Effect of initial perturbation amplitude on Richtmyer-Meshkov flows induced by strong shocks

Abstract

We systematically study the effect of the initial perturbation on Richtmyer-Meshkov (RM) flows induced by strong shocks in fluids with contrasting densities. Smooth Particle Hydrodynamics simulations are employed. A broad range of shock strengths and density ratios is considered. The amplitude of the initial single mode sinusoidal perturbation of the interface varies from 0% to 100% of its wavelength. The simulations results are compared, wherever possible, with four rigorous theories, and with other experiments and simulations, achieving good quantitative and qualitative agreement. Our study is focused on early time dynamics of the Richtmyer-Meshkov instability (RMI). We analyze the initial growth-rate of RMI immediately after the shock passage, when the perturbation amplitude increases linearly with time. For the first time, to the authors' knowledge, we find that the initial growth-rate of RMI is a non-monotone function of the initial perturbation amplitude, thus restraining the amount of energy that can be deposited by the shock at the interface. The maximum value of the initial growth-rate depends on the shock strength and the density ratio, whereas the corresponding value of the initial perturbation amplitude depends only slightly on the shock strength and density ratio.

On the Rayleigh-Taylor unstable dynamics of three-dimensional interfacial coherent structures with time-dependent acceleration

“…Our theory finds that in RMI with variable acceleration, nonlinear bubbles decelerate and flatten. This behaviour is observed in experiments and simulations, in agreement with our results 5,6,[14][15][16][17][18][19][20] . According to our theory, in nonlinear RMI with variable acceleration, flattened bubbles move more quickly and decelerate more rapidly when compared to curved bubbles because since the bubble velocity decays with time as C/kt, the deceleration is − C/kt 2 .…”

Interfacial instability at a heavy/light interface induced by rarefaction waves

“…In contrast, as the shock wave strength increases, i.e. M i increases, the dimensionless interface amplitude growth becomes smaller, which agrees with previous studies (Rikanati et al 2003;Stanic et al 2012;Dell, Stellingwerf & Abarzhi 2015). For the RM instability with a strong shock, the high pressure behind the shock front inhibits bubble growth (Rikanati et al 2003).…”

“…For the RM instability with a strong shock, the high pressure behind the shock front inhibits bubble growth (Rikanati et al 2003). Meanwhile, after the passage of the shock, a significant part of the shock energy goes to the compression and background motion of the fluids, and only a small part of it is available for interfacial mixing (Stanic et al 2012;Dell et al 2015). Third, the interface amplitude growth under the rarefaction wave condition is always larger than that under the shock wave condition.…”

Evolution of shock-accelerated heavy gas layer

“…The second interface growth rate is overestimated by the MIK model because the amplitude of the second interface after the TS 1 impact is smaller than the initial one. For the other three cases, the MIK model overestimates the first interface growth, which is ascribed to ignoring the secondary compression effect because of the high initial amplitude of the first interface (Rikanati et al 2003;Jourdan & Houas 2005;Dell, Stellingwerf & Abarzhi 2015). For the US case, the MIK model underestimates the second interface growth due to ignoring the weak vorticity induced by the rippled 886 A7-14 Y. Liang, L. Liu, Z. Zhai, T. Si and C.-Y.…”