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In the paper, the effects of initial perturbations on the Rayleigh-Taylorinstability (RTI), Kelvin-Helmholtz instability (KHI), and the coupledRayleigh-Taylor-Kelvin-Helmholtz instability (RTKHI) systems are investigatedusing a multiple-relaxation-time discrete Boltzmann model. Six differentperturbation interfaces are designed to study the effects of the initialperturbations on the instability systems. Based on the mean heat flux strength$D_{3,1}$, the effects of initial interfaces on the coupled RTKHI are examinedin detail. The research is focused on two aspects: (i) the main mechanism inthe early stage of the RTKHI, (ii) the transition point from KHI-like toRTI-like for the case where the KHI dominates at earlier time and the RTIdominates at later time. It is found that the early main mechanism is relatedto the shape of the initial interface, which is represented by both thebilateral contact angle $\theta_{1}$ and the middle contact angle $\theta_{2}$.The influence of inverted parabolic and inverted ellipse perturbations($\theta_{1}<90$) on the transition point of the RTKHI system is greater thanthat of other interfaces.

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