An improved turbulence model for atmospheric boundary Layer over earth's surface with large-scale roughness and local thermal inhomogeneity

A numerical model to represent the impact of large-scale roughness area on airflow in the meso'scale atmospheric models is presented. In the model, the roughness elements are not explicitly resolved, but their effects on the grid-averaged variables are parameterized. The improved, three-parametric (TKE-dissipation-temperature variance) turbulence model[1-3] for the computation of the wind field, temperature and pollutant dispersion was developed. The transport of momentum, heat and mass under the unstable and stable stratification is evaluated from the fully explicit anisotropic algebraic expressions. These expressions are derived based on the assumption of weak-equilibrium turbulence approach where transport effects on the turbulent stresses and heat fluxes are negligible but the stratification effects on the turbulent transfer are considered precisely. In particular, the vertical heat flux expression includes an additional countergradient term. The turbulent momentum and heat fluxes models encapsulate substantial physics and dynamics of atmospheric stratified flows. The comparison of the computational results obtained with the present model and existing observational data and numerical models shows that the present model is capable of predicting the structure turbulence in the daytime and nocturnal atmospheric boundary layer and of obtaining local wind and temperature with high-resolution. As example, one of modeling results of nocturnal boundary layer structure obtained in the 2D computational test is shown on Fig. 1. For the stable boundary layer over the surface with the local large-scale aerodynamic roughness and thermal inhomogeneity as the gradient Richardson number Ri_g increases (Ri_g > 0.2), the turbulence in the flow is inhibited by the stable stratification and thus the momentum and heat transfer by turbulent eddies diminishes. Nonetheless at strong stratifications, the flow can sustain propagating internal waves that can effectively transport momentum, but not heat. The turbulent Prandtl number (Pr=K_m/K_h, where K_m is eddy diffusivity for momentum and K_h is eddy diffusivity for temperature of an impruved the three-parametric turbulence model) is stability dependent from Ri_g (Fig. 1, 2). This contrasts with the constant Prandtl number assumption made in conventional schemes such MRS (Medium Range Forecast),Pr=1.3, and Blackadar scheme (Pr=1), as shown on Fig. 1. [1] A.F. Kurbatskii. Turbulent Penetrative Convection from an Area Heat Source in Stable Stratified Environment. Second Int. Symposium on TURBULENCE and SHEAR FLOW PHENOMENA – 2, June 27-29, 2001, Stockholm, Sweden. Vol. III. P. 89-94. [2] Kurbatskii, A. F. 2001. Computational Modeling of the Turbulent Penetrative Convection above the Urban Heat Island in Stably Stratified Environment. Journal Applied Meteorology, 40 (10), 1748-1761. [3]. A. F. Kurbatskii and L. I. Kurbatskaya. Three-Parametric Model of Turbulence for the Atmospheric Boundary Layer over an Urbanized Surface. Izvestia, Atmospheric and Oceanic Physics, 2006, 42 (4), 439-455. This study was supported by the Russian Foundation for Basic Research, project 06-05-64002.