable coherence length. Those that are further endowed with lack of
reflectional symmetry by virtue of being rotationally constrained are
further associated with inverse cascades that can generate magnetic
structures on larger scales still. The picture that emerges is one
in which dynamo action proceeds on different time scales all over the
convection zone. But only in very special regions, like for instance the
solar tachocline, is the magnetic field organized on large scales. This
idea provides a natural explanation for the origin of active regions,
ephemeral regions, and intra--network fields.
Title: Surface Dynamics of the Solar Granular Flow
Authors: Lenz, D. D.; Cattaneo, F.
Bibcode: 1999AAS...194.2106L
Altcode: 1999BAAS...31..858L
Flow patterns on the solar surface can provide insight into the dynamics
of the solar convection zone and photosphere. Since basic properties of
the solar fluid can be very difficult to observe directly, simulations
of solar convection are necessary to explore the interplay between the
solar fluid and surface features. We investigate flow dynamics on the
surface of a convective fluid and discuss the relationship of the flow
patterns to observable characteristics. Passive floaters advected by
the surface velocity field rapidly collect in the downflow lanes. At
large times, the floaters collect in quasi-stagnant regions that
are long-lived with respect to the granular pattern. We identify
this larger, longer-lived pattern with mesogranular flows. The
relationship between the mesogranules and the surface distribution
of magnetic features is discussed. This work is supported by NASA
SR&T NAG5-4953 and by a TRACE subgrant from Lockheed Martin to
the University of Chicago.
Title: A Dynamo Driven by Turbulent Thermal Convection.
Authors: Thelen, J. -C.; Cattaneo, F.
Bibcode: 1999AAS...194.2105T
Altcode: 1999BAAS...31..858T
We consider the possibility that a significant part of the magnetic
field in the quiet photosphere is generated locally by dynamo action
associated with the granular flow. This argument is based on recent
advances in fast dynamo theory, which show that almost any complicated,
chaotic flow generates some magentic field. Numerical simulations
of convectively driven, non-rotating, dynamos, in domains with large
aspect ratios, have been performed in order to verify this idea. Our
results show that thermally driven turbulent convection can indeed be
an efficient dynamo even in the absence of rotation in term of both
growth rate and final amplitude of the generated field. Some aspects of
the resulting magnetic field strength and the degree of intermittency,
as well as the influence of the boundary conditions on the behaviour
of the dynamo will be discussed.
Title: On the Origin of Magnetic Fields in the Quiet Photosphere
Authors: Cattaneo, Fausto
Bibcode: 1999ApJ...515L..39C
Altcode:
We consider the possibility that a substantial fraction of the magnetic
field in the quiet photosphere is generated locally by dynamo action
associated with the granular and supergranular flows. The argument is
based on recent advances in the theory of fast dynamos and is supported
by large-scale numerical simulations that show that thermally driven
turbulent convection can indeed be an efficient source of small-scale,
highly intermittent magnetic fields. Some aspects of the resulting
magnetic field, such as its strength and degree of intermittency,
are discussed.
Title: Nonlinear Dynamo Action in a Time-Dependent ABC Flow
Authors: Brummell, N. H.; Cattaneo, F.; Tobias, S. M.
Bibcode: 1999ASPC..178...23B
Altcode: 1999sdnc.conf...23B
No abstract at ADS
Title: Dynamo Theory and the Origin of Small Scale Magnetic Fields
Authors: Cattaneo, F.
Bibcode: 1999ASSL..239..119C
Altcode: 1999msa..proc..119C
Dynamo action describes the sustained conversion of kinetic energy
into magnetic energy throughout the bulk of an electrically conducting
fluid. Dynamo processes are commonly invoked to explain the origin
of the solar cycle and of the large scale component of the solar
magnetic field. The origin of small scale magnetic fields can also be
understood in terms of dynamo processes. Recent advances in the theory
of dynamo operating in fluids with high electrical conductivity --
fast dynamos, indicate that most sufficiently complicated chaotic flows
should act as dynamos. The resulting magnetic fields have a complex
structure characterised by amplitude and polarity fluctuations on small
scales. Some of the geometrical properties of these fluctuations can
be described in terms of scaling behaviour and exponents. We review
some of these ideas and illustrate them by simple examples. Possible
extensions to the (nonlinear) dynamical regime are also discussed.
