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

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 in...

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Published inEuropean journal of mechanics, B, Fluids Vol. 91; pp. 141 - 151
Main Authors Shin, Suyeon, Sohn, Sung-Ik, Hwang, Woonjae
Format Journal Article
LanguageEnglish
Published Elsevier Masson SAS 01.01.2022
Subjects
Mixing
Rayleigh–Taylor instability
Surface tension
Vortex sheet
Mixing
Surface tension
Rayleigh–Taylor instability
Vortex sheet
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Abstract 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.
AbstractList 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.
Author Shin, Suyeon
Sohn, Sung-Ik
Hwang, Woonjae
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  givenname: Woonjae
  surname: Hwang
  fullname: Hwang, Woonjae
  organization: Division of Applied Mathematical Sciences, Korea University, Sejong 30019, Republic of Korea
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Surface tension
Rayleigh–Taylor instability
Vortex sheet
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Snippet 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...
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SubjectTerms Mixing
Rayleigh–Taylor instability
Surface tension
Vortex sheet
Title Numerical simulation of single- and multi-mode Rayleigh–Taylor instability with surface tension in two dimensions
URI https://dx.doi.org/10.1016/j.euromechflu.2021.10.005
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