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

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.