Entropy jump across an inviscid shock wave

The Shock jump conditions for the Euler equations in their primitive form are derived by using generalized functions. The shock profiles for specific volume, speed, and pressure and shown to be the same, however, density has a different shock profile. Careful study of the equations that govern the entropy shows that the inviscid entropy profile has a local maximum within the shock layer. We demonstrate that because of this phenomenon, the entropy propagation equation cannot be used as a conservation law.This research was supported in part under NASA Contract No. NAS1-19480, while the second author was in residence at the Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, Hampton, VA 23681-0001, U.S.A.