A coarse-grain, quasi-normal model of stably stratified turbulent flows and its implementation in Κ - ε modeling of atmospheric ABLs

A coarse-grain, quasi-normal model of turbulence is applied to flows with stable stratification. The model's parameters are calculated based upon a self-consistent recursive procedure of small-scale modes elimination starting at the Kolmogorov scale. The model includes both vertical and horizontal eddy viscosities and diffusivities and, thus, explicitly recognizes the anisotropy introduced by stable stratification. There are significant differences in the behavior of these turbulent exchange coefficients with increasing stratification. Generally, the vertical coefficients are suppressed while their horizontal counterparts are enhanced. The model accounts for the combined effect of turbulence and internal waves on the exchange coefficients. When the process of scale elimination is extended up to the turbulence macroscale, the model yields the eddy viscosities and eddy diffusivities in the RANS format. These parameters are utilized in a K-ε model of a stably stratified ABL. The use of the spectral model makes it possible to circumvent the problematics of the Reynolds stress closure models. The dependence of the coefficients of the dissipation equation on the flow characteristics is explored and tested in the limiting case of the structural equilibrium. The new K-ε model is validated in simulations of the atmospheric stable boundary layer (SBL) over sea ice. The new model performs well in the neutral and both moderately and strongly stratified ABLs.