Instabilities of shock and detonation waves

It is shown that the compatibility conditions for spontaneous splitting of a single shock into two shocks plus a contact discontinuity are satisfied whenever the instability limits derived by D’yakov, Kontorovich, and Erpenbeck are violated. They can be stated as −1<j2 (dV/dP)H <(1−M2−M2V0/V)(1−M2+M2V0/V)−1 <1+2M, where j2=( P−P0)/(v0−v), M=‖(D−u)/c‖, and the derivative is along the Hugoniot curve. One-dimensional splitting can occur when the outer limits are exceeded. Violation of the intermediate upper limit (Kontorovich condition) admits spontaneous generation of steady transverse waves similar to those often observed in detonations.