D'yakov-Kontorovich instability of expanding shock waves

The D’yakov-Kontorovich (DK) instability of a steady planar shock front theoretically discovered in the 1950s is the hardest-to-detect and the least understood among the hydrodynamic instabilities. At certain combinations of the EoS and shock-loading conditions, non-decaying oscillations of an isolated shock front are generated, accompanied by a spontaneous acoustic emission (SAE). We report an analytical study of the DK instability for spherical and cylindrical steadily expanding accretion shock waves. The acoustic feedback from the center or axis of symmetry changes the perturbation dynamics entirely compared to the classical isolated-shock case. When the DK instability emission conditions are satisfied, shock-front perturbations grow as a power of time. Shock divergence is a stabilizing factor: only high modes are unstable. In Bates and Montgomery’s example for a van der Waals fluid, cylindrical and spherical expanding shocks become unstable at mode numbers m>148 and l>213, respectively. Our analytical results constitute a challenging verification test for hydrocodes used in inertial confinement fusion.