Spherical wave propagation through inhomogeneous, anisotropic turbulence: Log-amplitude and phase correlations

Ostashev, Vladimir E.; Wilson, D. Keith; Goedecke, George H.

doi:doi:10.1121/1.1628680

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Journal of the Acoustical Society of America / Volume 115 / Issue 1 / AEROACOUSTICS, ATMOSPHERIC SOUND [28]

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Spherical wave propagation through inhomogeneous, anisotropic turbulence: Log-amplitude and phase correlations

J. Acoust. Soc. Am. Volume 115, Issue 1, pp. 120-130 (2004); (11 pages)

Vladimir E. Ostashev^1,2, D. Keith Wilson³, and George H. Goedecke⁴

¹NOAA/Environmental Technology Laboratory, 325 Broadway, Boulder, Colorado 80305
²Department of Physics, New Mexico State University, Las Cruces, New Mexico 88003
³U.S. Army Research Laboratory, 2800 Powder Mill Road, Adelphi, Maryland 20783-1197
⁴Department of Physics, New Mexico State University, Las Cruces, New Mexico 88003

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Abstract

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Inhomogeneity and anisotropy are intrinsic characteristics of daytime and nighttime turbulence in the atmospheric boundary layer. In the present paper, line-of-sight sound propagation through inhomogeneous, anisotropic turbulence with temperature and velocity fluctuations is considered. Starting from a parabolic equation and using the Markov approximation, formulas are derived for the correlation functions and variances of log-amplitude and phase fluctuations of a spherical sound wave. These statistical moments of a sound field are important for many practical applications in atmospheric acoustics. The derived formulas for the correlation functions and variances generalize those already known in the literature for two limiting cases: (a) homogeneous, isotropic turbulence, and (b) inhomogeneous, anisotropic turbulence with temperature fluctuations only. Furthermore, the formulas differ from those for the case of plane wave propagation. Using the derived formulas and Mann’s spectral tensor of velocity fluctuations for shear-driven turbulence, the correlation functions and variances of log-amplitude and phase fluctuations are studied numerically. The results obtained clearly show that turbulence inhomogeneity and anisotropy significantly affect sound propagation in the atmosphere. © 2004 Acoustical Society of America.

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KEYWORDS and PACS

Keywords

atmospheric turbulence, fluctuations, atmospheric boundary layer, atmospheric acoustics

PACS

43.28.Gq

Outdoor sound propagation and scattering in a turbulent atmosphere, and in non-uniform flow fields
43.28.Lv

Statistical characteristics of sound fields and propagation parameters