Modeling of the Dissipation Rate of Turbulent Kinetic Energy

We consider a relaxation equation for turbulence wavenumber in semi-empirical turbulence closures. It is shown that the well-known phenomenological equation for the dissipation rate of turbulent kinetic energy can be related to this relaxation equation as a close approximation of the latter for stably stratified quasi-stationary flows. The proposed approach makes possible clarification of turbulent closures in the boundary layers of the atmosphere and ocean by specifying the equilibrium states and relaxation relations consistent with the direct and large eddy simulation data.