Rayleigh Taylor Instability in multiple finite-thickness fluid layers

We consider the Rayleigh-Taylor instability in a fluid system with spatially varying density and viscosity. We analytically treat this system as a multi-layered fluid system, each layer with a fixed density. We use the inviscid flow approximation to find analytic solutions for the growth of the instability. We discuss the importance of these results and other approximations that also yield analytic solutions to an otherwise general approach.