The vorticity jump across a gasdynamic discontinuity

Abstract

An expression is obtained for the jump in the vorticity across a gasdynamic discontinuity in an inviscid flow. This result generalized results of Truesdell (1952) and Lighthill (1957) for the vorticity behind a steady curved shock in a uniform flow and that of Emmons (1957) for the vorticity jump across a steady flame. The derivation is a dynamical one, and no assumptions on the composition or thermodynamic properties of the fluid are made. The jump in vorticity in the steady flow case is found to depend upon the jump in density and upon gradients along the discontinuity surface of the tangential velocity component and of the normal mass flow. An analogous result is found with unsteady flow.