Nonlinear growth of the converging Richtmyer-Meshkov instability in a conventional shock tube

In convergent geometry, the Bell-Plesset (BP) effects modify the growth of hydrodynamic instability in comparison with the planar geometry. They account for acceleration, convergence of the flow, and compressibility of the fluids. To study these effects, the Richtmyer-Meshkov (RM) instability is examined in cylindrical geometry through shock tube experiments. To ease comparisons with models, the canonical single-mode sinusoidal perturbation at the gas interface is considered. The experimental results display a linear timedependent growth of the amplitude of the instability. First, by cross-checking experiments and numerical simulations with the Hesione code, this peculiar growth for convergent geometry is confirmed. Second, we theoretically explain these results. We derive a new model for the growth of the perturbation in the linear regime of the instability for compressible fluids. Then, it is used to initiate a weakly nonlinear model. This model demonstrates that the linear time-dependent growth of the studied RM instability is due to the nonlinear saturation of the destabilizing BP effects at the interface. This study indicates the importance of taking into account even a slight deceleration of the interface and the compressibility of fluids by correctly describing the background velocity field, which is generated by converging shock waves.