R. S. Kulkarni
W. L. Siegmann
Rensselaer Polytech. Inst., Troy, NY 12180-3590
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.]