Freeze-out of the linear Richtmyer-Meshkov instability

When a planar shock refracts a corrugated contact surface separating two fluids with different thermodynamic properties, a transmitted and reflected wavefronts run inside each fluid. Due to the surface ripple, pressure, density and velocity perturbations are generated in both materials. When the fronts separate away, a steady normal velocity develops at the contact surface. For specific choices of the pre-shock parameters, the final value of the normal velocity at the surface ripple may become zero. This effect, known as ``freeze-out'' has been proposed by G.Fraley [Phys. Fluids \textbf{29}, 376 (1986)] and has been later on studied by K. Mikaelian [Phys. Fluids \textbf{6}, 356 (1994)]. We present here an analytical to study freeze-out in both situations of shock and rarefaction reflected at the contact surface. Freeze-out contours are derived as well as the detailed temporal evolution of the pressure and velocity perturbations in linear theory. Weak/strong incident shock limits are discussed. \\[4pt] [1] J. G. Wouchuk and K. Nishihara, Phys. Rev. E \textbf{70}, 026305 (2004).\\[0pt] [2] J. G. Wouchuk and T. Sano, Phys. Rev. E \textbf{91}, 023005 (2015).