Acoustic heating in resonators is studied. The governing equation of acoustic heating is derived by means of the special linear combination of conservation equations in differential form, allowing the reduction of all acoustic terms in the linear part of the final equation, but preserving terms belonging to the thermal mode responsible for heating. This equation is instantaneous and includes nonlinear acoustic terms that form a source of acoustic heating, it is valid for weakly nonlinear flows with weak attenuation. In general, dynamics of sound in a resonator is described by coupling nonlinear equations. Though the equation for heating relates to any sound field that may exist in a resonator, establishing a sound field is a problem itself. It is well known that employment of the different scales method and averaging over the sound period makes it possible to consider sound waves of opposite directions separately, without accounting for their interaction in the volume of the resonator, if they are periodic with zero mean perturbations. It also allows the adding together of contributions of oppositely propagating waves in the production of heat. Some examples of acoustic heating in resonators, relating to periodic sound branches with zero mean perturbations, are discussed.
Weakly nonlinear ion sound waves in gravitational systems
