The D'yakov-Kontorovich Instability of Shock Fronts in Condensed Media

The studies of shock compression of condensed media and shock-front stability started simultaneously in the 1940s within nuclear weapons projects. Notwithstanding the impressive progress made in both fields since then, the fundamental shock-front instability theoretically discovered by D'yakov (1954) and Kontorovich (1957) (DK) in the USSR still challenges our understanding of shock compression in condensed media. DK predicted non-decaying oscillations of an isolated planar shock front, accompanied by spontaneous acoustic emission. This subtle effect is only possible under strict constraints on the equation of state and shock strength resulting in a specific shape of the Hugoniot curve. It took 20 years since the DK discovery to find realistic shock-compression conditions for its manifestation (in copper, Bushman, 1976) and many more years till its first numerical demonstration (in van der Waals fluid, Bates & Montgomery, 2000). The discussion about the nature of this elusive phenomenon continues in the literature to this day, still bringing unexpected findings. We present a theoretical stability analysis for an expanding accretion shock applicable to an arbitrary equation of state and shock strength. An explicit dispersion relationship for the perturbation growth rate is given.