Finite-Aperture Riemann’s Wave

Abstract

The Riemann compression wave describes a 2D flow behind an infinite wave front, but is used for describing its propagation in channels. The effect of walls on the process of its propagation is disregarded in this case. However, friction against the walls and diffraction divergence of elementary plane waves compensating the friction change the conditions of wave propagation. These effects, which are inevitable in a channel, violate the constancy of entropy and the jet nature of the flow, which contradicts the definition of a “simple wave.” Analysis of diffraction divergence makes it possible to solve the problem of formation of a finite-aperture simple wave (a wave beam with a large Rayleigh length). The evolution of friction processes explains the emergence of a turbulent flow and makes it possible to describe the mechanism of a spontaneous transition of deflagration into detonation more accurately.