Diffraction of nonlinear acoustic waves: Matched-area method

Abstract

This is a brief overview of a series of investigations undertaken by the author together with his collaborators at the Institute of Applied Physics, Russian Academy of Science. In these works, a simplified theory was developed for the acoustic waves which profile is distorted due to both nonlinearity and diffraction. The theory is based on an often existing possibility to separate the regions of nonlinear geometrical acoustics and linear diffraction and match the corresponding solutions in an intermediate area(s) where neither effect is cumulative. The problems addressed on this way include: (i) broadening of the beam pattern of an intensive acoustic radiation (with V. Fridman); (ii) behavior of a nonlinear acoustic wave near a caustic (with E. Pelinovsky and V. Fridman); (iii) radiation and focusing of nonlinear waves (with A. Sutin). In a number of cases, theoretical results were corroborated by comparison with the experimental data obtained by D. Blackstock and other researchers. This approach is believed to be an efficient tool for treating many realistic situations, and to deserve further development. This work benefited greatly from numerous contacts with Professor Blackstock, starting in the early stages of the investigation.