Parabolic approximation versus geometrical acoustics for describing nonlinear acoustic waves in inhomogeneous media

Abstract

Propagation of intense periodic acoustic waves in inhomogeneous media is studied in the nonlinear geometrical acoustics (NGA) approximation and using nonlinear parabolic equation (NPE). Various types of 2-D inhomogeneities are considered, such as a phase screen, single Gaussian inhomogeneities, and random inhomogeneous media. Distributions of acoustic rays are obtained by numerical solution of the eikonal equation. Pressure field patterns are calculated numerically with account for nonlinear effects and diffraction using a frequency-domain algorithm for the NPE. The location of caustics and shadow zones in the ray patterns are compared with the results of the parabolic model for the areas of increased and decreased sound pressure. Both linear and nonlinear propagation is investigated in order to reveal the validity of NGA in predicting the acoustic field structure and to better understand how the combined effects of inhomogeneities, diffraction, and nonlinearity determine the overall peak and average parameters of the acoustic field. It is shown that NGA does not accurately represent all the locations of enhanced or reduced acoustic pressure even for single scattering inhomogeneities, and the discrepancies become larger for smaller size inhomogeneities and at longer distances in random inhomogeneous medium. [Work supported by CNRS, RFBR, and NIH Fogarty.]