Sound propagation in a turbulent atmosphere near the ground: a parabolic equation approach.

The interference of the direct wave from the point source to the receiver and the wave reflected from the impedance ground in a turbulent atmosphere is studied. A parabolic equation approach for calculating the sound pressure p at the receiver is formulated. Then, the parabolic equation is solved by the Rytov method yielding expressions for the complex phases of direct and ground-reflected waves. Using these expressions, a formula for the mean squared sound pressure [absolute value(p)2] is derived for the case of anisotropic spectra of temperature and wind velocity fluctuations. This formula contains the "coherence factor," which characterizes the coherence between direct and ground-reflected waves. It is shown that the coherence factor is equal to the normalized coherence function of a spherical sound wave for line-of-sight propagation. For the case of isotropic turbulence, this result allows one to obtain analytical formulas for [absolute value(p)2] for the Kolmogorov, Gaussian, and von Karman spectra of temperature and wind velocity fluctuations. Using these formulas, the effects of temperature and wind velocity fluctuations, and the effects of different spectra of these fluctuations on the mean squared sound pressure, are numerically studied. Also the effect of turbulent anisotropy on the interference of direct and ground reflected waves is numerically studied. Finally, it is shown that the mean squared sound pressure [absolute value(p)2] calculated for the von Karman spectrum of temperature fluctuations agrees well with experimental data obtained in a laboratory experiment.

[1]  Steven F. Clifford,et al.  Turbulence effects on acoustic wave propagation over a smooth surface , 1983 .

[2]  Vladimir E. Ostashev,et al.  Acoustics in Moving Inhomogeneous Media , 1998 .

[3]  Matthew A. Nobile,et al.  Acoustic propagation over an impedance plane , 1985 .

[4]  Kenneth E. Gilbert,et al.  An exact Laplace transform formulation for a point source above a ground surface , 1993 .

[5]  CALCULATED COHERENCE AND EXTINCTION OF SOUND WAVES PROPAGATING THROUGH ANISOTROPIC, SHEAR-INDUCED TURBULENT VELOCITY FLUCTUATIONS , 1999 .

[6]  M. West,et al.  A tutorial on the parabolic equation (PE) model used for long range sound propagation in the atmosphere , 1992 .

[7]  S F Clifford,et al.  Sound propagation in a turbulent atmosphere near the ground: an approach based on the spectral representation of refractive-index fluctuations. , 2001, The Journal of the Acoustical Society of America.

[8]  D. Wilson,et al.  Acoustic propagation through anisotropic, surface‐layer turbulence , 1994 .

[9]  K. Gilbert,et al.  Calculation of turbulence effects in an upward refracting atmosphere , 1988 .

[10]  Akira Ishimaru,et al.  Wave propagation and scattering in random media , 1997 .

[11]  P. Chevret,et al.  A numerical model for sound propagation through a turbulent atmosphere near the ground , 1996 .

[12]  K. Attenborough,et al.  Propagation of sound above a porous half‐space , 1980 .

[13]  V. Mellert,et al.  Coherence functions of plane and spherical waves in a turbulent medium with the von Karman spectrum of medium inhomogeneities , 1998 .

[14]  G. A. Daigle.  Correlation of the phase and amplitude fluctuations between direct and ground‐reflected sound , 1980 .

[15]  J. Mann.  The spatial structure of neutral atmospheric surface-layer turbulence , 1994, Journal of Fluid Mechanics.