We develop a general transfer-matrix formalism for determining the 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.

Close

PrevNext

View figure in article

• Rayleigh-Taylor instability
• Navier-Stokes equation