Title: The Solar Dynamo Problem
Authors: Cattaneo, F.
Bibcode: 1997ASSL..225..201C
Altcode: 1997scor.proc..201C
The solar dynamo problem is reviewed in the light of recent developments
in dynamo theory. We distinguish between the generation of magnetic
fields on scales smaller than the velocity correlation length-small
scale dynamo, and larger than the velocity correlation length-large
scale dynamo. We argue that small scale dynamo action is likely to
occur everywhere in the convection zone. The field thus generated
however is disordered both in space and time. Large scale dynamo
action on the other hand is responsible for the activity cycle and
the large scale organization of the solar field. The existence of a
large scale dynamo is related to the breaking of symmetries in the
underlying field of turbulence.
Title: Nonlinear saturation of the turbulent α effect
Authors: Cattaneo, Fausto; Hughes, David W.
Bibcode: 1996PhRvE..54.4532C
Altcode:
We study the saturation of the turbulent α effect in the nonlinear
regime. A numerical experiment is constructed based on the full
nonlinear magnetohydrodynamics equations that allows the α effect
to be measured for different values of the mean magnetic field. The
object is to distinguish between two possible theories of nonlinear
saturation. It is found that the results are in close agreement with
the theories that predict strong suppression and are incompatible with
those that predict that the turbulent α effect persists up to mean
fields of order of the equipartition energy.
Title: Suppression of chaos in a simplified nonlinear dynamo model
Authors: Cattaneo, Fausto; Hughes, David W.; Kim, Eun-Jin
Bibcode: 1996PhRvL..76.2057C
Altcode:
A simplified nonlinear dynamo model is constructed that allows the
transition from the kinematic to the dynamic regime to be studied in
detail. We apply this construction to a chaotic flow recently studied in
the context of fast dynamo action. It is found that the structure of the
magnetic field in the two regimes is markedly different. Furthermore,
the saturation of the exponential growth of the magnetic field is
achieved by a drastic suppression of the chaotic properties of the flow.
Title: Turbulent Dynamics in the Solar Convection Zone
Authors: Brummell, Nicholas; Cattaneo, Fausto; Toomre, Juri
Bibcode: 1995Sci...269.1370B
Altcode:
Observations of the sun reveal highly complex flows and magnetic
structures that must result from turbulent convection in the solar
envelope. A remarkable degree of large-scale coherence emerges
from the small-scale turbulent dynamics, as seen in the cycles of
magnetic activity and in the differential rotation profile of this
star. High-performance computing now permits numerical simulations
of compressible turbulence and magnetohydrodynamics with sufficient
resolution to show that compact structures of vorticity and magnetic
fields can coexist with larger scales. Such structured turbulence
is yielding transport properties for heat and angular momentum at
considerable variance with earlier models. These simulations are
elucidating the coupling of turbulent fluid motions with rotation
and magnetic fields, which must control the interlinked differential
rotation and magnetic dynamo action.
Title: Fluctuations in Quasi-Two-Dimensional Fast Dynamos
Authors: Cattaneo, Fausto; Kim, Eun-Jin; Proctor, Michael; Tao, Louis
Bibcode: 1995PhRvL..75.1522C
Altcode:
The ratio R1 between the average magnetic energy and the
square-averaged flux plays an important role in the study of nonlinear
dynamos, as a measure of the efficiency of a dynamo at generating
flux. For large values of Rm, R1 displays a
scaling behavior of the type R1~R nm,
where Rm is the magnetic Reynolds number. We show by direct
numerical evaluation that n depends sensitively on the flow complexity
for small-scale dynamos. Furthermore, by relating n to the cancellation
exponent and the correlation dimension of the magnetic field, we argue
that n is not likely to be close to zero in general.
Title: On the Spatial Distribution of Magnetic Fields on the Solar
Surface
Authors: Tao, L.; Du, Y.; Rosner, R.; Cattaneo, F.
