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

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. It is found that the initial perturbation has a significant influence on the evolution of RTI. The sharper the interface, the faster the growth of bubble or spike. While the influence of initial interface shape on KHI evolution can be ignored. Based on the mean heat flux strength D-3,D-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 theta(1) and the middle contact angle theta(2). The increase of theta(1) and the decrease of theta(2) have opposite effects on the critical velocity. When theta(2) remains roughly unchanged at 90 degrees,if theta(1) is greater than 90 degrees (such as the parabolic interface), the critical shear velocity increases with the increase of theta(1), and the ellipse perturbation is its limiting case; If theta(1) is less than 90 degrees (such as the inverted parabolic and the inverted ellipse disturbances), the critical shear velocities are basically the same, which is less than that of the sinusoidal and sawtooth disturbances. The influence of inverted parabolic and inverted ellipse perturbations on the transition point of the RTKHI system is greater than that of other interfaces: (i) For the same amplitude, the smaller the contact angle theta(1), the later the transition point appears; (ii) For the same interface morphology, the disturbance amplitude increases, resulting in a shorter duration of the linear growth stage, so the transition point is greatly advanced.

Automated summary

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. It is found that the initial perturbation significantly influences the evolution of RTI, while the influence on KHI can be ignored. The study on RTKHI focuses on the main mechanism in the early stage and the transition point from KHI-like to RTI-like behavior. The shape of the initial interface and the inverted parabolic and inverted ellipse disturbances have a major impact on the RTKHI system.