Nonlinear generation of non-acoustic modes by low-frequency sound in a vibrationally relaxing gas

Abstract

Two dynamic equations referring to a weakly nonlinear and weakly dispersive flow of a gas in which molecular vibrational relaxation takes place, are derived. The first one governs an excess temperature associated with the thermal mode, and the second one describes variations in vibrational energy. Both quantities refer to non-wave types of gas motion. These variations are caused by the nonlinear transfer of acoustic energy into thermal mode and internal vibrational degrees of freedom of a relaxing gas. The final dynamic equations are instantaneous; they include a quadratic nonlinear acoustic source, reflecting the nonlinear character of interaction of low-frequency acoustic and non-acoustic motions of the fluid. All types of sound, periodic or aperiodic, may serve as an acoustic source of both phenomena. The low-frequency sound is considered in this study. Some conclusions about temporal behavior of non-acoustic modes caused by periodic and aperiodic sound are made. Under certain conditions, acoustic cooling takes place instead of heating .