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