The transmission of sound through a turbulent shear layer is reviewed both with respect to the mathematical theory of the distortion of signals during propagation and also as the basis of the analysis in part 2 of the spectral broadening evinced by experimental results relevant to the study of aircraft noise. The reflexion and transmission coefficients, which involve both amplitude and phase changes, are obtained for scattering by an irregular and unsteady interface convected between two media; diffraction of high frequency sound by small-scale turbulence in a shear layer is accounted for by means of a phase shift and conservation laws for energy, wavenumber and amplitude. These results may be used to construct the sound field transmitted through a turbulent shear layer from a source in the interior of a jet; multiple internal reflexions are accounted for in the case of transmission through two parallel shear layers, i.e. a jet of finite width shielding a noise source. A statistical description is given of the process of attenuation of the transmitted wave as energy is diffracted by the turbulence, and of the partial compensation by interference between correlated components of the refracted wave; the reference case is a monochromatic point source, which, when placed behind a system of shear layers, has its energy redistributed directionally and spread over a range of frequencies. The expressions obtained for the energy flux include as particular cases the results of Howe for the plane (1975) and impedance (1976) layers, the effects of turbulence being shown to be consistent with the experiments of Schmidt & Tilmann (1970) and Ho & Kovasznay (1976a, b).

This review on some aspects of waves in gases concentrates first (Part I) on modern research in the acoustics of fluids at rest or in steady or turbulent motion, in free space, in the presence of obstacles, or in ducts. The study of sound, for which the sole restoring force is pressure, will be extended in a later paper (Part II) to include the other three restoring forces, namely, gravity, electromagnetic, and Coriolis forces, leading to current research on internal, magnetic, and inertial waves and their couplings. The Introduction at the beginning of Part I, and the discussion at the end of Part II, concern all four types of waves in gases, and their relevance in physics and engineering. In Part I, the following areas of acoustics are addressed: the generation of noise by turbulence, inhomogeneities or bubbles, in natural and engineering flows, e.g., wind or jets; the scattering of sound by interfaces and diffraction by turbulence, and their effects on spectral and directional redistribution of energy; propagation in ducts, without or with mean flow, e.g., the horns of musical instruments and loudspeakers, and inlets and exhausts of engines; the effects of dissipation and nonlinearity on waves, e.g., in laboratory and engineering shock tubes, and in geophysical and astrophysical conditions. Underlying these topics is the interaction of acoustics with manking, ranging from the processes of human hearing and speech to the reproduction of desirable sounds (music) and reduction of undesirable sounds (noise).

This work completes a two-part review on waves in gases, of which the first part [Rev. Mod. Phys. 58, 117 (1986)] dealt with the modern aspects of acoustics of jets, turbulence, and ducts; this second part extends the range of topics from sound to magnetic, internal, and (to a lesser extent) inertial waves, thus considering all four restoring forces (pressure, gravity, and Lorentz and Coriolis forces). The motivations for the study of these waves were outlined in the introduction to Part I. Part II reviews the coupling of acoustic, magnetic, and internal waves, in four stages: in Sec. I dispersion relations are used to study the propagation and radiation of magneto-acoustic-gravity-inertial waves in media for which the wave speeds and scattering scales are constant; in Sec. II the case of linear waves in stratified media, with nonuniform propagation velocity, is then discussed by means of special functions, appearing as exact solutions of second-order problems; in Sec. III the study of linear waves with variable propagation speeds is extended to certain classes of higher-order problems including a discussion of cutoff frequencies, critical levels, partition of energy, mode coupling and conversion, etc; in Sec. IV the preceding studies are extended to damped and nonlinear waves, to include dissipation with variable damping scales and large disturbances in media under nonuniform external forces, such as magnetic flux tubes. The conclusion (Sec. V) sums up both parts of the review, in the sense that it deals with all types of waves in fluids; it mentions a few currently controversial topics, points out some directions for future research, and indicates methods available to address these issues.

It has been observed experimentally by Candel, Julienne & Julliand (1975) that a monochromatic test tone generated by a source inside a jet is received outside as a broad frequency band of definite shape. This phenomenon of spectral broadening occurs during transmission through the shear layer, which generally has a randomly irregular and unsteady shape, contains in addition distributed turbulence, and separates the jet and the ambient medium. We show in the first place that, in the audible range of frequencies, neither the approximation which treats the shear layer as a scattering interface with a convected undulating shape nor the opposite, high frequency limit obtained by means of asymptotic estimation of integrals derived for the diffraction of rays in turbulence is sufficient to provide a satisfactory theory of the observations. The refraction integrals obtained in part 1 have to be evaluated exactly in order to account for the phenomenon of spectral broadening, the methods used possibly being of interest in other branches of wave theory. The formation of the transmitted spectrum from an incident tone can be illustrated by representing a simple shear layer as an array of elements each re-radiating energy received from the source with its own characteristic attenuation and frequency shift. A computer program is used to obtain spectra under conditions corresponding to the experiments of Candel, Guédel & Julienne (1975) and gives encouraging agreement with their measurements, which were made with high frequency sources immersed in low speed jets. The theory can also be applied to the prediction of spectra received at various angles to the axis of high subsonic jets, but depends on extrapolation when supersonic exhausts are considered. We conclude with an example of the possible relevance of spectral broadening as a means of reducing the noise disturbance from current jet-powered aircraft, such as Concorde.

The generation, and thence the dissipation, propagation and radiation, of waves in a compressible fluid subjected to a magnetic field is studied as an extension of the ‘acoustic analogy’ (Lighthill 1952) to magneto-acoustics. A formal theory of magneto-acoustic waves introduces (i) a single differential operator describing propagation, (ii) a dynamic and a magnetic tensor modelling generation and (iii) a dissipation tensor to complete the wave equation. The interpretation of these tensors indicates the magnitude of the physical processes of wave generation, by turbulence and inhomogeneities, and of wave dissipation, by viscous and electrical resistance and heat conduction. The total quadrupole components are classified according to the mode of emission. If the magnetic field or compressibility is neglected we obtain, respectively, ‘aerodynamic acoustics’ and a corresponding theory for Alfvén waves. These hydrodynamic and hydromagnetic results contrast with magnetodynamics, when the magnetic field is dominant. The magneto-acoustic far field implies a law of directivity and intensity of radiation. The main results have been collected in three summary tables (see appendix).