Propagation of sound in a turbulent medium. II. Spherical waves

Abstract

Formulas for the statistical moments of a spherical sound wave propagating in a medium with arbitrary (anisotropic) spectra of temperature and medium velocity fluctuations are obtained. These statistical moments are: the variances of log-amplitude and phase fluctuations, the correlation functions of log-amplitude and phase fluctuations, the mean sound field, and the coherence function of the sound field. Then, the statistical moments of a spherical sound wave are calculated analytically and numerically for Gaussian spectra of temperature and medium velocity fluctuations. It is shown that the temperature and medium velocity contributions to these statistical moments can differ not only quantitatively but also qualitatively. The useful relationships between the statistical moments of spherical and plane waves propagating in a moving random medium are derived. Some of the theoretical results obtained are compared with experimental data from the literature on sound propagation through the turbulent atmosphere.

Propagation of sound in a turbulent medium. I. Plane waves

“…The main goal of the present paper and the subsequent one, 19 which is referred to hereinafter as Paper II, is to calculate other statistical moments of the sound field p propagating in a moving random medium, namely, the correlation functions of log-amplitude and phase fluctuations, B (r) ϭ͗(x,r 1 )(x,r 1 ϩr)͘ and B (r)ϭ͗(x,r 1 )(x,r 1 ϩr)͘, the mean sound field ͗p(x,r)͘, the transverse coherence function ⌫(r 1 ,r 2 )ϭ͗p(x,r 1 )p*(x,r 2 )͘, and the sound scattering cross section per unit volume . Moreover, on the basis of the equations obtained, the temperature and medium velocity contributions to these statistical moments are compared.…”

Coherence functions of plane and spherical waves in a turbulent medium with the von Karman spectrum of medium inhomogeneities

“…Using the parabolic equation method, Markov approximation and results known for electromagnetic wave propagation in a turbulent medium, 3-5 the equations for ⌫ and ͗p(x,r)͘ have been derived for plane and spherical waves in a medium with arbitrary spectra of temperature and medium velocity fluctuations. 14,15 The coherence function of a plane wave in a statistically isotropic medium depends only on the modulus of the vector r and is given by…”

“…1,3,[10][11][12][13] We shall also compare the temperature and medium velocity contributions to the statistical moments of plane and spherical waves in a medium with the von Karman spectrum of medium inhomogeneities. In the recent references, 6,7,14,15 these contributions have been shown to be different for the case of sound propagation in media with the Kolmogorov and Gaussian spectra of medium inhomogeneities. Also it has been shown in these references that the temperature and medium velocity contributions to the statistical moments of a sound field were assumed incorrectly to be the same in previous theories of sound propagation in random media.…”

A boundary element method for the calculation of noise barrier insertion loss in the presence of atmospheric turbulence

“…An alternative and popular method to calculate the effect of turbulence on multiple source radiation is the use of a MCF to reduce coherence between each pair of sources. For a Gaussian turbulence model, the MCF is given by [7,8],…”

“…In this model Rayleigh's integral is applied to replace the propagating wavefront above the barrier with a plane of point sources. Turbulence effect is then incorporated by the degradation of coherence between the sources using a mutual coherence function (MCF) [7,8]. With the exception of Reference [9], most of these efforts have been applied to thin barriers.…”