Morphological and non-equilibrium analysis of coupled Rayleigh-Taylor-Kelvin-Helmholtz instability

In this paper, the coupled Rayleigh-Taylor-Kelvin-Helmholtz instability (RTI, KHI, and RTKHI, respectively) system is investigated using a multiple-relaxation-time discrete Boltzmann model. Both the morphological boundary length and thermodynamic non-equilibrium (TNE) strength are introduced to probe the complex configurations and kinetic processes. In the simulations, RTI always plays a major role in the later stage, while the main mechanism in the early stage depends on the comparison of buoyancy and shear strength. It is found that both the total boundary length L of the condensed temperature field and the mean heat flux strength D_3,1 can be used to measure the ratio of buoyancy to shear strength and to quantitatively judge the main mechanism in the early stage of the RTKHI system. Specifically, when KHI (RTI) dominates, L^KHI > L^RTIL^KHI < L^RTI (D_3,1^{K H I}>D_3,1^{R T I}) D_3,1^{K H I}<D_3,1^{R T I} ; when KHI and RTI are balanced, L^KHI = L^RTI, D_3,1^{K H I}=D_3,1^{R T I}, where the superscript "KHI (RTI)" indicates the type of hydrodynamic instability. It is interesting to find that (i) for the critical cases where KHI and RTI are balanced, both the critical shear velocity u_C and Reynolds number Re show a linear relationship with the gravity/acceleration g; (ii) the two quantities, L and D_3,1, always show a high correlation, especially in the early stage where it is roughly 0.999, which means that L and D_3,1 follow approximately a linear relationship. The heat conduction has a significant influence on the linear relationship. The second set of findings are as follows: For the case where the KHI dominates at earlier time and the RTI dominates at later time, the evolution process can be roughly divided into two stages. Before the transition point of the two stages, L^RTKHI initially increases exponentially and then increases linearly. Hence, the ending point of linear increasing L^RTKHI can work as a geometric criterion for discriminating the two stages. The TNE quantity, heat flux strength D_3,1^{R T K H I}, shows similar behavior. Therefore, the ending point of linear increasing D_3,1^{R T K H I} can work as a physical criterion for discriminating the two stages.