General Solution for Self-Similar Mixing Layers

Abstract

In this note, a longstanding indeterminacy in the solution of self-similar planar mixing layers is resolved. It is shown that the boundary condition that offers the largest set of self-similar solutions is the specification of the vertical velocity at infinity, which also quantifies the value of the stream function and the net inflow/outflow there. This is referred to as the entrainment boundary condition. Other conditions that have been suggested to close the problem yield a subset of solutions and thus represent a loss of generality. The entrainment boundary condition determines the spatial growth rate and the spreading parameter for a given mixing layer, which were previously thought to be determined through experiment and empirical matching to a linearized version of the problem. These statements are validated using existing experimental data.