Instability of isolated planar shock waves

Previously, expressions governing the temporal evolution of linear perturbations to an isolated, planar, two-dimensional shock front in an inviscid fluid medium with an arbitrary equation of state were derived using a methodology based on Riemann invariants and Laplace transforms [J. W. Bates, Phys. Rev. E 69, 056313 (2004)]. An overlooked yet immediate consequence of this theory is that the stability limits of shocks can be readily determined from an inspection of the poles of the transformed ripple amplitude. Here, it is shown that two classes of instabilities exist for isolated planar shock waves: one in which perturbations grow exponentially in time, and the other in which disturbances are stationary. These results agree with those derived by D’yakov and Kontorovich (by more arduous and somewhat ambiguous means), and serve as an important addendum to our earlier analysis.