### ASA 127th Meeting M.I.T. 1994 June 6-10

## 3pUW20. A high-order time-domain paraxial equation for weakly nonlinear
acoustic propagation.

**R. S. Kulkarni
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W. L. Siegmann
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*Rensselaer Polytech. Inst., Troy, NY 12180-3590
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A time-domain paraxial equation for acoustic propagation has been
developed that possesses capabilities for shallow-water propagation. The
equation incorporates effects of nonlinear wave steepening, wide propagation
angles, dissipation, and spatial variability in both ambient density and sound
speed. Dissipative mechanisms due to viscosity and heat conduction are
included, with extensions possible to incorporate relaxation effects. The
derivation procedure is a hybrid approach combining operator formalism with the
method of multiple scales. The operator formalism is used to factor the two-way
equation and to introduce a high-order Pade approximation to the square-root
operator, while multiscaling permits simplifying estimates of terms in the
equation. Comparisons have been made with other time-domain paraxial models. A
computational strategy, based on splitting the equation into components
representing distinct physical processes, will be discussed. Numerical results
for particular cases will be presented and compared with those from other
paraxial models. Effects of weak nonlinearity and dissipation will be
described. [Work supported by ONR.]