Direct and inverse scattering of acoustic waves by low-speed free shear layers

Document Type

Article

Publication Date

1-1-1990

Abstract

In this paper, a direct method and a simple inverse method, which can be used to determine the velocity profile of a shear layer, are presented. Specifically, an infinite acoustic medium, with constant density and sound speed, containing a free shear layer of infinite extent, is considered. The free shear layer is probed with a two-dimensional plane wave, incident on the layer from outside, and it is assumed that the maximum Mach numbers for the flows in the shear layers are small, e.g., M = 10–3to 10-4are typical values for oceanic shear layers. Then, the method of matched asymptotic expansions is employed to obtain an asymptotic expansion of the solution of the direct scattering problem as M→0 that is uniformly valid in the dimensionless wave number k and the angle a of the incident plane wave. It is found that the reflection coefficient of the scattered wave is proportional to the Fourier transform of the velocity profile of the free shear layer. This transform is inverted to obtain an asymptotic approximation of the solution of the inverse scattering problem. That is, given an incident plane wave and measurements of the reflected wave for a sequence of frequencies, approximations of the thickness and flow velocity distribution of the layer are determined. These results may be useful for studies that use acoustic exploration methods to determine oceanographic properties. © 1990, Acoustical Society of America. All rights reserved.

Identifier

0025026372 (Scopus)

Publication Title

Journal of the Acoustical Society of America

External Full Text Location

https://doi.org/10.1121/1.400318

ISSN

00014966

First Page

1596

Last Page

1602

Issue

3

Volume

88

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