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

2019/01/30 by Dou, Changsheng, Wang, Jialiang, Wang, Weiwei
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1901.11012

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 ϑ is less than a threshold ϑ_{\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 ϑ goes from zero to the threshold ϑ_{\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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