Bibcode: 1995ApJ...443..434T
Altcode:
Recent measurements of solar surface magnetic fields suggest that the
spatial distribution of these fields is fractal. In order to understand
the physical basis for such geometric complexity, we study here the
advection of magnetic flux tubes relatively simple random motions on
the surface of a fluid and investigate the spatial statistics of the
resulting surface field. While this study does not directly address
the question of why solar surface fields have the observed spatial
structure, it is designed to build our intuition about how surface
flows lead to complex spatial structuring of magnetic fields. As part
of our study, we discuss the various methods by which one can describe
the spatial distribution of the surface magnetic flux and relate them
mathematically; this turns out to be a crucial point of our work since,
as we show, a number of previous analyses have misinterpreted the
analysis procedures for determining fractal dimensions. Our principal
result is the explicit demonstration that simple random flows lead
to magnetic flux spatial distributions with a multifractal dimension
spectrum. Furthermore, we demonstrate that this magnetic spatial
structure is generic, i.e., is characteristic of a very large class
of random flows.
Title: On the Origin of ``Dividing Lines'' for Late-Type Giants
and Supergiants
Authors: Rosner, R.; Musielak, Z. E.; Cattaneo, F.; Moore, R. L.;
Suess, S. T.
Bibcode: 1995ApJ...442L..25R
Altcode:
We show how a change in the nature of the stellar dyanmo can lead to
a transition in the topological character of stellar magnetic fields
of evolved stars, from being mainly closed on the blueward side of the
giant tracks in the Hertzsprung-Russell (H-R) diagram to being mainly
open on their redward side. If such a topological transition occurs,
then these stars naturally segregate into two classes: those having hot
coronae on the blueward side, and those having massive cool winds on the
redward side, thus leading naturally to the so-called dividing lines.
Title: On the Effects of a Weak Magnetic Field on Turbulent Transport
Authors: Cattaneo, F.
Bibcode: 1994ApJ...434..200C
Altcode:
We discuss the effects of a weak large-scale magnetic field on turbulent
transport. We show by means of a series of two-dimensional numerical
experiments that turbulent diffusion can be effectively suppressed
by a (large scale) magnetic field whose energy is small compared to
equipartition. The suppression mechanism is associated with a subtle
modification of the Lagrangian energy spectrum, and it does not require
any substantial reduction of the turbulent amplitude. We exploit the
relation between diffusion and random walking to emphasize that the
effect of a large-scale magnetic field is to induce a long-term memory
in the field of turbulence. The implications of the general case of
three-dimensional transport are briefly discussed.
Title: Convection and Magnetic Fields
Authors: Cattaneo, Fausto
Bibcode: 1994ASPC...68..108C
Altcode: 1994sare.conf..108C
No abstract at ADS
Title: Magnetoconvection (Invited Review)
Authors: Cattaneo, F.
Bibcode: 1994smf..conf..261C
Altcode:
No abstract at ADS
Title: On the Generation of Sound by Turbulent Convection. I. A
Numerical Experiment
Authors: Bogdan, Thomas J.; Cattaneo, Fausto; Malagoli, Andrea
Bibcode: 1993ApJ...407..316B
Altcode:
Motivated by the problem of the origin of the solar p-modes, we study
the generation of acoustic waves by turbulent convection. Our approach
uses the results of high-resolution 3D simulations as the experimental
basis for our investigation. The numerical experiment describes the
evolution of a horizontally periodic layer of vigorously convecting
fluid. The sound is measured by a procedure, based on a suitable
linearization of the equations of compressible convection that allows
the amplitude of the acoustic field to be determined. Through this
procedure we identify unambiguously some 400 acoustic modes. The
total energy of the acoustic field is found to be a fraction of a
percent of the kinetic energy of the convection. The amplitudes of the
observed modes depend weakly on (horizontal) wavenumber but strongly on
frequency. The line widths of the observed modes typically exceed the
natural linewidths of the modes as inferred from linear theory. This
broadening appears to be related to the (stochastic) interaction
between the modes and the underlying turbulence which causes abrupt,
episodic events during which the phase coherence of the modes is lost.
Title: Evidence for the suppression of the alpha-effect by weak
magnetic fields.
Authors: Tao, L.; Cattaneo, F.; Vainshtein, S. I.
