Mean and turbulent kinetic energy budgets inside and above very large wind farms under conventionally-neutral condition

In this study, large-eddy simulations (LES) is combined with a turbine model to investigate all the terms in the budgets of mean and turbulent kinetic energy (TKE) inside and above very large wind farms. Emphasis is placed on quantifying the relative contribution of the thermal stratification in the free-atmosphere and wind-turbine spacing on the energy balance. The mean kinetic energy budget through the wind farms indicates that the magnitude of the kinetic energy entrainment form the free atmosphere into the boundary layer increases by increasing the density of the farms and decreasing the static stability in the free atmosphere, leading to larger power output from the wind farms. This entrainment is the only source of kinetic energy to balance that extracted by the turbines inside very large wind farms. In addition, it is shown that the distribution of the kinetic energy flux above the wind turbines, at top-tip level, is quite heterogeneous and its magnitude just behind the wind turbines is much larger due to the strong wind shear at that level. The simulation results also show that increasing the wind-farm density leads to an increase in the boundary-layer height, the ratio of the ageostrophic to the geostrophic velocity component inside the boundary layer, and the potential temperature near the surface. Detailed analysis of the TKE budget through the wind farms reveals also an important effect of the thermal stratification and wind turbine spacing on the magnitude and spatial distribution of the shear production, dissipation rate and transport terms. In particular, the shear production and dissipation rate have a peak at the turbine-top level, where the wind shear is largest, and their magnitude increases as the static stability in the free atmosphere and the wind-turbine spacing decrease.