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arXiv · 1109.5657

The viscous surface-internal wave problem: nonlinear Rayleigh-Taylor instability

Yanjin Wang·Ian Tice
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Abstract

We consider the free boundary problem for two layers of immiscible, viscous, incompressible fluid in a uniform gravitational field, lying above a rigid bottom in a three-dimensional horizontally periodic setting. The effect of surface tension is either taken into account at both free boundaries or neglected at both. We are concerned with the Rayleigh-Taylor instability, so we assume that the upper fluid is heavier than the lower fluid. When the surface tension at the free internal interface is below a critical value, which we identify, we establish that the problem under consideration is nonlinearly unstable.

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Yanjin Wang, Ian Tice. 2011-09-26. The viscous surface-internal wave problem: nonlinear Rayleigh-Taylor instability. https://arxiv.org/abs/1109.5657

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