Bibcode: 1993spd..conf..303T
Altcode:
No abstract at ADS
Title: Turbulent magnetic transport effects and their relation to
magnetic field intermittency.
Authors: Vainshtein, S. I.; Tao, L.; Cattaneo, F.; Rosner, R.
Bibcode: 1993spd..conf..311V
Altcode:
No abstract at ADS
Title: Evidence for Transonic Flows in the Solar Granulation
Authors: Nesis, A.; Bogdan, T. J.; Cattaneo, F.; Hanslmeier, A.;
Knoelker, M.; Malagoli, A.
Bibcode: 1992ApJ...399L..99N
Altcode:
High-resolution observations of the solar granulation are interpreted
in the light of recent numerical simulations of compressible
convection. The observations show a negative correlation between
the width of suitably chosen, nonmagnetic lines and the continuum
intensity. This result is consistent with a model of granular convection
where regions of supersonic horizontal flow form intermittently in
the vicinity of the downflow lanes. We conjecture that the observed
line broadening in the regions of low intensity is caused by enhanced
turbulent fluctuations generated by the passage of shock fronts bounding
the regions of supersonic motion.
Title: Nonlinear Restrictions on Dynamo Action
Authors: Vainshtein, Samuel I.; Cattaneo, Fausto
Bibcode: 1992ApJ...393..165V
Altcode:
Astrophysical dynamos operate in the limit of small magnetic
diffusivity. In order for magnetic reconnection to occur, very small
magnetic structures must form so that diffusion becomes effective. The
formation of small-scale fields is accompanied by the stretching of
the field lines and therefore by an amplification of the magnetic
field strength. The back reaction of the magnetic field on the motions
leads to the eventual saturation of the dynamo process, thus posing
a constraint on the amount of magnetic flux that can be generated by
dynamo action, It is argued that in the limit of small diffusivity
only a small amount of flux, many orders of magnitude less than the
observed fluxes, can be created by dynamo processes.
Title: Numerical Models of Stellar Convection (Invited Review)
Authors: Cattaneo, F.; Malagoli, A.
Bibcode: 1992ASPC...26..139C
Altcode: 1992csss....7..139C
No abstract at ADS
Title: What is a stellar dynamo?
Authors: Cattaneo, F.; Hughes, D. W.; Weiss, N. O.
Bibcode: 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: Development of hard-turbulent convection in two dimensions:
Numerical evidence
Authors: Werne, J.; Deluca, E. E.; Rosner, R.; Cattaneo, F.
Bibcode: 1991PhRvL..67.3519W
Altcode:
New numerical evidence for a transition to hard turbulence in 2D
Boussinesq convection is presented. These 2D simulations agree with
some, but not all, experimental results for the scaling properties of
3D hard turbulence. The transition to 2D hard turbulence, as measured
by a change in the Nusselt-Rayleigh scaling law, coincides with a
gradual change in the velocity probability distribution from Gaussian
to exponential form and with the development of a ``well-mixed''
central region.
Title: Suppression of Turbulent Transport by a Weak Magnetic Field
Authors: Cattaneo, Fausto; Vainshtein, Samuel I.
Bibcode: 1991ApJ...376L..21C
Altcode:
Two-dimensional numerical simulations with high spatial resolution
are used to study the effects of a large-scale magnetic field on
its turbulent transport. It is commonly believed that the nonlinear
back-reaction of the magnetic field on the turbulence becomes important
when the field strength is close to equipartition. However, turbulent
diffusion is effectively reduced even when the large-scale field is
much weaker than equipartition.
Title: On Magnetic Diffusion in a Turbulent Fluid
Authors: Vainshtein, S.; Cattaneo, F.; Rosner, R.
Bibcode: 1991BAAS...23.1049V
Altcode:
No abstract at ADS
Title: Turbulent Compressible Convection
Authors: Cattaneo, Fausto; Brummell, Nicholas H.; Toomre, Juri;
Malagoli, Andrea; Hurlburt, Neal E.
Bibcode: 1991ApJ...370..282C
Altcode:
Numerical simulations with high spatial resolution (up to 96-cubed
gridpoints) are used to study three-dimensional, compressible
convection. A sequence of four models with decreasing viscous
dissipation is considered in studying the changes in the flow structure
and transport properties as the convection becomes turbulent.
