Theory of the corrugation instability of a piston-driven shock wave

We analyze the two-dimensional stability of a shock wave driven by a steadily moving corrugated piston in an inviscid fluid with an arbitrary equation of state. For h <= -1 or h > h(c), where h is the D'yakov parameter and hc is the Kontorovich limit, we find that small perturbations on the shock front are unstable and grow-at first quadratically and later linearly-with time. Such instabilities are associated with nonequilibrium fluid states and imply a nonunique solution to the hydrodynamic equations. The above criteria are consistent with instability limits observed in shock-tube experiments involving ionizing and dissociating gases and may have important implications for driven shocks in laser-fusion, astrophysical, and/or detonation studies.