Mechanism and modelling of the secondary baroclinic vorticity in the Richtmyer–Meshkov instability

Abstract

Abstract

Effects of the secondary baroclinic vorticity on the energy cascade in the Richtmyer–Meshkov instability

“…The consistent results in RMI and DDM demonstrate that the present multi-mode RMI with a weak incident shock is mainly driven by the synergistic effect of the density difference across the perturbed interface and the PBV (see § § 4.2 and 4.3 in Peng et al 2021), whereas the pressure perturbation from distorted waves only plays a minor role in reducing the growth rate (e.g. Velikovich et al 2000) and their effect on the PBV distribution is neglected.…”

“…t S = 0.11 ms t = 1 ms t * = 2 ms t = 5 ms t = 10 ms t = 20 ms k −5/3 k −3/2 10 0 10 1 10 2 10 0 10 1 10 2 Xiao 2016), is satisfied with N = 256, where k max = 3/Δx is the maximum wavenumber (see Yeung & Pope 1989) and η = ( ν 3 M / M ) 1/4 is the Kolmogorov length scale with the mixture kinematic viscosityν =μ/ρ and the local dissipation rate = (τ : S)/ρ. Moreover, the resolution N = 256 also satisfies the criterion proposed by Groom & Thornber (2019, 2021 based on the initial Reynolds number.…”

“…Groom & Thornber 2021) and the gird convergence test, while it is downgraded to an implicit large-eddy simulation if the flow field is under-resolved because the LAD can serve as a subgrid-scale model (Cook 2007). The HOTS has been validated to be stable and reasonably accurate for DNS of RMI at M S ≤ 1.6 (Liu & Xiao 2016;Peng et al 2021), and M S can be further increased (e.g. M S ≥ 2) by using the shock-resolved technique to solve the NS equations (see Kramer et al 2010).…”

“…In the RMI with a single-mode light/heavy interface accelerated by a weak incident shock, Peng et al (2021) demonstrated that the instability and asymmetric growth of the interface are mainly caused by the density difference and the PBV, whereas the pressure perturbation from distorted waves can be neglected. To distinguish the role of each factor in the present multi-mode RMI, we apply two vorticity-based simplified models, the double-density model (DDM) and the single-density model (SDM), which were developed in Peng et al (2021).…”

“…The interfacial evolution is initiated by the primary baroclinic vorticity (PBV) which is generated by the interaction of the shock and interface. Subsequently, the secondary baroclinic vorticity (SBV), produced by the interaction of the interface and vortex-induced velocity (see Zabusky et al 2003), is found to be important for the interfacial growth in the single-mode RMI (see Peng et al 2021). On the other hand, the effect of the SBV on the generation of small-scale vortical structures and the energy cascade in turbulent mixing has not been elucidated and quantified.…”