Numerical simulation of single- and multi-mode Rayleigh–Taylor instability with surface tension in two dimensions

• Published in: European journal of mechanics, B, Fluids Vol. 91; pp. 141 - 151
• Main Authors: Shin, Suyeon, Sohn, Sung-Ik, Hwang, Woonjae
• Format: Journal Article
• Language: English
• Published: Elsevier Masson SAS 01.01.2022
• Subjects: Mixing; Rayleigh–Taylor instability; Surface tension; Vortex sheet; Mixing; Surface tension; Rayleigh–Taylor instability; Vortex sheet
• ISSN: 0997-7546; 1873-7390
• DOI: 10.1016/j.euromechflu.2021.10.005

In this paper, we study the long-time evolutions of the single- and multi-mode Rayleigh–Taylor instability with surface tension in two dimensions by using the vortex sheet model. Applying a spectrally accurate numerical method, we investigate the effects of surface tension and density jump on the instability in various regimes of parameters. Complex phenomena of pinching, capillary waves, elongation, and roll-up appear at the interfaces. For a single-mode interface, surface tension retards the growths of bubble and spike. The effect of surface tension on the bubble and spike velocity is generally small but is large for a spike of an infinite density ratio. For multi-mode interfaces, we focus on an infinite density ratio. We show that bubbles grow with the scaling law h=αAgt2 even in the presence of surface tension, while spikes follow the scaling law weakly. It is found that both the growth rates of bubbles and spikes decrease with surface tension and the growth rate of spikes decreases larger than that of bubbles. The growth rate of the bubble front is in agreements with results of previous numerical simulations and experiments. •The long-time evolution of Rayleigh–Taylor instability with surface tension is studied.•A spectrally accurate method based on the vortex sheet model is used for computations.•For a single-mode interface, surface tension retards the growths of bubble and spike.•For multi-mode interfaces, the growth rates of bubbles and spikes decrease with surface tension.