Late-time description of immiscible Rayleigh–Taylor instability: A lattice Boltzmann study
Hong Liang, Zhenhua Xia, Haowei Huang
Abstract
In this paper, the late-time description of immiscible Rayleigh–Taylor instability (RTI) in a long duct is numerically investigated over a comprehensive range of the Reynolds numbers (1≤Re≤10 000) and Atwood numbers (0.05≤A≤0.7) using the mesoscopic lattice Boltzmann method on high-resolution meshes. It is found that the instability with a high Reynolds number undergoes a sequence of distinguishing stages, which are termed as the linear growth, saturated velocity growth, reacceleration and chaotic development stages. The dynamics of the spike and bubble from the saturated velocity growth stage to the final chaotic development stage are studied, and the growth rates of the spike and bubble during the late-time chaotic stage are analyzed quantitatively by using five popular statistical methods. When Re is gradually reduced, some later stages, such as the chaotic and reacceleration stages, cannot successively be reached and the phase interfaces in the evolutional process become relatively smooth. The influence of A on the late-time RTI development at a high Reynolds number is also examined. It is shown that the late-time growth rate of the spike will overall increase with A, while the growth rate of the bubble is approximately constant, being around 0.0215.