Author name code: lighthill ADS astronomy entries on 2022-09-14 author:"Lighthill, M.J." ------------------------------------------------------------------------ Title: Dynamics of ionized gases; proceedings. Authors: Lighthill, M. J.; Imai, Isamu; Sato, H. Bibcode: 1973digp.book.....L Altcode: No abstract at ADS Title: Dynamic Response of the Indian Ocean to Onset of the Southwest Monsoon Authors: Lighthill, M. J. Bibcode: 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 × 107 m3/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. 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. Bibcode: 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.

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.

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.

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. Title: Einfuehrung in die Theorie der Fourieranalysis und der verallgemeinerten Funktionen Authors: Lighthill, M. J. Bibcode: 1966etfu.book.....L Altcode: No abstract at ADS Title: Dynamics of rotating fluids: a survey Authors: Lighthill, M. J. Bibcode: 1966JFM....26..411L Altcode: No abstract at ADS Title: Group Velocity Authors: Lighthill, M. J. Bibcode: 1965JIMIA...1....1L Altcode: No abstract at ADS Title: The Bakerian Lecture, 1961. Sound Generated Aerodynamically Authors: Lighthill, M. J. Bibcode: 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. Title: Studies on Magneto-Hydrodynamic Waves and other Anisotropic Wave Motions Authors: Lighthill, M. J. Bibcode: 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. Title: The Effect of Compressibility on Turbulence Authors: Lighthill, M. J. Bibcode: 1955IAUS....2..121L Altcode: No abstract at ADS Title: On Sound Generated Aerodynamically. I. General Theory Authors: Lighthill, M. J. Bibcode: 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 vivj + pij - a02ρ δ ij, where ρ is the density, vi the velocity vector, pij the compressive stress tensor, and a0 the velocity of sound outside the flow. This quadrupole strength density may be approximated in many cases as ρ 0vivi. 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. Title: Contributions to the Theory of Heat Transfer through a Laminar Boundary Layer Authors: Lighthill, M. J. Bibcode: 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 2)1/3int0l(intxlsurd \{τ (z)\} dz)2/3 dT0(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 T0(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 1/231/3/ (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 1/3(R{surd Cf})2/3 for Nusselt number in terms of the Reynolds number R and the mean square root of the skin friction coefficient Cf, 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. Title: On the instability of small planetary cores (II) Authors: Lighthill, M. J. Bibcode: 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.