Hydrodynamically driven two-phase flow, a theory of hydrodynamically driven dynamic mix

The author writes the dynamic equations describing the intermixing of two materials starting from the conservation laws. The result is a set of equations for mixing driven by the Rayleigh-Taylor buoyancy force, and amplified by terms which incorporate the Richtmyer-Meshkov and Kelvin-Helmholtz instabilities. Making the assumption of pressure equilibration, the author arrives at equations which predict that mixing will begin, even in the limit of small initial perturbations, and even in a 1-d calculation, when an interface goes Rayleigh-Taylor unstable, unless the drag or material strength forces are sufficiently large to prevent this. The equations given here may be incorporated into 1-d, 2-d, or 3-d codes, for either Lagrangian or Eulerian formulation. They have the nice feature for Lagrangian codes of keeping the zone mass fixed, thus eliminating the need for rezoning