International EMMI Workshop on Plasma Physics at FAIR, GSI Darmstadt, June 21 - 23, 2017

A physical model has been developed for the linear Rayleigh-Taylor instability of a finite thickness elastic slab that lays on the top a semi-infinite ideal fluid. The model includes the non-ideal effects of elasticity as boundary conditions at the top and bottom interfaces of the slab, and takes also into account the finite transit time of the elastic waves across the slab thickness. For Atwood number AT = 1 the asymptotic growth rate is found to be in excellent agreement with the exact solution by Plohr and Sharp [1], and a physical explanation is given for the reduction of the stabilizing effectiveness of the elasticity for the thinner slabs. The feed-through factor is also calculated. Figure 1: Asymptotic dimensionless growth rate σ = γ /√k0g as a function of the dimensionless wave number κ = k/k0 for several values of a = k0h, and AT =1. Dots for a ≤ 1are calculated with the theory of Ref.[1], and for a ≫ 1 Ref.[2] has been used. References [1] B. J. Plohr and D. H. Sharp, Z. angew. Math. Phys. 49, 786 (1998), [2] G. Terrones, Phys. Rev. E 71, 036306 (2005).