Numerical analysis of coupled Kelvin–Helmholtz and Rayleigh–Taylor instability on inclined walls

Abstract

The front tracking method was used to study the 2D Kelvin–Helmholtz (K–H) instability on an inclined wall for three-component immiscible fluids. Coupled effects between K–H instability and Rayleigh–Taylor (R–T) instability were studied by analyzing the effect of inclination angle, Atwood number (At), and Richardson number (Ri) on interface evolution. The results show that the coupling of R–T instability has an important influence on the development of K–H instability. The R–T instability first affects the lower interface and then the upper interface at different inclination angles, and it is also observed that the critical time of the coupled effect is earlier with an inclined wall. The R–T instability promotes the development of upper and lower interfaces at different At numbers. In addition, the billow height increases with the increase in At number and the influence of R–T instability on the upper interface can be neglected when the dimensionless time is less than critical time t = 0.6. The R–T instability has little effect on the different surface tension in terms of Richardson number (Riσ).