Propagation and interaction of two collinear finite amplitude sound beams

Abstract

Propagation and interaction of two collinear finite amplitude sound beams is investigated using Fourier series expansions and numerical methods to solve the nonlinear parabolic equation. The analysis extends to ranges beyond the shock formation distance. Propagation curves and beam patterns for various components of the acoustic field (harmonics and combination frequencies) are shown. Wave profiles at various ranges are also presented. In order to fully appreciate the importance of nonlinear effects on the parametric generation of sound, the results obtained from the fully nonlinear model are compared with those obtained for sources operating at moderate intensity (linear/quasilinear theory) for various source levels, downshift ratios, and absorption lengths. Also discussed is the possibility of matching the solutions of the nonlinear parabolic equation and of the spherical Burgers equation in the far field. The numerical results are compared with some earlier experimental observations by other authors.