Nonlinear effects in focused sound fields

Abstract

Focused finite amplitude sound fields are investigated with numerical solutions of the Khokhlov‐Zabolotskaya‐Kuznetsov (KZK) equation. The numerical solution is based on the algorithm developed by Aanonsen et al. [J. Acoust. Soc. Am. 75, 749–768 (1984)], who used a Fourier series expansion of the sound pressure to reduce the KZK equation to a set of coupled parabolic equations. The basic algorithm has been modified by introducing a coordinate system that follows the convergent geometry of focused sound fields. In this way, more efficient numerical evaluation of the detailed field structure within the focal region is achieved. Arbitrary axisymmetric sources can be modeled. Here, circular sources having linear focusing gains of order 50 will be considered. The calculated time waveforms, propagation curves, and beam patterns illustrate clearly the combined effects of nonlinearity, diffraction, and absorption on finite amplitude sound that passes through a focal region. Among the new results are power curves ...