The growth and decay of weak discontinuities in relativistic fluids with vibrational relaxation

Abstract

The propagation of weak discontinuities in relativistic fluids with vibrational relaxation has been studied. The velocity of propagation of a relativistic weak discontinuity has been determined. The fundamental equation governing the growth and decay of a relativistic weak wave has been obtained and solved. The relativistic results are shown to be in full agreement with earlier results of classical gasdynamics. The problem of breakdown of weak discontinuities has also been investigated. The critical time tc is determined when the breakdown of the wave will occur and consequently a shock wave will be formed due to non-linear steepening. It is shown 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 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. The local and global behaviour of the wave amplitude is also discussed. © 1979 with the authors.