Title: The Organization of Turbulent Convection
Authors: Brummell, Nicholas; Cattaneo, Fausto; Malagoli, Andrea;
Toomre, Juri; Hurlburt, Neal E.
Bibcode: 1991LNP...388..187B
Altcode: 1991ctsm.conf..187B
Highly resolved numerical simulations are used to study
three-dimensional, compressible convection. The viscous dissipation is
sufficiently low that the flow divides itself in depth into two distinct
regions: (i) an upper thermal boundary layer containing a smooth flow
with a granular appearance, and (ii) a turbulent interior pierced
by the strongest downflows from the surface layer. Such downflows
span the whole depth of the unstable layer, are temporally coherent,
and are thermodynamically well correlated. A remarkable property of
such convection, once it becomes turbulent, is that the enthalpy and
kinetic fluxes carried by the strong downflows nearly cancel, for they
are of opposite sense and nearly equal in amplitude. Thus, although the
downflows serve to organize the convection and are the striking feature
that emerges from effects of compressibility, it is the small-scale,
disorganized turbulent motions (between the coherent downflow structures
that serve as the principal carriers of net convected flux.
Title: A new twist to the solar cycle
Authors: Cattaneo, Fausto; Chiueh, Tzihong; Hughes, David W.
Bibcode: 1990MNRAS.247P...6C
Altcode:
Recent numerical simulations of magnetic buoyancy instabilities suggest
a new mechanism for the variation with the solar cycle in the scale
and structure of surface magnetic flux. The nonlinear evolution of
a predominantly toroidal field is found to depend crucially on the
distribution of the weaker poloidal ingredient. For certain field
configurations large, helical magnetic fragments are produced; for
others the escaping field is small-scale and untwisted. We propose
that the observed structural variations in flux may be accounted for by
small changes in the twist of a deep-seated field. The large fragments
will appear at the surface as active regions, which dominate at solar
maximum, while the small-scale field will emerge as ephemeral regions
which constitute practically all of the flux at solar minimum.
Title: Turbulent Supersonic Convection in Three Dimensions
Authors: Malagoli, Andrea; Cattaneo, Fausto; Brummell, Nicholas H.
Bibcode: 1990ApJ...361L..33M
Altcode:
Previous numerical calculations of two-dimensional, compressible
convection are extended to three dimensions, using a higher order
Godunov scheme. The results show that the flow readily becomes
supersonic in the upper boundary layer, where shock structures form
intermittently in the vicinity of the strong downflow lanes. The
convection as a whole is strongly time-dependent and evolves on a
time scale comparable to the sound crossing time. The motions in
the upper layers are characterized by the rapid expansion of the
upward-moving fluid elements. In the interior, most of the heat is
carried by a small fraction of the fluid residing in strong, highly
coherent downflows. The remaining fluid is dominated by small-scale,
disorganized turbulent motions.
Title: Three-dimensional compressible convection at low Prandtl
numbers.
Authors: Toomre, Juri; Brummell, Nicholas; Cattaneo, Fausto; Hurlburt,
Neal E.
Bibcode: 1990CoPhC..59..105T
Altcode:
Numerical simulations are used to study fully compressible thermal
convection at large Rayleigh numbers. The authors present results from a
sequence of three-dimensional simulations that reveal a transition from
gradually-evolving laminar convection to nearly turbulent convection
as the Prandtl number is reduced from a value of unity to one-tenth.
Title: Numerical simulations of soft and hard turbulence: Preliminary
results for two-dimensional convection
Authors: Deluca, E. E.; Werne, J.; Rosner, R.; Cattaneo, F.
Bibcode: 1990PhRvL..64.2370D
Altcode:
We report results on the transition from soft to hard turbulence in
simulations of 2D Boussinesq convection. The computed probability
densities for temperature fluctuations are exponential in form in both
soft and hard turbulence, unlike what is observed in experiments; in
contrast, we obtain a change in the Nusselt number scaling on Rayleigh
number in good agreement with the 3D experiments.
