The growth and decay of weak waves in relativistic flows of dissociating gases

Abstract

The propagation of a weak wave in a relativistic flow of a dissociating gas has been studied. The velocity of propagation of a relativistic weak wave has been determined. The fundamental growth equation governing the growth and decay of the wave has been obtained and solved. The relativistic results have been shown in full agreement with earlier results of classical gas dynamics. The problem of breakdown of weak discontinuities has also been solved. The critical time tc is determined when the breakdown of the wave and the consequent formation of a shock wave occur due to nonlinear steepening. It is concluded that there exists a critical amplitude of the wave such that all compressive waves with an initial amplitude greater than the critical one will break down after a finite time tc and a shock-type discontinuity will be formed, while an initial amplitude less than the critical one will result in a decay of the wave. On the other hand, an expansion wave will always decay and will ultimately be damped out. The global behavior of the wave amplitude has also been studied. It is concluded that the dissociative character of the gas is to increase the critical time. The relativistic and dissociative effects on the global behavior of weak discontinuities have also been discussed.