### ASA 126th Meeting Denver 1993 October 4-8

## 2aPAb12. First-order acoustical wave equations and scattering by
atmospheric turbulence and turbules.

**George H. Goedecke
Paul M. Pellegrino
Michael De Antonio
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*Dept. of Phys., NMSU, Las Cruces, NM 88003-0001
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**Harry J. Auvermann
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*Army Res. Lab., WSMR, NM 88002-5501
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The first Born approximation has often been used to predict acoustical
scattering by the quasistatic temperature fluctuations and velocities
associated with atmospheric turbulence. For this approximation, only terms
linear in these disturbances need be retained in the wave equation. Terms in
this first-order wave equation involving spatial derivatives of the flow field
have often been dropped. It is shown that retaining these terms yields a Born
scattering amplitude equal to cos((theta)) times that obtained when they are
dropped, where (theta) is the scattering angle. It is also shown that this Born
scattering amplitude is identically zero in the forward direction for any
solenoidal flow velocity field that goes to zero faster than r[sup -3] as
r->(infinity). Analytic expressions and numerical results for the first Born
differential and total cross sections are obtained for a model localized
turbule. The model employs nonuniform rotation about an axis, as modulated by
an axisymmetric Gaussian, plus commensurate temperature variation.