Nonlinear wide-angle paraxial propagation in shallow-water channels.

Abstract

A model that describes wide-angle paraxial propagation of acoustic pulses in shallow water has been developed. This time-domain, range-marching model incorporates weak nonlinear effects and depth variability in both ambient density and sound speed, with extensions to include dissipative effects. The derivation is based on an iterative approach, in which the wide-angle approximation is obtained by using a narrow-angle equation to approximate the second range derivative in the two-way nonlinear wave equation. Scaling arguments are used to obtain a more tractable simplification of the equation. Higher-order approximations can be derived by continuing the iterative procedure. The wide-angle equation is solved numerically by splitting it into components representing distinct physical processes and employing a predictor-corrector strategy. A high-order upwind flux-correction method is used to handle the nonlinear component, in order to eliminate spurious artifacts that otherwise degrade the solution. Numerical results are presented for different types of sources in several horizontally stratified environments. Effects of nonlinearities on wide-angle propagation and differences between narrow- and wide-angle nonlinear propagation will be discussed. [Work supported by ONR.]