Rayleigh Taylor Instability in Multiple Finite-Thickness Fluid Layers

We discuss a recently developed [1] transfer-matrix formalism for determining the linear growth rate of the Rayleigh-Taylor instability in a fluid system with spatially varying density and viscosity. We use this formalism to analytically and numerically treat the case of a stratified heterogeneous fluid. We introduce the inviscid-flow approximation in our transfer-matrix formalism to find analytic solutions in the limit of uniform kinematic viscosity for a stratified heterogeneous fluid. We discuss the applicability of these results and a related approximation that also yields analytical solutions in the large viscosity limit. [1] Sharma, P. Rayleigh-Taylor instability in multiple finite-thickness fluid layers. Phys. Rev. E 110, L063101 (2024).