Modes and projectors of the viscous non-uniform flow. Heating caused by an acoustic beam between two parallel plates

Abstract

The modes of the thermoviscous flow over a strongly non-uniform background have been obtained. Corresponding matrix projecting operators that decompose every mode, or every possible type of the hydrodynamic motion, from the overall field perturbation have been written in the explicit form. Projecting has been used in order to get dynamic nonlinear equations. Acting by the projector corresponds to the entropy mode of the system of conservation laws, while the acoustic mode which is supposed to be dominating yields in the governing equation for the acoustic heating caused by the attenuated acoustic beam. An example of calculations of heating in the viscous flow between two parallel plates has been given. Key words: non-uniform thermoviscous flow, boundary layer, acoustic heating.