The boundary layer nature of shock transition in a real fluid

The usual way to deal with the so-called shoch phenomenon in compressible fluids is the following. On the one hand there is the fact that in many cases of observable flow there exist narrow zones across which pressure, density and velocity undergo rapid changes. On the other hand, it is well-known that the differential equations of inviscid perfect fluids fail to supply solutions satisfying certain boundary conditions that can be realized physically. One therefore makes the assumption that these differential equations are valid in regions of the (x, y, z, t) space which are separated from each other by discontinuity surfaces whose shape is a priori unknown. From physically plausible hypotheses one then derives necessary conditions for the values assumed by the physical variables on either side of the discontinuity surfaces. Such conditions were first given by Riemann, and later modified by Rankine and Hugoniot. It is finally assumed--and confirmed at least in special cases-that the differential equations combined with these transition conditions are sufficient to determine both the discontinuity surfaces themselves and the continuous flows in the regions between them (see [4], pp. 116-118, 134-138).