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Author name code: lighthill
ADS astronomy entries on 2022-09-14
author:"Lighthill, M.J."
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Title: Dynamics of ionized gases; proceedings.
Authors: Lighthill, M. J.; Imai, Isamu; Sato, H.
1973digp.book.....L Altcode:
No abstract at ADS
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Title: Dynamic Response of the Indian Ocean to Onset of the Southwest
Monsoon
Authors: Lighthill, M. J.
1969RSPTA.265...45L Altcode:
The linearized theory of unsteady wind-driven currents in a
horizontally stratified ocean is applied to the northern part of
the Indian Ocean. This is argued to be a suitable area for detailed
application and evaluation of the theory because (i) the theory has
certain advantages near the equator (for example, influence of detailed
bottom topography is reduced, thermoclines are somewhat less variable in
character, and speeds of baroclinic propagation are enhanced relative
to current speeds), and (ii) the wind-stress pattern undergoes a well
marked change with onset of the Southwest Monsoon, a change to which the
pattern of currents shows a more or less identifiable, and rather quick,
response which may be compared with theoretical predictions. Response
is predicted to be found principally in two modes as far as vertical
distribution of current is concerned; to a somewhat lesser extent
in the barotropic mode with uniform distribution, and to a somewhat
greater extent in the first baroclinic mode with current distribution
as in figure 7, concentrated predominantly in the uppermost 200 m
(see Appendix for detailed analysis of the modes appropriate to the
equatorial Indian Ocean). Of particular interest is the strong Somali
Current, that flows northward along the Somali coast only during the
northern hemisphere summer (after monsoon onset) but during that time is
comparable in volume flow (about 5 × 10<SUP>7</SUP> m<SUP>3</SUP>/s)
to other western boundary currents such as the Gulf Stream. Detailed
discussion of the application of linearized theory to equatorial
oceans with western boundaries leads the author to conclude, both
in the barotropic (section 2) and baroclinic (section 4) cases, that
'wave packets' of current pattern reaching such a boundary deposit the
'flux' they carry (velocity normal to the boundary integrated along it)
in a boundary current which rather rapidly takes a rather concentrated
form. Linear theory with horizontal transport neglected indicates that
such flux requires of the order of 10 days to become concentrated
in a current of 100 km width, but that thereafter it continues to
become still thinner; however, with horizontal transport included,
a steady-state finite thickness of current is reached. In reality,
nonlinear effects would play an important additional part in limiting
steady-state current thickness to the observed 100 km or thereabouts,
but the time scale required to bring the thickness down to this value
is probably given reasonably well by linear theory. Calculations
for a zonal distribution of winds, which rather rapidly make a
reversal of direction and increase of strength somewhat north of the
Equator characteristic of the onset of the Southwest Monsoon, predict
westward propagation of both barotropic and baroclinic wave energy at
comparable speeds of the order of 1 m/s; the marked contrast here with
other oceans (in the comparability of speeds) is given particularly
detailed study. Calculations indicate that the barotropic signal is
considerably distorted (figure 3) by the fact that low-wavenumber
components reach the western boundary first. Baroclinic propagation
takes the form of special planetary-wave modes concentrated near the
equator (section 3), of which perhaps four, delivering flux patterns
depicted in figure 5, and possessing wave velocities of 0.9, 0.55, 0.4
and 0.3 m/s towards the west, are specially relevant to generation of
the Somali Current. Peak surface flows in that current are predicted to
be influenced about three times as much by this baroclinic propagation
as by the barotropic. Theory indicates 1 month (of which two-thirds
is needed for propagation of current patterns and one-third for
their concentration in a boundary current) as characteristic time
scale for formation of the Somali Current (see figure 6 in particular
for the calculated baroclinic component) in contradistinction to the
'decades' predicted by the same type of theory in mid-latitude oceans
(Veronis & Stommel 1956). Observations do, indeed, make clear that
the time scale is not significantly more than 1 month, although the
possibility that it might be still less cannot yet be decided on the
basis of observational evidence. The flow is calculated as reaching 40%
of a typical maximum value (observed in August) already within 1 month
of monsoon onset (May), even though no effect of wind stress acting
within 500 km of the coast has been taken into account. The linearized
theory predicts the current as reaching as far north as 6 degrees N or
7 degrees N, but nonlinear terms are generally found in computational
studies (Bryan 1963; Veronis 1966) to bring about some 'inertial
overshoot' in concentrated boundary currents, which may explain why
the current does not in fact separate until about 9 degrees N.
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Title: Predictions on the Velocity Field Coming from Acoustic Noise
and a Generalized Turbulence in a Layer Overlying a Convectively
Unstable Atmospheric Region
Authors: Lighthill, M. J.
