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arXiv · 1901.11012

A New Upper Bound for the Largest Growth Rate of Linear Rayleigh--Taylor Instability

Changsheng Dou·Jialiang Wang·Weiwei Wang
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Abstract

We investigate the effect of surface tension on the linear Rayleigh--Taylor (RT) instability in stratified incompressible viscous fluids with or without (interface) surface tension. The existence of linear RT instability solutions with largest growth rate $Λ$ is proved under the instability condition (i.e., the surface tension coefficient $\vartheta$ is less than a threshold $\vartheta_{\rm c}$) by modified variational method of PDEs. Moreover we find a new upper bound for $Λ$. In particular, we observe from the upper bound that $Λ$ decreasingly converges to zero, as $\vartheta$ goes from zero to the threshold $\vartheta_{\rm c}$. The convergence behavior of $Λ$ mathematically verifies the classical RT instability experiment that the instability growth is limited by surface tension during the linear stage.

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Changsheng Dou, Jialiang Wang, Weiwei Wang. 2021-02-20. A New Upper Bound for the Largest Growth Rate of Linear Rayleigh--Taylor Instability. https://arxiv.org/abs/1901.11012

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