Interaction of small perturbations with shock waves

Interaction of hydrodynamic waves with plane shock waves under the linear approximation is studied. Two classical problems, namely, wave transformation and a rippling instability on a shock wave, are examined. Starting from 1945, these problems have been analyzed repeatedly. A number of enigmas have been revealed during more than half a century. We argue that some of them can be obviated by a revision of the existing approach to description of shock oscillations. These oscillations originate either due to incident perturbations or spontaneously (the latter case is relevant to the problem of shock stability) and are a first order of smallness. It is well known that the linear approximation enables solution of the problem on the unperturbed discontinuity surface, with the surface oscillations taken as a linearly independent mode. This mode signifies a transition from a local reference frame connected with the perturbed shock surface to a laboratory frame related to the unperturbed plane shock. It is traditi...