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Effects of the initial perturbations on the Rayleigh-Taylor-Kelvin-Helmholtz instability system

In the paper, the effects of initial perturbations on the Rayleigh-Taylor instability (RTI), Kelvin-Helmholtz instability (KHI), and the coupled Rayleigh-Taylor-Kelvin-Helmholtz instability (RTKHI) systems are investigated using a multiple-relaxation-time discrete Boltzmann model. Six different perturbation interfaces are designed to study the effects of the initial perturbations on the instability systems. Based on the mean heat flux strength $D_{3,1}$, the effects of initial interfaces on the coupled RTKHI are examined in detail. The research is focused on two aspects: (i) the main mechanism in the early stage of the RTKHI, (ii) the transition point from KHI-like to RTI-like for the case where the KHI dominates at earlier time and the RTI dominates at later time. It is found that the early main mechanism is related to the shape of the initial interface, which is represented by both the bilateral contact angle $θ_{1}$ and the middle contact angle $θ_{2}$. The influence of inverted parabolic and inverted ellipse perturbations ($θ_{1}<90$) on the transition point of the RTKHI system is greater than that of other interfaces.