The classical Rankine-Hugoniot jump conditions, an important cornerstone of modern shock wave physics: ideal assumptions vs. reality

The purpose of this paper is to discuss from a historical point of view the classical Rankine-Hugoniot (RH) relations in more detail than usually done in standard textbooks. Particularly focusing on the last seventy years, this paper (i) reviews their validity and limitations as interpreted by numerous users; (ii) summarizes their enormous extension also to other branches of science and engineering; and (iii) discusses the nontrivial problem of error estimation. Originally, the RH relations were derived for a plane-parallel steadily propagating aerial shock with a step wave profile; i.e., a wave with zero rise-time and constant thermodynamic as well as kinematic parameter values behind the shock front. But real shock waves are in most cases three-dimensional, have finite rise-times, and in almost all cases are unsteady waves. These real properties must produce a systematic error when applying the RH relations and the cardinal question arises how large this error will be in comparison with a random error caused by the applied high-speed diagnostics. However, numerical procedures of studying systematic errors of unsteady wave propagation are difficult to carry out because of various reasons and still pending.