Characteristics of the diffraction of acoustic waves in stratified sound channels

The results of calculations performed in the framework of the approximate approach developed by the authors are presented for the diffraction of sound waves by a stiff spheroid in an acoustic waveguide. The scattered sound field is analyzed as a function of the following parameters of the problem: the spheroid dimensions, its position relative to the sound source and the receiver, the vertical profile of sound velocity in the waveguide, and the acoustic parameters of the waveguide bottom.     

Guided waves in a stratified half-space

The dispersion and excitation mechanisms and the energy distribution of guided waves in a stratified half-space are studied. All possible guided waves excited by a symmetric point source in two or three-layer medium models and their relation to the medium parameters are analyzed in detail. The excitation and propagation characteristics, as well as the energy distribution along the depth direction, of all modes of the surface waves and trapped waves are numerically investigated and analyzed thoroughly not only in the case when the shear wave velocity increases from up to down layers but also when a low-velocity layer is contained in halfspace, especially when the shear wave velocity decreases from up to down layers. It is found that there exist many guided wave modes in the case where the shear wave velocity of each layer increases from up to down layers. However, there is less than one guided wave mode in the case where the shear wave velocity of each layer decreases from up to down layers. The trapped waves exist and propagate along the low-velocity structure in the stratified half-space. It is also found that the characteristic of a mode is related to the source frequency. It is possible that a surface wave at one value of frequency is like a trapped wave at another value of frequency. Finally, the relation of the characteristics of all guided waves (surface waves and trapped waves) to the parameters of media is studied.     

Convection in a slowly diffusing,weakly stratified salt field

We examine thermohaline convection in the small Lewis number limit for a background salt field with a weak gradient. As a result of small diffusivity, the problem cannot be reduced to a simple amplitude equation in the usual manner, but the salt field is described by an advection-diffusion equation coupled to an equation for the amplitude of the convective pattern.     

Nonlinear vortex dynamo in a rotating stratified moist atmosphere

We have found a new type of large-scale instability in a rotating stratified moist atmosphere with small-scale turbulence. The turbulence is excited by an external small-scale force with a low Reynolds number. We have constructed the theory based on the method of multiscale asymptotic expansions. The nonlinear equations for large-scale motion have been derived in the third order of the perturbation theory. We have investigated the linear instability and stationary nonlinear regimes. Solutions in the form of localized vortex structures or kinks of a new type have been obtained.     

Sound and light propagation in a weakly inhomogeneous atmosphere

Small-scale inhomogeneities caused by atmospheric turbulence have a considerable effect on sound and light propagation, producing the fluctuations of these wave fields. V A Krasilnikov [1, 2] performed experiments on phase and amplitude variations of a sound wave propagating through the atmosphere. Fluctuations of light-wave parameters occur, for example, in the well known phenomenon of star scintillation, apparently strongly connected with turbulent irregularities of the atmospheric temperature field [3, 4]‡.

Some calculations of phase (arrival angle) and amplitude fluctuations for a wave propagating through a turbulent medium are described by Krasilnikov [1, 3, 8]. All these and similar calculations are based on the geometrical optics (acoustics) approximation, which may be the reason for disagreement between calculation and experimental data in some cases. Thus, for example, amplitude fluctuations in the geometrical approximation turn out to be proportional to the distance of propagation through a turbulent medium to the power of 3/2. However, observations usually show much slower fluctuation growth.

This paper represents an attempt to consider the problem of amplitude and phase variations for a scalar wave field in terms of more general equations including some diffraction effects. Incidentally, the range of validity of geometrical optics theory becomes clear.     

