Cylindrical effects on Richtmyer-Meshkov instability for arbitrary Atwood numbers in weakly nonlinear regime

Abstract

When an incident shock collides with a corrugated interface separating two fluids of different densities, the interface is prone to Richtmyer-Meshkov instability (RMI). Based on the formal perturbation expansion method as well as the potential flow theory, we present a simple method to investigate the cylindrical effects in weakly nonlinear RMI with the transmitted and reflected cylindrical shocks by considering the nonlinear corrections up to fourth order. The cylindrical results associated with the material interface show that the interface expression consists of two parts: the result in the planar system and that from the cylindrical effects. In the limit of the cylindrical radius tending to infinity, the cylindrical results can be reduced to those in the planar system. Our explicit results show that the cylindrical effects exert an inward velocity on the whole perturbed interface, regardless of bubbles or spikes of the interface. On the one hand, outgoing bubbles are constrained and ingoing spikes are accelerated for different Atwood numbers (A) and mode numbers k 0 . On the other hand, for ingoing bubbles, when jAjk 03=2 . 1, bubbles are considerably accelerated especially at the small jAj and k 0 ; otherwise, bubbles are decelerated. For outgoing spikes, when jAjk 0 & 1, spikes are dramatically accelerated especially at large jAj and k 0 ; otherwise, spikes are decelerated. Furthermore, the cylindrical effects have a significant influence on the amplitudes of the ingoing spike and bubble for large k 0 . Thus, it should be included in applications where the cylindrical effects play a role, such as inertial confinement fusion ignition target design. V C 2012 American Institute of Physics. [http://dx.

Finite-thickness effect of the fluids on bubbles and spikes in Richtmyer–Meshkov instability for arbitrary Atwood numbers

“…A large number of the studies on RMI have been performed, such as some experiments [19] and numerical simulations [20][21][22] on the growth rate, and other theories [23][24][25][26][27][28][29][30][31][32] using different explicit methods. Most of these express great concern over the earlier growth rate of the interface, and with the asymptotic behavior of the RMI interface fingers: bubbles and spikes which are, respectively, formed by the light fluid entering into the heavy one, and by the heavy fluid traveling in the light fluid.…”

“…l with r h (r l ) being the density of the heavy (light) fluid, and t is time. As for detailed discussions of the first three harmonics, see [31].…”