General intergral properties of mixing layers

Abstract

If the usual integrals defining displacements and momentum thicknesses are used for mixing layers with a change in the range of integration, they diverge in general. Consequently, the familiar von Karman equation is not generally applicable to a mixing layer. Previous works used the device of dividing the layer into two sub-layers and using one integral for each separately with a continuity condition on shear stress. Suitable definitions of displacement and other thicknesses are given here, and a momentum integral relation is obtained. Its form is different from von Karman's equation. The formulation given here is applicable to incompressible and compressible fluids, laminar and turbulent flows and to two-dimensional and axisymmetric flows.