The relativistic theory of weak discontinuities in high temperature phenomena

Abstract

A relativistic theory of the propagation of weak discontinuities in an optically thick medium at temperature 1050K or higher is presented. The effects of radiation pressure and radiation energy density have been taken into account, while the profiles structured by radiant heat transfer are assumed imbedded in the discontinuities. The velocity of propagation of a relativistic weak discontinuity has been determined. The fundamental growth 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 the earlier results of classical gasdynamics. The problem of breakdown of weak waves and the consequent formation of shock waves has also been studied and a finite critical time tc is determined when a weak wave will terminate into a shock wave due to nonlinear steepening. A critical wave amplitude is determined, which provides a critical line for the decay and growth of a weak discontinuity in a relativistic flow referred to an instantaneous rest frame. The local and global behaviour of the wave amplitude is also examined. © 1980.