Title: Supersonic Convection
Authors: Cattaneo, Fausto; Hurlburt, Neal E.; Toomre, Juri
Bibcode: 1990ApJ...349L..63C
Altcode:
Numerical simulations with high spatial resolution are used to study
that the combined effects of stratification, pressure gradients,
and nonadiabatic processes can lead to the formation of regions of
supersonic motions near the upper thermal boundary layer. Within
these regions, the dynamics is dominated by nonstationary shock
structures. These form near the downflow sites and propagate upstream
along the boundary layer to the upflow regions where they weaken and
eventually disappear. The shock cycle, consisting of the formation,
propagation, and disappearance of shock structures, has a time scale
comparable to the sound crossing time over a portion of the convective
cell, giving rise to vigorous time dependence in the convection.
Title: Multiple states for quasi-geostrophic channel flows
Authors: Cattaneo, Fausto; Hart, John E.
Bibcode: 1990GApFD..54....1C
Altcode:
We consider nonlinear baroclinic instabilities of two-layer
quasi-geostrophic flow in a rectilinear channel. The full potential
vorticity equations are shown to possess a countable infinity of
invariant wavenumber sets. Each set is composed of a particular
pattern in wavenumber space in which many Fourier modes have zero
energy. Solutions with initial conditions confined to a particular
wavenumber pattern will remain forever in that pattern. There is also a
general asymmetric state with non-zero energy in all wavenumbers. The
final state of a long-time evolution calculation depends on initial
conditions and internal stability.
Title: The Normal Modes of a Resonant Cavity Containing Discrete
Inhomogeneities: The Influence of Fibril Magnetic Fields on the
Solar Acoustic Oscillations
Authors: Bogdan, Thomas J.; Cattaneo, Fausto
Bibcode: 1989ApJ...342..545B
Altcode:
Motivated by considerations of the interaction between fibril magnetic
fields and solar p-modes, the acoustic spectrum of a cylindrical
cavity filled with ideal gas in which a number of magnetic flux
tubes are embedded is studied. A formalism, based on the T-matrix
approach to acoustic scattering, is developed which can be used to
determine the eigenfrequencies and eigenfunctions for any arbitrary
distribution of flux tubes. For weak scatterers, the frequency shifts
and velocity eigenfunctions are calculated using perturbation theory
for the cases of a single flux tube and a random distribution of up to
100 flux tubes. The results of this 'exact' approach are used to give
a critical appraisal of the predictions of theories based on some form
of averaging, such as the one discussed recently by Bogdan and Zweibel
(1987).
Title: Magnetic buoyancy instabilities of a sheared magnetic layer.
Authors: Cattaneo, F.; Tzihong, Chiueh; Hughes, D. W.
Bibcode: 1989BAPS...34.1294C
Altcode:
No abstract at ADS
Title: Two and Three-Dimensional Simulations of Compressible
Convection
Authors: Cattaneo, F.; Hurlburt, N. E.; Toomre, J.
Bibcode: 1989ASIC..263..415C
Altcode: 1989ssg..conf..415C
No abstract at ADS
Title: The Nonlinear Breakup of the Sun's Toroidal Field
Authors: Hughes, D. W.; Cattaneo, F.
Bibcode: 1989ASSL..156...31H
Altcode: 1989admf.proc...31H
There are good reasons for believing that the sun has a strong toroidal
magnetic field in the stably stratified region of convective overshoot
sandwiched between the radiative zone and convective zone proper. The
magnetic field in this region is modeled by studying the behavior of
a layer of uniform field embedded in a subadiabatic atmosphere. Since
the field can support extra mass, such a configuration is top-heavy,
and instabilities of the Rayleigh-Taylor type can occur. Numerical
integration of the two-dimensional compressible MHD equations makes it
possible to follow the evolution of this instability into the nonlinear
regime. The initial buoyancy-driven instability of the magnetic field
gives rise to strong shearing motions, thereby exciting secondary
Kelvin-Helmholtz instabilities which wrap the gas into regions of
intense vorticity. The somewhat surprising subsequent motions are
determined primarily by the strong interactions between vortices.
Title: The nonlinear breakup of a magnetic layer - Instability to
interchange modes
Authors: Cattaneo, F.; Hughes, D. W.
