Asymptotic behavior of the Rayleigh-Taylor instability

Laurent Duchemin (1, 2) , Christophe Josserand (2) , Paul Clavin (1)

1 IRPHE - Institut de Recherche sur les Phénomènes Hors Equilibre
2 LMM - Laboratoire de modélisation en mécanique

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 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

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Laurent Duchemin, Christophe Josserand, Paul Clavin. Asymptotic behavior of the Rayleigh-Taylor instability. 2005 APS Division of Fluid Dynamics - 58th Annual Meeting (DFD05), 2005, Chicago, United States. ⟨hal-00090976⟩