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When a planar shock wave interacts with a random pattern of pre-shock densitynon-uniformities, it generates an anisotropic turbulent velocity/vorticityfield. This turbulence plays an important role at the early stages of themixing process in the compressed fluid. This situation emerges naturally inshock interaction with weakly inhomogeneous deuterium-wicked foam targets inInertial Confinement Fusion (ICF) and with density clumps/clouds inastrophysics. We present an exact small-amplitude linear theory describing suchinteraction. It is based on the exact theory of time and space evolution of theperturbed quantities behind a corrugated shock front for a single-modepre-shock non-uniformity. Appropriate mode averaging in 2D results in closedanalytical expressions for the turbulent kinetic energy, degree of anisotropyof velocity and vorticity fields in the shocked fluid, shock amplification ofthe density non-uniformity, and sonic energy flux radiated downstream. Theseexplicit formulas are further simplified in the important asymptotic limits ofweak/strong shocks and highly compressible fluids. A comparison with therelated problem of a shock interacting with a pre-shock isotropic vorticityfield is also presented.

Turbulence generation by a shock wave interacting with a random density inhomogeneity field