Large-eddy simulation of the neutral planetary boundary layer with a capping inversion over a very large wind farm

Predicting wind and turbulent transport of heat, water vapor and pollutants through wind farms is of great importance for wind engineering, wind energy and environmental applications. It requires detailed knowledge of atmospheric boundary layer (ABL) over a wide range of spatial and temporal scales. The complexity of such flows makes it difficult to obtain all the needed information through field experiments alone, and often necessitates high-resolution eddy-resolving numerical tools such as large-eddy simulation (LES). In this study, large-eddy simulation is used to simulate the neutrally stratified planetary boundary layer (PBL) under the stably stratified free atmosphere through a very large wind farm. In this type of flow the stable stratification aloft puts a constraint on the growth of the largest turbulent eddies in the vertical direction and leads to lower boundary layer depth compared with the standard Ekman layer. To do this, tuning-free Lagrangian scale-dependent dynamic models (Stoll and Porte-Agel 2006) are used to model the subgrid-scale fluxes and the turbine-induced forces are parameterized using the actuator disk model (Wu and Porte-Agel 2011). Considering the effects of earth's rotation and static stability in the free atmosphere has two important advantages with respect to using a constant pressure gradient forcing and no capping inversion. First, considering the Coriolis forces in the governing equations allows to investigate how the direction of the wind changes inside and above the farm due to the presence of the turbines, which is not possible in the unidirectional boundary layer flow resulting from an imposed pressure gradient. Second, the important effect of the wind farm on the boundary-layer height growth can be explicitly resolved and studied. In the present work the influence of a very large wind farm on the vertical distribution of momentum and scalar fluxes inside the ABL is assessed. The influence of different configurations on the extracted power by the turbines and spatial distribution of surface fluxes is evaluated as well as the effect of the magnitude of the geostrophic wind and the resulting effective surface roughness. Finally, the influence of the stratification on the growth of the PBL depth, surface fluxes and the power produced by the turbines is evaluated.