Three-Dimensional Burgers’s Equation in Gas Dynamics

Abstract

An expansion procedure is developed for studying the effects of dissipative mechanisms and nonlinearity on a linear three-dimensional wave. The procedure is considered general enough to use all the ideas of ray theory and singular surface theory in problems when no real characteristics exist. An appropriate similarity hypothesis relates all smallness parameters to an inner parameter, interpreted as the reciprocal Reynolds number. In the frame of reference chosen to describe the vicinity of the linear wave, one obtains compatability conditions and speed in the first stage and a generalized Burgers’s equation in the second stage.