Variable density model for the Rayleigh-Taylor instability and its transformation to the diffusive, inhomogeneous, incompressible Navier-Stokes equations

Abstract

The Rayleigh-Taylor (RT) instability occurs at the interface between two fluids of different densities when the lighter fluid pushes against the heavier. For example, RT instability fingers are evident in the Crab Nebula. It plays a critical role in all known forms of fusion. The variable density model (VDM), which is comprised of a set of partial differential equations, best models the flow in the mixing layer. This paper shows that the VDM can be exactly transformed into the inhomogeneous, incompressible, forced Navier-Stokes equations.