1967IAUS...28..429L Altcode:
The rapid increase of temperature with altitude in the Sun's atmosphere
(chromosphere and corona) is believed to be due to turbulence in
the lower photosphere generating mechanical waves, whose amplitude
increases on propagation into rarefied regions, where their energy
can be progressively dissipated into heat. Here, I review the waves
that are possible under the combined influences of compressibility,
gravity and the magnetic field, and study the efficiency of their
generation and the linear and non-linear mechanisms available for their
dissipation. <P />I conclude that the generation of gravity waves (also
known as 'internal waves') by tongues of turbulence penetrating above
the turbulent convection zone should be at least as efficient as the
generation of sound waves within the convection zone. Oscillations
observed in the upper photosphere and lower chromosphere can be
interpreted as gravity waves generated in this way. Radiative damping
of such gravity waves provides a mechanism of heating of the lower
chromosphere. <P />Magnetic fields can transform gravity waves into
Alfven waves at higher altitudes, preventing their reflection from
regions of increasing temperature. This is a possible for the observed
increased chromospheric heating in regions of large magnetic field;
another is the direct generation of Alfven waves by the tongues
of turbulence. Sound waves, by contarst, are transformed into fast
hydromagnetic waves, and their reflection is not so prevented. <P
/>Above 1000 km altitude, non-linear transformations of the waves
become dominant and the main heating is expected to be of shock-wave
type. Higher still, in the corona, collisionless fast hydromagnetic
shocks may become a particularly important heating mechanism.
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Title: Einfuehrung in die Theorie der Fourieranalysis und der
verallgemeinerten Funktionen
Authors: Lighthill, M. J.
1966etfu.book.....L Altcode:
No abstract at ADS
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Title: Dynamics of rotating fluids: a survey
Authors: Lighthill, M. J.
1966JFM....26..411L Altcode:
No abstract at ADS
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Title: Group Velocity
Authors: Lighthill, M. J.
1965JIMIA...1....1L Altcode:
No abstract at ADS
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Title: The Bakerian Lecture, 1961. Sound Generated Aerodynamically
Authors: Lighthill, M. J.
1962RSPSA.267..147L Altcode: 1962RSLPS.267..147L
The author's original theory of sound generated aerodynamically,
that is, of sound radiation fields which are by-products of airflows,
has been extended and improved by Curle and Ffowes Williams. It is
explained in this lecture fully but simply, and used as a framework
for short analyses of our experimental knowledge on pulse-jet noise,
hydrodynamic sound generation, aeolian tones, propeller noise, and
boundary-layer noise, as well as for a somewhat extensive discussion
of the noise of jets, both stationary and in flight. Improved knowledge
of space-time correlations in turbulent flow is used to throw new light
on the noise radiated by turbulent boundary layers, as well as by jets
at the higher Mach numbers. Supersonic bangs and the scattering of
both sound and shock waves by turbulence are briefly touched upon. The
lecture ends with a discussion of the methods used for the reduction of
jet aircraft noise, in the light of our knowledge of its physical basis.
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Title: Studies on Magneto-Hydrodynamic Waves and other Anisotropic
Wave Motions
Authors: Lighthill, M. J.
1960RSPTA.252..397L Altcode: 1960RSLPT.252..397L
There are two separate but closely interwoven strands of argument
in this paper; one mainly mathematical, and one mainly physical. The
mathematical strand begins with a method of asymptotically evaluating
Fourier integrals in many dimensions, for large values of their
arguments. This is used to investigate partial differential equations
in four variables, x, y, z and t, which are linear with constant
coefficients, but which may be of any order and represent wave motions
that are anisotropic or dispersive or both. It gives the asymptotic
behaviour (at large distances) of solutions of these equations,
representing waves generated by a source of finite or infinitesimal
spatial extent. The paper concentrates particularly on sources of
fixed frequency, and solutions satisfying the radiation condition;
but an Appendix is devoted to waves generated by a source of finite
duration in an initially quiescent medium, and to unstable systems. The
mathematical results are given a partial physical interpretation by
arguments determining the velocity of energy propagation in a plane
wave traversing an anisotropic medium. These show, among other facts
not generally realized, that even for non-dispersive (e.g. elastic)
waves, the energy propagation velocity is not in general normal to
the wave fronts, although its component normal to them is the phase
velocity. The second, mainly physical, strand of argument starts
from the important and striking property of magneto-hydrodynamic
waves in an incompressible, inviscid and perfectly conducting medium,
of propagation in one direction only-a given disturbance propagates
only along the magnetic lines of force which pass through it, and
therefore suffers no attenuation with distance. There are cases of
astrophysical importance where densities are so low that attenuation
due to collisional effects-for example, electrical resistivity-should
be negligible over relevant length scales. We therefore ask how far the
effects of a non-collisional nature which are neglected in the simple
theory, particularly compressibility and Hall current, would alter
the unidirectional, attenuation-less propagation of the waves. These
effects have been included previously in magneto-hydrodynamic wave
theory, but the directional distribution of waves from a local source
was not obtained. This problem explains the need for the mathematical
theory just described, and gives a comprehensive illustration of
its application.
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Title: The Effect of Compressibility on Turbulence
Authors: Lighthill, M. J.
1955IAUS....2..121L Altcode:
No abstract at ADS
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Title: On Sound Generated Aerodynamically. I. General Theory
Authors: Lighthill, M. J.
