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Asymptotic behaviour of the Rayleigh--Taylor instability

Laurent Duchemin·Christophe Josserand·Paul Clavin
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Abstract

We investigate long time numerical simulations of the inviscid Rayleigh-Taylor instability at Atwood number one using a boundary integral method. We are able to attain the asymptotic behavior for the spikes predicted by Clavin & Williams\cite{clavin} for which we give a simplified demonstration. In particular we observe that the spike's curvature evolves like $t^3$ while the overshoot in acceleration shows a good agreement with the suggested $1/t^5$ law. Moreover, we obtain consistent results for the prefactor coefficients of the asymptotic laws. Eventually we exhibit the self-similar behavior of the interface profile near the spike.

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Laurent Duchemin, Christophe Josserand, Paul Clavin. 2004-12-19. Asymptotic behaviour of the Rayleigh--Taylor instability. https://doi.org/10.1103/physrevlett.94.224501

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