Hydrodynamic instabilities of two successive slow/fast interfaces induced by a weak shock

Abstract

Shock-induced instability developments of two successive interfaces have attracted much attention, but remain a difficult problem to solve. The feedthrough and reverberating waves between two successive interfaces significantly influence the hydrodynamic instabilities of the two interfaces. The evolutions of two successive slow/fast interfaces driven by a weak shock wave are examined experimentally and numerically. First, a general one-dimensional theory is established to describe the movements of the two interfaces by studying the rarefaction waves reflected between the two interfaces. Second, an analytical, linear model is established by considering the arbitrary wavenumber and phase combinations and compressibility to quantify the feedthrough effect on the Richtmyer–Meshkov instability (RMI) of two successive slow/fast interfaces. The feedthrough significantly influences the RMI of the two interfaces, and even leads to abnormal RMI (i.e. phase reversal of a shocked slow/fast interface is inhibited) which is the first observational evidence of the abnormal RMI provided by the present study. Moreover, the stretching effect and short-time Rayleigh–Taylor instability or Rayleigh–Taylor stabilisation imposed by the rarefaction waves on the two interfaces are quantified considering the two interfaces’ phase reversal. The conditions and outcomes of the freeze-out and abnormal RMI caused by the feedthrough are summarised based on the theoretical model and numerical simulation. A specific requirement for the simultaneously freeze-out of the instability of the two interfaces is proposed, which can potentially be used in the applications to suppress the hydrodynamic instabilities.

Mode coupling between two different interfaces of a gas layer subject to a shock

“…Due to the very short durations of the waves interacting with the interfaces, the Dirac -function is always used to model the shock impacting the gas layer (Jacobs et al. 1995; Liang & Luo 2023 a ). Therefore, the accelerations and can be expressed as where , and have been defined in (3.1).…”

“…For the second interface, the jump velocities induced by the transmitted shock (TS 1 ) and the compression waves (CW) are u 2 and u C , respectively. Due to the very short durations of the waves interacting with the interfaces, the Dirac δ-function is always used to model the shock impacting the gas layer (Jacobs et al 1995;Liang & Luo 2023a). Therefore, the accelerations g 1 and g 2 can be expressed as…”

“…2000) to verify the vortex model. Recently, the soap-film technique was used widely in creating a gas layer, and extensive studies have been conducted (Liang & Luo 2021, 2023 a , b ; Zhang et al. 2023), focusing on the effects of initial amplitude, width of the gas layer, and perturbation phase on a fluid layer development.…”

Hydrodynamic instabilities of a dual-mode air–SF6 interface induced by a cylindrically convergent shock

“…2020 b ; Liang et al. 2020; Liang 2022 b ; Liang & Luo 2023). A comprehensive review of the numerical scheme and its extensive applications was recently reported by Jiang, Wen & Zhang (2020).…”

“…The contact discontinuity restoring Harten-Lax-van Leer contact Riemann solver (Toro, Spruce & Speares 1994) is used to determine the numerical fluxes between the conservation elements. The use of this scheme in capturing shocks and details of complex flow structures for the RM instability issues and shock-droplet interactions have been well validated Guan et al 2018;Fan et al 2019;Zhai et al 2017Zhai et al , 2019bZhou et al 2020b;Liang et al 2020;Liang 2022b;Liang & Luo 2023). A comprehensive review of the numerical scheme and its extensive applications was recently reported by Jiang, Wen & Zhang (2020).…”