Oscillations of a standing shock wave generated by the Richtmyer-Meshkov instability

In a typical Richtmyer-Meshkov experiment a fast moving flat shock strikes a stationary perturbed interface between fluids A and B creating a transmitted and a reflected shock, both of which are perturbed. We propose shock tube experiments in which the reflected shock is stationary in the laboratory. Such a standing perturbed shock undergoes well-known damped oscillations. We present the conditions required for producing such a standing shock wave, which greatly facilitates the measurement of the oscillations and their rate of damping. We define a critical density ratio R-critical, in terms of the adiabatic indices of the two fluids, and a critical Mach number M-s(critical) of the incident shock wave, which produces a standing reflected wave. If the initial density ratio R of the two fluids is less than R-critical then a standing shock wave is possible at M-s = M-s(critical) . Otherwise a standing shock is not possible and the reflected wave always moves in the direction opposite the incident shock. Examples are given for present-day operating shock tubes with sinusoidal or inclined interfaces. We consider the effect of viscosity, which affects the damping rate of the oscillations. We point out that nonlinear bubble and spike amplitudes depend relatively weakly on the viscosity of the fluids and that the interface area is a better diagnostic.