Nonlinear and Thermoviscous Phenomena in Acoustics, Part III

The present paper is intended as a review (over 300 Refs.) of some basic concepts and modern investigations of nonlinear and thermoviscous phenomena in acoustic fields in fluids. The focus is on theoretical models of nonlinear acoustics for acoustic time-averages, sound beams, and nonlinear standing waves. The well-known topics of general use are considered and the facts which are essential to implementation are also given. Special attention is paid to the combined analysis of the effects of nonlinearity and absorption, to secondary processes in intense sound fields, and to numerical simulation of nonlinear waves.

The content includes:

Section 1: Equations of state. Fluid state.

Section 2: Energy and momentum transfer in the sound field.

Section 3: Non-linear wave equation.

Section 4: Evolution equations and their solutions.

Section 5: Standing waves.

Part III of the paper includes section 5. In this section nonlinear standing waves are reviewed. The method of Krylov, Bogoljubov, and Mitropolski is described as a general calculation tool for treating weak nonlinear wave equations. This method can be divided into the asymptotic method and the averaging method. The asymptotic method and its extension are applied to problems without internal resonances. For example, nonlinear Helmholtz resonators are investigated. The averaging method is used for studying problems with internal resonances and is applied to standing waves in closed tubes, in thermoacoustic systems, and in rods with dispersion. Finally, the combination of the averaging method with the Green's function approach and an integral equation, which is suited especially for numerical calculations, are presented.