Linear and Nonlinear Ocean Acoustic Propagation Models

Abstract

A review of basic linear ocean sound propagation models as derived from fluid dynamics is presented. By retaining nonlinear terms in the equations of fluid dynamics a nonlinear time domain wave equation is then derived. A unidirectional approximation leads to a nonlinear time domain version of the parabolic equation, a nonlinear progressive wave equation (NPE), which can treat propagation of finite amplitude signals in a refracting medium in a wave theoretic sense and hence includes propagation through a caustic. In the limit of infinitesimal acoustics a linear time domain parabolic equation results which can be directly solved numerically without Fourier synthesis. Inserting a harmonic solution into this equation and taking the far field limit reduces this equation to the standard parabolic equation. Linear and nonlinear time domain examples are presented including the propagation of a shock wave through a caustic.