Quasi-irrotational approximation for the Rayleigh-Taylor instability in a solid bounded by a rigid wall

A quasi-irrotational approximation for the linear Rayleigh-Taylor instability in elastic solids with finite thickness has been developed for the case in which the slab is in contact with a rigid wall. The approximation yields simple but still reasonably accurate expressions for the instability growth rate. They have the same character as the completely irrotational approximations already developed for semi-infinite media, and they recover its results in the limit for very thick slabs. The model is applied to an analysis of the boundary of stability and the boundary for the elastic to plastic transition in elastic-plastic media. The approach allows for consideration of the presence of a viscous fluid beneath the elastic-plastic slab, extending previous results for ideal fluids.