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.
The nonlocality of the mechanism of turbulent heat transfer in the atmospheric boundary layer over a rough surface manifests itself in the form of bounded areas of countergradient heat transfer, which are diagnosed from analysis of balance items in the transport equation for the variance of temperature fluctuations and from calculation of the coefficients of turbulent momentum and heat transfer invoking the model of gradient diffusion. It is shown that countergradient heat transfer in local regions is caused by turbulent diffusion or by the term of the divergence of triple correlation in the balance equation for the temperature variance.
The RANS high close approach for the turbulent fluxes of momentum, heat and mass for simulating of the circulation structure and dispersion pollutant over the urban heat island in a stably stratified environment under nearly calm conditions is formulated. The turbulent fluxes of momentum − u<sub>i</sub>u<sub>j</sub> , heat −u<sub>i</sub>θ and mass −u<sub>i</sub>c in this approach determined from the gradient diffusion type models with the turbulent kinetic energy (TKE), its spectral consumption (or dissipation), the temperature variance and the covariance for cθ as parameters which are obtained from transport equations. Such the RANS approach minimizes difficulties in the turbulent transport modeling in a stably stratified environment and reduces efforts needed for the numerical implementation of the numerical model. The simulation results demonstrates that the three-four equations RANS approach is able to predict the structure of turbulent circulation flow induced by the heat island that is in good agreement with the experimental data.
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.
The modified three-parameter model of turbulence for a thermally stratified atmospheric boundary layer (ABL) is developed. The
model is based on tensor-invariant parameterizations for the pressure-strain and pressure-temperature correlations that are more complete
than the parameterizations used in the Mellor-Yamada model. The turbulent momentum and heat fluxes are calculated with explicit
algebraic models obtained with the aid of symbol algebra from the transport equations for momentum and heat fluxes in the approximation
of weakly equilibrium turbulence. The three-parameter model of thermally stratified turbulence is employed to obtain
closed form algebraic expressions for the fluxes. The effects of urban roughness are parameterized. Results of 2D computational test
of a 24-hour of the ABL evolution are presented. Comparison of the computed results with the available observational data and other
numerical models shows that the proposed model is able to reproduce both the most important structural features of the turbulence in
an urban canopy layer near the urbanized PBL surface and the effect of urban roughness on a global structure of the fields of wind and
temperature over a city.