Evaluating the stretching/compression effect of Richtmyer–Meshkov instability in convergent geometries

An asymptotic matching modal model is established based on the singular perturbation method for predicting mode evolution in single- and dual-mode interfaces accelerated by a shock wave. The startup process is incorporated into the model to provide a complete description of the mode evolution after the shock impact. Through considering the feedback from high-order harmonic to the third-order harmonic, the model accuracy is improved and the model divergence is prevented. In addition, the model can evaluate the mutual-coupling effect on the amplitude variations of high-order harmonics besides the ‘beat modes’. To validate the model, experiments on both light–heavy and heavy–light interfaces subject to a shock wave are conducted, and both single- and dual-mode interfaces formed by the soap-film technique are involved. The interface profiles extracted from mode decomposition and predicted by the model show high consistency with the experimental counterparts. Good agreement of the mode amplitude growths between the experiments and theoretical predictions shows the superiority of the model, especially for the heavy–light interface.

Asymptotic matching modal model on Richtmyer–Meshkov instability

Li,

Chen,

Zhai

et al. 2024

Impact of axial strain on linear, transitional and self-similar turbulent mixing layers

Pascoe,

Groom,

Youngs

et al. 2024

In convergent geometry, the effect of convergence and compression on the Rayleigh–Taylor instability (RTI) and Richtmyer–Meshkov instability (RMI) modifies the growth rate and behaviour of the instabilities. In order to better understand how compression/expansion caused by axial strain rates (i.e. strain rates normal to the interface) change the instability dynamics, axial strain rates are applied to RMI in planar geometry, isolated from the effects of convergence. Potential flow theory for the linear regime shows the growth rate of the instability is modified to include the background velocity difference of the instability's width. Resolved two-dimensional simulations of single-mode RMI showed the potential flow model is accurate whilst the amplitude is small compared with the wavelength. The application of strain rate to an RMI-induced mixing layer was investigated using three-dimensional implicit large eddy simulations (ILES) of the quarter-scale $\theta$ -group case by Thornber et al. (Phys. Fluids, vol. 29, 2017, 105107). Whilst the background strain rate contributed to the mixing layer's growth, it was to a smaller extent than expected. The shear production of axial turbulent kinetic energy from the strain rate modified the rate of bulk entrainment, affecting the mixing layer's growth and mixedness, such that the strained simulations no longer attained the same self-similar state. The capability of the buoyancy-drag model by Youngs & Thornber (Physica D, vol. 410, 2020, 132517) to predict the mixing layer width was investigated, using a model calibrated to the unstrained case. New terms were introduced into the buoyancy-drag model, which correspond to the shear production of turbulent kinetic energy.

Instability evolution on a shock-accelerated cylindrical fluid layer with arbitrary Atwood numbers

Yuan,

Zhao,

Liu

et al. 2024

Developing a model to describe the shock-accelerated cylindrical fluid layer with arbitrary Atwood numbers is essential for uncovering the effect of Atwood numbers on the perturbation growth. The recent model (J. Fluid Mech., vol. 969, 2023, p. A6) reveals several contributions to the instability evolution of a shock-accelerated cylindrical fluid layer but its applicability is limited to cases with an absolute value of Atwood numbers close to $1$ , due to the employment of the thin-shell correction and interface coupling effect of the fluid layer in vacuum. By employing the linear stability analysis on a cylindrical fluid layer in which two interfaces separate three arbitrary-density fluids, the present work generalizes the thin-shell correction and interface coupling effect, and thus, extends the recent model to cases with arbitrary Atwood numbers. The accuracy of this extended model in describing the instability evolution of the shock-accelerated fluid layer before reshock is confirmed via direct numerical simulations. In the verification simulations, three fluid-layer configurations are considered, where the outer and intermediate fluids remain fixed and the density of the inner fluid is reduced. Moreover, the mechanisms underlying the effect of the Atwood number at the inner interface on the perturbation growth are mainly elucidated by employing the model to analyse each contribution. As the Atwood number decreases, the dominant contribution of the Richtmyer–Meshkov instability is enhanced due to the stronger waves reverberated inside the layer, leading to weakened perturbation growth at initial in-phase interfaces and enhanced perturbation growth at initial anti-phase interfaces.