The flow of a compressible fluid with weak entropy changes

Abstract

Perturbations of a given flow are considered, and the equations which govern the one-dimensional, non-steady flow of an inviscid, ideal compressible gas are linearized in the neighbourhood of this known solution, assumed isentropic, by a formal perturbation expansion. The perturbed flow is not assumed isentropic. Explicit solutions are obtained for a basic flow which is uniform or a centred simple wave and for an arbitrary simple wave if the perturbed flow is isentropic.The perturbation of a uniform shock and perturbations in a shock tube lead to functional equations of a particular type, and a discussion of their solution is given.A similar analysis is used to discuss the flow in a tube of slowly varying cross-section.