Asymptotic spike evolution in Rayleigh-Taylor instability

Paul Clavin (1) , Forman A. Williams (2)

1 IRPHE - Institut de Recherche sur les Phénomènes Hors Equilibre
2 CER - Center for Energy Research, Department of Mechanical and Aerospace Engineering

An analytical study of the asymptotic behaviour of descending spikes is carried out for the idealized limit of an inviscid, incompressible fluid without surface tension, bounded by a vacuum. A self-similar solution is obtained for the shape of the free surface at the spike tip, yielding the evolution in time of the surface curvature there. The approach to free-fall acceleration is shown to follow an inverse power law in time. Results are given for both planar (two-dimensional) and axisymmetric spikes. Potential areas of application include ablation-front dynamics in inertial-confinement fusion.

Paul Clavin, Forman A. Williams. Asymptotic spike evolution in Rayleigh-Taylor instability. Journal of Fluid Mechanics, 2005, 525, pp.105 - 113. ⟨10.1017/S0022112004002630⟩. ⟨hal-00014917⟩