A Two Phase Flow Model of the Rayleigh-taylor Mixing Zone

The Rayleigh-Taylor instability of an interface separating uids of distinct density is driven by an acceleration across the interface. Low order statistical moments of uctuating uid quantities characterize the hydrodynamics of the mixing zone. A new model is proposed for the momentum coupling between the two phases. This model is validated against computational data for compressible ows, including ows near the incompressible limit. Our main result is a zero parameter rst order closure for ensemble averaged two phase ow equations. We do not, however, fully solve the closure problem, as the equations we derive are missing an (internal) boundary condition along any surface for which either phase goes to zero volume fraction. In this sense, the closure problem is reduced from a volume to a surface condition, rather than being solved completely. A new understanding of the compressibility dependent loss of universality of the mixing rate is obtained in terms of a one parameter family of solutions of the two phase ow equations. This parameter measures the initial perturbation amplitude in dimensionless units which eliminate this eeect in the incompressible limit. We compare two formulations of the statistical moments, one based on two phase ow and the other on turbulence models. These formulations describe diierent aspects of the mixing process. For the problem considered, the two phase ow moments appear to be preferable, in that they subsume the turbulence moments but not conversely.