A Helmholtz resonator buried in the ground as a source of seismic waves and low-frequency sound in the atmosphere

The procedure is given for calculating the total power of low-frequency sound and seismic waves produced by a Helmholtz resonator in the form of an air-filled spherical cavity buried in the ground and supplied with a hole through which it is connected with the atmosphere. The sound is generated by air oscillations in the resonator’s neck section that is open to the atmosphere, while the compression and shear elastic waves are generated in the bulk of the ground by cyclic pressure fluctuations that act on the spherical walls of the cavity. Calculations show that the coincidence of the resonance frequencies (within approximately ten to hundred hertz), at which both the sound radiation to the atmosphere and the elastic seismic radiation in the form of longitudinal and transverse bulk waves are maximum, can occur only when the resonator is placed in a loose ground characterized by reduced elastic characteristics. In these conditions, the power of transverse waves exceeds the sound power by a factor of two and the power of longitudinal waves is smaller than the sound power by a factor of several tens.     

Ray stability in weakly range-dependent sound channels

Ray stability is investigated in environments consisting of a range-independent background sound-speed profile on which a range-dependent perturbation is superimposed. Theoretical arguments suggest and numerical results confirm that ray stability is strongly influenced by the background sound speed profile. Ray instability is shown to increase with increasing magnitude of alpha(I)=(I/omega)d omega/dI, where 2pi/omega(I) is the range of a ray double loop and I is the ray action variable. This behavior is illustrated using internal-wave-induced scattering in deep ocean environments and rough surface scattering in upward refracting environments.     

Nonlinear internal waves in a stratified fluid in a closed basin

Summary The problem of two layers of homogeneous inviscid incompressible fluid of density ϱ₁ and ϱ₂ (ϱ₁>ϱ₂) separated by a free surface in a closed basin is studied via a variational principle. A system of ordinary differential equations in the time variable, which approximate the original problem, is derived and discussed.

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Riassunto Si usa un principio variazionale per studiare il problema del moto di due fluidi omogenei incompressibili non viscosi di densità ϱ₁, ϱ₂ (ϱ₁>ϱ₂) separati da una superficie libera in un bacino chiuso. Dopo alcune approssimazioni si deriva e discute un sistema di equazioni differenziali ordinarie.

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Резюме С помоыью вариационного принципа исследуется проблема двух слоев однородной невязкой несжимаемой жидкости с плотностями ϱ₁ и ϱ₂ (ϱ₁>ϱ₂), раазделенных свободной поверхностью в замкнутом резервуаре. Выводится и обсуждается система обыкновенных дифференциальных уравнений по временной переменной, которая аппроксимирует исходную проблему.

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Work done under the auspices of C.N.R.-G.N.A.F.A.

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Partially supported by NSF under grant PHY77-18762.     

On coupled waves in stratified CGL-plasma

Starting from the Chew-Goldbsrger-Low equations we derive wave-equations describing small amplitude disturbances in a horizontally stratified, continuously varying CGL-plasma. A set of equations of first-order matrix form is treated by the method of Clemmow and Heading.     

Propagation of p-polarized electromagnetic waves obliquely incident on stratified random media: Random phase approximation

We consider the propagation of p-polarized electromagnetic waves obliquely incident on stratified random dielectric media. Using the invariant imbedding method generalized to random media and applying the random phase approximation, we derive a simple analytical expression of the localization length and calculate the disorder-averaged reflectance and transmittance and the fluctuations of the localization length and the reflectance as functions of the incident angle. We also calculate the disorder-averaged intensity profile of the magnetic field inside the random medium. We find that within the random phase approximation, the p wave can be delocalized and transmitted completely at a certain critical incident angle, which is bigger than the Brewster angle in the uniform case.     

On slow flows of a weakly stratified relativistic fluid in a static gravitational field

Simplified equations for slow flows of a weakly stratified (in entropy) fluid inside or near a massive astrophysical object have been derived from the variational formulation of ideal general relativistic hydrodynamics under the conditions that the gravitational field in the leading order is centrosymmetric and static and that the effect of a magnetic field is negligibly small. Internal waves and vortices in such systems are soft modes as compared to sound. This circumstance allows the formulation of a “soundproof” Hamiltonian model. This model is an analog of nonrelativistic hydrodynamic anelastic models, which are widely used in studies of internal waves and/or convection in spatially inhomogeneous compressible media in atmospheric physics, geophysics, and astrophysics.     

