444 / 2019-03-13 09:45:14

Mode Coupling effect on Converging Richtmyer-Meshkov Instability

Richtmyer-Meshkov,Shock wave,Mode Coupling

全体主题 > Interface Instabilities at Extremes

Richtmyer-Meshkov instability (RMI) occurs as a shock wave strikes a contact interface separating two fluids of different properties. After the shock impact, the perturbations on the interface first grow linearly, then nonlinearly, and finally trigger a flow transition to turbulent mixing. Over the past decades, the RMI has been a subject of intensive research due to its significance in scientific research and crucial role in practical applications such as inertial confinement fusion (ICF). Previous studies on RMI mainly considered the planar shock-induced case, and several review articles have been published. Nevertheless, in realities, the RMI usually takes place in a curved or convergent geometry. As compared to the planar RMI, the instability in a convergent geometry is much more complicated due to the presence of Bell-plesset (BP) and Rayleigh-Taylor (RT) effects. So far, there is no published research on the converging RMI of a multi-mode interface, which motivates the present study. In this work, the instability of a dual-mode interface impacted by a cylindrically converging shock is simulated by an upwind space-time conservation element and solution element (CE/SE) scheme. The upwind CE/SE scheme inherits most properties of the original CE/SE scheme and further avoids spurious oscillations by breaking the space–time inversion invariance. A series of dual-mode interfaces with different amplitude ratios and phase differences are considered.
Results show that for dual-mode cases the second mode significantly breaks the symmetry of the interface. As a consequence, interpenetrating bubble and spike structures emerge earlier than that of the single-mode case. The distinct nonlinear structures between in-phase and out-of-phase dual-mode cases suggests a significant influence of the initial small second mode on the evolution of the fundamental mode. Interaction of fundamental mode and second perturbation is carefully analyzed through comparing Fast Fourier Transform (FFT) results. It is indicated that each wave grows independently at early stage and then diverge in the nonlinear phase due to the increasingly strong mode coupling effect. For dual-mode interfaces, new harmonics with wave numbers of k_1±k_2 are evidently generated due to the mode coupling, and they greatly inhibit or promote the growth of the fundamental mode. At late stages, the interface undergoes an evident deceleration, which cause an RT stabilization. The promoted fundamental mode suffers a stronger suppression by RT effect while the one suppressed undergoes a much weaker RT effect. Hence, the deviation among three curves in the deceleration phase becomes progressively smaller, which suggests a unique negative feedback mechanism in converging multimode RMI.