## A New Upper Bound for the Largest Growth Rate of Linear Rayleigh--Taylor Instability. (arXiv:1901.11012v1 [math-ph])

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 \$\Lambda\$ is proved under the instability condition (i.e., the surface tension coefficient \$\vartheta\$ is less than a threshold \$\vartheta_{\mm{c}}\$) by modified variational method of PDEs. Moreover we find a new upper bound for \$\Lambda\$. In particular, we observe from the upper bound that \$\Lambda\$ decreasingly converges to zero, as \$\vartheta\$ goes from zero to the threshold \$\vartheta_{\mm{c}}\$. The convergence behavior of \$\Lambda\$ mathematically verifies the classical RT instability experiment that the instability growth is limited by surface tension during the linear stage.查看全文

## Solidot 文章翻译

 你的名字 留空匿名提交 你的Email或网站 用户可以联系你 标题 简单描述 内容 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 \$\Lambda\$ is proved under the instability condition (i.e., the surface tension coefficient \$\vartheta\$ is less than a threshold \$\vartheta_{\mm{c}}\$) by modified variational method of PDEs. Moreover we find a new upper bound for \$\Lambda\$. In particular, we observe from the upper bound that \$\Lambda\$ decreasingly converges to zero, as \$\vartheta\$ goes from zero to the threshold \$\vartheta_{\mm{c}}\$. The convergence behavior of \$\Lambda\$ mathematically verifies the classical RT instability experiment that the instability growth is limited by surface tension during the linear stage.
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