Plane waves in a layered weakly dissipative randomly inhomogeneous medium

In the framework of the embedding method the authors consider the stationary and non-stationary problem of a plane-wave incident on a randomly inhomogeneous medium. For the stationary problem there are three regions of sufficiently different behaviour of the wavefield intensity moments inside a weakly dissipative medium. For the non-stationary problem they succeeded in calculating the average intensity at t→+∞ by means of analytical prolongation of the stationary problem solution with respect to the absorption parameter. The time asymptotic of the averaged intensity on the boundary slab is also obtained for a finite-thickness slab.     

Plane waves in a layered weakly dissipative randomly inhomogeneous medium

Abstract

In the framework of the embedding method the authors consider the stationary and non-stationary problem of a plane-wave incident on a randomly inhomogeneous medium. For the stationary problem there are three regions of sufficiently different behaviour of the wavefield intensity moments inside a weakly dissipative medium. For the non-stationary problem they succeeded in calculating the average intensity at t→+∞ by means of analytical prolongation of the stationary problem solution with respect to the absorption parameter. The time asymptotic of the averaged intensity on the boundary slab is also obtained for a finite-thickness slab.     

Dynamics of weakly localized waves

We develop a transport theory to describe the dynamics of (weakly) localized waves in a quasi-1D tube geometry both in reflection and in transmission. We compare our results to recent experiments with microwaves and to other theories, such as random matrix theory and supersymmetric theory.     

Over-reflection of travelling internal waves in a rotating stratified fluid

Summary It has been known for many years that waves of different kind propagating in a fluid and incident on a mean flow localized shear layer can exhibit, in the linear theory, a reflection coefficient larger than unity. When this phenomenon takes place the wave is said to be over-reflected at the shear layer. In this paper the over-reflection of inertial-gravity waves in a stratified rotating fluid in horizontal sheared motion is studied by making use of the constancy of the net vertical energy flux associated with the wave field. It is found that over-reflection can take place if some physical conditions, explicitly evaluated, are locally satisfied in the fluid. Such conditions are discussed and a comparison is carried out with the same phenomenon in a nonrotating system.

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Riassunto Si sa da molti anni che la teoria lineare di onde di diversa natura, propagantesi in un fluido ed interagenti con uno strato localizzato di shear, prevede, in alcuni casi, un coefficiente di riflessione maggiore dell'unità. Questo fenomeno prende il nome di super riflessione. In questo articolo si studia la super riflessione delle onde gravito-inerziali in un fluido stratificato in moto orizzontale con la velocità dipendente dalla sola coordinata verticale. Lo studio è portato a termine servendosi della condizione di continuità e costanza del flusso netto verticale di energia associata al campo d'onda. Si trova che la super riflessione avviene se sono soddisfatte alcune condizioni fisiche che sono esplicitamente determinate: tali condizioni sono inoltre discusse in dettaglio ed i risultati sono confrontati con quelli, classici, relativi alla propagazione di onde interne nei fluidi stratificati in assenza di rotazione.

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Резюме В течение многих лет известно, что линейная теория волн различной природы, которые распространяются в жидкости и взаимодействуют с локализованным пограничным слоем, предсказывает, что в некоторых случаях коэффициенты отражения могут превьщать единицу. Зто явление носит название супер-отражения (сверх-отражение) на пограничном слое. В этой статье исследуется супер-отражение инерциальной гравитационной волны в стратифицированной вращающейся жидкости в случаэ горизонтального движения со скоростью, зависящей только от вертикальной координаты. При рассмотрении учитывается постоянство результирующей вертикальной энергии, связанной с полем волны. Получено, что сверх-отражение может иметь место, если локально в жидкости выполняются некоторые физические условия. Проводится обсуждение этих условий и полученные результаты сравниваются с классическими результатами по распространению внутренних волн в стратифицированной жидкости в отсутствии вращения.