Time domain approach to the propagation of nonlinear acoustic pulses near caustics

Abstract

Nonlinear acoustic ray tracing in the ocean fails whenever a wave front converges to a caustic of focus, and neighboring rays intersect. It is the purpose of this paper to construct a numerical algorithm for dealing with propagation of large amplitude pulses in the neighborhood of a caustic. A time‐straining transformation of the nonlinear acoustic equation is introduced that enables a perturbation expansion of the pressure in powers of signal strength to be attempted. An essential ingredient of the procedure is the knowledge of the solution of the corresponding linearized problem. An efficient procedure for calculating this for incident pulses of N waveform of arbitrary two‐dimensional wave front geometry is described. The corresponding calculation of the nonlinear time straining is also presented. The procedure could readily be adapted to pulses of more general shape. [Work done in collaboration with Applied Research Laboratories, University of Texas at Austin, and supported by ONR.]