On the shock change equations

Abstract

We revisit and derive the shock-change equations relating the dynamics of a shock wave with the partial derivatives describing the motion of a reactive fluid with general equation of state in a stream-tube with arbitrary area variation. We specialize these to a perfect gas, in which we obtain all shock-change equations in closed form. These are further simplified for strong shocks. We discuss the general usefulness of these equations in problems of reactive compressible flow and in the development of intrinsic evolution equations for the shock, such as the approximations made by Whitham and Sharma.