Effect of shock-generated turbulence on the Hugoniot jump conditions

Interaction of a shock wave with preshock random density nonuniformities is known to generate turbulence in the postshock flow. The turbulent motion, in turn, modifies the shock jump conditions. As first detected in the simulations by Hazak et al. [Phys. Plasmas 5, 4357 (1998)], shock compression of a deuterium-filled foam is less than that predicted for a uniform medium of the same average density. Exact analytical small-amplitude theory of this shock undercompression effect is reported, and explicit formulas for the turbulent corrections to the strong-shock Hugoniot jump conditions are presented.