Finite-thickness effects on the Rayleigh-Taylor instability in accelerated elastic solids

A physical model has been developed for the linear Rayleigh-Taylor instability of a finite-thickness elastic slab laying on top of a semi-infinite ideal fluid. The model includes the nonideal effects of elasticity as boundary conditions at the top and bottom interfaces of the slab and also takes 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 [Plohr and Sharp, Z. Angew. Math. Mech. 49, 786 (1998)10.1007/s000330050121], and a physical explanation is given for the reduction of the stabilizing effectiveness of the elasticity for the thinner slabs. The feedthrough factor is also calculated.