Bibcode: 1988JFM...196..323C
Altcode:
Motivated by considerations of the solar toroidal magnetic field,
the behavior of a layer of uniform magnetic field embedded in a
convectively stable atmosphere is studied. Since the field can support
extra mass, such a configuration is top-heavy and thus instabilities
of the Rayleigh-Taylor type can occur. For both static and rotating
basic states, the evolution of the interchange modes (no bending of
the field lines) is followed by integrating numerically the nonlinear
compressible MHD equations. The initial Rayleigh-Taylor instability
of the magnetic field gives rise to strong shearing motions, thereby
exciting secondary Kelvin-Helmholtz instabilities which wrap the
gas into regions of intense vorticity. The subsequent motions are
determined primarily by the strong interactions between vortices which
are responsible for the rapid disruption of the magnetic layer.
Title: Topology of Plumes in Nonlinear Compressible Convection
Authors: Toomre, J.; Cattaneo, F.; Hurlburt, N. E.
Bibcode: 1988BAAS...20..678T
Altcode:
No abstract at ADS
Title: Mean advection effects in turbulence
Authors: Cattaneo, F.; Hughes, D. W.; Proctor, M. R. E.
Bibcode: 1988GApFD..41..335C
Altcode:
The connection between the effective convection velocities for scalar
and vector fields due to the action of turbulence is discussed. An
explicit relation between the two is calculated for the special case of
two-dimensional flows and fields and it is shown that both velocities
are zero for homogeneous turbulence. The calculation leads to new
insights on the rde of symmetry in determining the advection velocity
for the case of a vector field.
Title: Magnetic fields in the overshoot zone: the great escape.
Authors: Cattaneo, F.; Hughes, D. W.
Bibcode: 1987NASCP2483..101C
Altcode: 1987tphr.conf..101C
In order that magnetic flux be confined within the solar interior for
times comparable to the solar cycle period it has been suggested that
the bulk of the solar toroidal field is stored in the convectively
stable overshoot region situated beneath the convection zone
proper. Such a magnetic field, though, is still buoyant and is therefore
subject to Rayleigh-Taylor type instabilities. The model problem of an
isolated region of magnetic field embedded in a convectively stable
atmosphere is considered. The fully nonlinear evolution of the two
dimensional interchange of modes is studied, thereby shedding some
light on one of the processes responsible for the escape of flux from
the solar interior.
Title: A new look at the instability of a stratified horizontal
magnetic field
Authors: Hughes, D. W.; Cattaneo, F.
Bibcode: 1987GApFD..39...65H
Altcode:
Although the undular instabilities of a stratified horizontal magnetic
field have been studied in a number of contexts we believe that the
physical mechanism responsible for the instability has not been fully
explained. In this paper we present a new explanation of why these
instabilities occur, considering in detail the differing cases of
two-dimensional and three-dimensional motions.
Title: Nonlinear dynamos: A complex generalization of the Lorenz
equations
Authors: Jones, C. A.; Weiss, N. O.; Cattaneo, F.
Bibcode: 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: Oscillatory convection in sunspots.
Authors: Cattaneo, F.
Bibcode: 1984ESASP.220...47C
Altcode: 1984ESPM....4...47C
The structure of oscillatory convection in the layers below the
umbral photosphere is discussed. A linear stability analysis of a
simple model problem describing a polytropic layer with a vertical
magnetic field shows that when the Alfvén speed and sound speed are
comparable oscillatory convection has a mixed character exhibiting
properties of both fast and slow magnetoacoustic waves. The analysis
further reveals that in this regime overstability is possible even in
convectively stable layers. The nature of the destabilizing mechanism
is briefly discussed.
Title: Periodic and aperiodic dynamo waves
Authors: Weiss, N. O.; Cattaneo, F.; Jones, C. A.
Bibcode: 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>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: Compressible magnetoconvection
Authors: Cattaneo, Fausto
Bibcode: 1984PhDT.......174C
Altcode:
No abstract at ADS
Title: Periodic and aperiodic behaviour in stellar dynamos
Authors: Cattaneo, F.; Weiss, N. O.; Jones, C. A.
Bibcode: 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.