Weak Scattering of Sound Waves in Random Media That Have Arbitrary Power-Law Spectra

Report No. ARL-TR-1866
Authors: Wilson, D. K.
Date/Pages: April 1999; 25 pages
Abstract: Log-amplitude and phase variances of a weakly scattered acoustic signal are calculated for line-of-sight propagation through a random medium. The spectrum of the index-of-refraction fluctuations in the random medium is assumed to scale in proportion to the wavenumber raised to an arbitrary power in the limit of large wavenumbers (small spatial scales). Both scalar and vector contributions to the index of refraction are considered. Most of the calculated results reduce to those given by Tatarskii (1971) and Ostashev (1994) when the power law exponent is -5/3, which is the value characteristic of turbulence. However, the results do not exactly reduce to an equation given by Flatte et al (1994) for the log-amplitude variance in terms of strength and diffraction parameters. The equation from Flatte et al is shown to be an approximation, strictly valid only when the spectral energy in the random medium is concentrated at a well-defined outer scale.
Distribution: Approved for public release
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Last Update / Reviewed: April 1, 1999