The results obtained from both atmospheric and laboratory experiment and from LES data show that, in the stably stratified flows of the atmospheric boundary layer, turbulent mixing occurs at gradient Richardson number that significantly exceed one: the inverse turbulent Prandtl number decreases with an increase in the thermal stability. The decreasing trend of the inverse turbulent Prandtl number is reproduced in a stably stratified planetary boundary layer in agreement with measurement data with aid of the high closure RANS turbulence scheme, which takes into account the influence of internal gravity waves on the eddy mixing of momentum and heat. Applicability of such RANS turbulence approach for the estimate of eddy diffusivities of momentum and heat in the upper troposphere and lower stratosphere also examined. It is concluded that the high closure RANS turbulence scheme shows the good agreement with the direct measurement data of eddy diffusivities for momentum and heat in the upper troposphere and lower stratosphere during clear-air conditions.
Modeling turbulence is an important object of environmental sciences for describing an essential turbulent transport of heat and momentum in the boundary layer of the atmosphere. The many turbulence model used in the simulation of flows in the environment, based on the concept of eddy viscosity, and buoyancy effects are often included in the expression for the turbulent fluxes through empirical functions, based on the similarity theory of Monin-Obukhov, fair, strictly speaking, only in the surface layer. Furthermore, significant progress has been made in recent years in the development broader than standard hypothesis turbulent viscosity models for the eddy diffusivity momentum and heat, as a result of the recording of differential equations for the Reynolds stresses and vector turbulent heat flux in a weakly-equilibrium approximation, which neglects advection and the diffusion of certain dimensionless quantities. Explicit algebraic model turbulent Reynolds stresses and heat flux vector for the planetary boundary layer is tested in the neutral atmospheric boundary layer over the homogeneous rough surface. The present algebraic model of turbulence built on physical principles RANS (Reynolds Average Navier Stokes) approach for stratified turbulence uses three prognostic equations and shows correct reproduction of the main characteristics of the Ekman neutral ABL: the components average of wind velocity, the angle of wind turn, turbulence statistics. Test calculations shows that this turbulence model can be used for the purposeful researches of the atmospheric boundary layer for solving of various problems of the environment.
Abstract The paper analyzes the features of turbulent momentum and heat transfer in a stably stratified atmospheric boundary layer (ABL), in the upper troposphere and lower stratosphere, and the possibility of taking them into account in RANS (Reynolds Average Navier Stokes) turbulence models. Such features, for example, include the transfer of momentum (but not heat) by internal gravitational waves under conditions of strong stability, the formation of a low-level jet. Models for the coefficients of eddy diffusion of momentum and heat were obtained by writing the differential equations for the Reynolds stresses and the turbulent heat flux vector in the weakly equilibrium approximation, in which the advection and diffusion of some dimensionless quantities are neglected. In the considered version of the algebraic model built on the physical principles of the RANS approximation for stratified turbulence, three prognostic equations are used: for the kinetic energy of turbulence, the rate of its spectral consumption and the dispersion of temperature fluctuations. It is shown that the profile of the vertical diffusivity for momentum, which was calculated using three-parametric turbulent model, is in agreement with data of direct measurements either within a stable stratified atmospheric boundary layer or beyond this layer in free atmosphere.
