Numerical simulation of the propagation of three-dimensional helical shock waves in a weakly heterogeneous medium.

Abstract

A numerical method for the simulation of 3-D acoustical shock wave propagation through a homogeneous or weakly heterogeneous medium is presented. It is based on a generalization of the KZ equation taking into account weak heterogeneities. The algorithm is based on a spectral treatment of the linear diffraction (angular spectrum), coupled with quasianalytical solutions for the heterogeneous part and for the nonlinear one. This last one solves Burgers’ equation with the so-called Burgers-Hayes method using the potential instead of the pressure field. The combination of these several algorithms lead to the development of an efficient software, allowing to solve full 3-D problems for standard personal computers. This software is used to study the dynamics of helical shock waves also called acoustical vortices (AVs) which are the acoustical equivalent of optical vortices. The 3-D helical spatiotemporal wave field is characterized by azimuthal shocks. The dynamics of the so-called topological charge, an intrinsic property of AVs, is studied in the nonlinear regime through different focusing lenses.