The radiatively driven discrete acoustic wave

Abstract

A complete and detailed study of a radiatively driven plane acoustic wave in a non-grey radiating and absorbing gas is carried out on the assumption of local molecular equilibrium. Specifically, the response of the gas in a semi-infinite space to a step input of radiation from a stationary black wall is investigated. The problem is physically interesting because radiative heat addition is the only driving mechanism, and this mechanism is unique and fundamental to the field of radiative gas dynamics. The solution shows that the heat addition gives rise initially to a compression-expansion wave in the gas, with the wave front controlled by radiation. This wave-front disturbance, though caused initially by the direct effect of radiative transfer, eventually outruns the region of appreciable heating near the wall and becomes a modified-classical disturbance that propagates away from the wall at the isentropic speed of sound. The radiative heat addition continues directly to affect the gas near the wall and in this manner drives the modified-classical wave indirectly by causing the formation of an ‘effective gas piston’. The solution thus exhibits a linearized phenomenology corresponding to that observed in the non-linear leading wave associated with the nuclear fireball.