On the growth and decay of acceleration waves in transient gas flows with vibrational relaxation

Abstract

The problem of breakdown of acceleration waves in the neighbourhood of the leading frozen characteristics in transient gas flows with vibrational relaxation has been studied. The critical time tc is determined when the breakdown of the wave will occur at the cusp of the envelope of the intersectying forward characteristics. 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 and a shock-type discontinuity will be formed due to non-linear steepening, while an initial amplitude less than the critical one will result in a decay of the wave. It is also concluded that the point of breakdown moves outward along the leading characteristics as the relaxation time decreases and that there is no breakdown, if the gas has a sufficiently small, but not zero, relaxation time. © 1979 Springer-Verlag.