Statistical Evolution of Chaotic Fluid Mixing

Abstract

We describe a new constitutive theory for two-phase flow models of chaotic mixing layers, which form as two incompressible fluids interpenetrate. This theory is compatible with arbitrary velocities of the edges of a mixing layer, and it gives analytic solutions for the distribution of fluid variables across the layer in terms of these velocities. Our results are in agreement with all available data from planar Rayleigh-Taylor instability experiments. The model that we discuss can be embedded in a larger system of two-phase flow equations in order to predict other important physical quantities, such as the fluid pressures and internal energies in compressible mixing.