Shock induced turbulence in composite materials at moderate Reynolds numbers

Numerical simulation is used to study the turbulence generated by the passage of strong shocks (typical Mach number 7.3) through an inhomogeneous fluid at moderate Reynolds numbers. Before passage of the shock, the material consists of mass-density inhomogeneities embedded in a background fluid. The entire system is initially at uniform temperature, pressure, and number density, with the nonuniform mass density resulting from differing mass species in different regions. In the present application, the substances are treated as ideal gases, though in the motivating physical problems they are more complex materials. The shock retains its identity and a sharp front, but leaves behind it a turbulent state whose locally averaged properties only slowly become spatially uniform. The shock acquires a turbulent “thickness” (the linear dimension of the nonuniform region behind the shock front) that seems ultimately damped by viscous and thermally conducting properties that are dependent on transport coefficients and (highly uncertain) Reynolds numbers. Typically, the turbulence is highly compressible, with comparable mean divergences and curls in the velocity field, and fractional rms density fluctuations of the order of 0.25 in the parameter ranges studied. The rms vorticity generated can be estimated reasonably well from dimensional considerations. The effect of the high density inhomogeneities is primarily to create a wide region of compressible turbulence behind the shock. The inhomogeneities create both a succession of reflected shocks and considerable vorticity.