Direct numerical simulations of multi-mode immiscible Rayleigh-Taylor instability with high Reynolds numbers

Abstract

In this paper, we conduct the high-resolution direct numerical simulations of multimode immiscible Rayleigh-Taylor instability (RTI) with a low Atwood number (At = 0.1) using an improved phase field lattice Boltzmann method. The effect of the Reynolds number on the evolutional interfacial dynamics and bubble/spike amplitudes is first investigated by considering its wide range, from 100 up to a high value of 30 000. The numerical results show that, for sufficiently large Reynolds numbers, a sequence of distinguishing stages in the immiscible RTI can be observed, which includes the linear growth, saturated velocity growth, and chaotic development stages. At the late stage, the RTI induces a complex topology structure of the interface and a mass of dissociative drops can be significantly observed in the system. The accelerations of the bubble and spike front are also measured, and it is reported that their normalized values at the late time are, respectively, approximate to the constant values of around 0.025 and 0.027, exhibiting a terminally quadratic growth. As the Reynolds number is reduced to small ones, the multiple disturbances of the RTI are found to merge into a larger one at the initial stage. Then, the evolutional interfaces display the patterns familiar from the single-mode RTI. The phase interfaces in the whole process become very smooth without the appearance of the breakup phenomenon, and the spike and bubble velocities at the late time approach constant values. Furthermore, we also analyze the effects of the initial conditions in terms of the perturbation wavelength and amplitude, and it is found that the instability undergoes a faster growth at the intermediate stage for a larger wavelength, while the late-time bubble and spike growth rates are insensitive to the changes of the initially perturbed wavelength and amplitude.