1952RSPSA.211..564L Altcode: 1952RSLPS.211..564L
A theory is initiated, based on the equations of motion of a gas, for
the purpose of estimating the sound radiated from a fluid flow, with
rigid boundaries, which as a result of instability contains regular
fluctuations or turbulence. The sound field is that which would
be produced by a static distribution of acoustic quadrupoles whose
instantaneous strength per unit volume is ρ v<SUB>i</SUB>v<SUB>j</SUB>
+ p<SUB>ij</SUB> - a<SUB>0</SUB><SUP>2</SUP>ρ δ <SUB>ij</SUB>, where
ρ is the density, v<SUB>i</SUB> the velocity vector, p<SUB>ij</SUB>
the compressive stress tensor, and a<SUB>0</SUB> the velocity of sound
outside the flow. This quadrupole strength density may be approximated
in many cases as ρ <SUB>0</SUB>v<SUB>i</SUB>v<SUB>i</SUB>. The
radiation field is deduced by means of retarded potential solutions. In
it, the intensity depends crucially on the frequency as well as on the
strength of the quadrupoles, and as a result increases in proportion
to a high power, near the eighth, of a typical velocity U in the
flow. Physically, the mechanism of conversion of energy from kinetic
to acoustic is based on fluctuations in the flow of momentum across
fixed surfaces, and it is explained in section 2 how this accounts
both for the relative inefficiency of the process and for the increase
of efficiency with U. It is shown in section 7 how the efficiency is
also increased, particularly for the sound emitted forwards, in the
case of fluctuations convected at a not negligible Mach number.
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Title: Contributions to the Theory of Heat Transfer through a Laminar
Boundary Layer
Authors: Lighthill, M. J.
1950RSPSA.202..359L Altcode:
An approximation to the heat transfer rate across a laminar
incompressible boundary layer, for arbitrary distribution of
main stream velocity and of wall temperature, is obtained by
using the energy equation in von Mises's form, and approximating
the coefficients in a manner which is most closely correct near
the surface. The heat transfer rate to a portion of surface of
length l (measured downstream from the start of the boundary
layer) and unit breadth is given as -frac{1/2k}{(1/3)!}(3σ ρ/μ
<SUP>2</SUP>)<SUP>1/3</SUP>int<SUB>0</SUB><SUP>l</SUP>(int<SUB>x</SUB><SUP>l</SUP>surd
\{τ (z)\} dz)<SUP>2/3</SUP> dT<SUB>0</SUB>(x), where k is the thermal
conductivity of the fluid, σ its Prandtl number, ρ its density,
μ its viscosity, τ (x) is the skin friction, and T<SUB>0</SUB>(x)
the excess of wall temperature over main stream temperature. A
critical appraisement of the formula (section 3) indicates that it
should be very accurate for large σ , but that for σ of order
0\cdot 7 (i.e. for most gases) the constant 1/23<SUP>1/3</SUP>/
(1/3)! = 0\cdot 807 should be replaced by 0\cdot 73, when the
error should not exceed 8% for the laminar layers that occur in
practical aerodynamics. This yields a formula Nu = 0\cdot 52σ
<SUP>1/3</SUP>(R{surd C<SUB>f</SUB>})<SUP>2/3</SUP> for Nusselt
number in terms of the Reynolds number R and the mean square root of
the skin friction coefficient C<SUB>f</SUB>, in the case of uniform
wall temperature. However, for the boundary layer with uniform main
stream, the original formula is accurate to within 3% even for σ =
0\cdot 7. By known transformations an expression is deduced for heat
transfer to a surface, with arbitrary temperature distribution along
it, and with a uniform stream outside it at arbitrary Mach number
(equation (42)). From this, the temperature distribution along such a
surface is deduced (section 4) in the case (of importance at high Mach
numbers) when heat transfer to it is balanced entirely by radiation
from it. This calculation, which includes the solution of a non-linear
integral equation, gives higher temperatures near the nose, and lower
ones farther back (figure 2), than are found from a theory which
assumes the wall temperature uniform and averages the heat transfer
balance. This effect will be considerably mitigated for bodies of high
thermal conductivity; the author is not in a position to say whether
or not it will be appreciable for metal projectiles. But for stony
meteorites at a certain stage of their flight through the atmosphere
it indicates that melting at the nose and re-solidification farther
back may occur, for which the shape and constitution of a few of them
affords evidence. An appendix shows how the method for approximating
and solving von Mises's equation could be used to determine the skin
friction as well as heat transfer rate, but this line seems to have
no advantage over established approximate methods.
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Title: On the instability of small planetary cores (II)
Authors: Lighthill, M. J.
1950MNRAS.110..339L Altcode:
The property that, for a spherically symmetrical planet in which the
density is a fLinction of the pressure, three states of equilibrium are
possible in a certain range of values of the total mass, is shown to
hold whenever the density is continuous up to a critical pressure Pc,
at which (owing to a change of phase) it rises discontinuously by a
factor exceeding 2 The question of transitions between the states is
briefly discussed.
