Simple Phenomenological Theory of Turbulent Shear Flows

A rate equation is proposed to govern the variation of the effective turbulent viscosity. The effects of generation, convection, diffusion, and decay are each represented by appropriate terms leaving only two empirical constants to be determined by experiment. This rate equation together with the equations of motion form a closed system applicable to quasiparallel turbulent shear flows. For an incompressible turbulent boundary layer with zero pressure gradient, solutions were obtained by assuming local similarity and a linear growth of the boundary-layer thickness. Another problem, the turbulent-nonturbulent interface at the outer edge of the boundary layer was treated by using the further assumption that the large scale motion of the interface has no significant contribution to the Reynolds stress. It can be shown that for a nearly homogeneous domain, Prandtl's mixing length theory is a limiting case of the present theory.