Selection of boundary conditions for modeling the turbulent exchange processes within the atmospheric surface layer

One- and two-dimensional hydrodynamic models of turbulent transfer within the atmospheric surface layer under neutral thermal stratification are considered. Both models are based on the solution of system of the time-averaged equations of Navier – Stokes and continuity using a 1.5-order closure scheme as well as equations forturbulent kinetic energy and the rate of its dissipation. The influence of the upper and lower boundary conditionson vertical profiles of wind speed and turbulence parameters within the atmospheric surface layer was derivedusing an one-dimensional model usually applied in case of an uniform ground surface. The boundary conditionsin the model were prescribed in such way that the vertical wind and turbulence patterns were well agreed withwidely used logarithmic vertical profile of wind speed, linear dependence of turbulent exchange coefficient onheight above ground surface level and constancy of turbulent kinetic energy within the atmospheric surfacelayer under neutral atmospheric conditions. On the basis of the classical one-dimensional model it is possibleto obtain a number of relationships which link the vertical wind speed gradient, turbulent kinetic energy andthe rate of its dissipation. Each of these relationships can be used as a boundary condition in our hydrodynamicmodel. The boundary conditions for the wind speed and the rate of dissipation of turbulent kinetic energy wereselected as parameters to provide the smallest deviations of model calculations from classical distributions ofwind and turbulence parameters. The corresponding upper and lower boundary conditions were used to define theinitial and boundary value problem in the two-dimensional hydrodynamic model allowing to consider complextopography and horizontal vegetation heterogeneity. The two-dimensional model with selected optimal boundaryconditions was used to describe the spatial pattern of turbulent air flow when it interacted with the forest edge.The dynamics of the air flow establishment depending on the distance from the forest edge was analyzed. Forall considered initial and boundary value problems the unconditionally stable implicit finite-difference schemesof their numerical solution were developed and implemented.