From gigawatt to multi-gigawatt wind farms: wake effects, energy budgets and inertial gravity waves investigated by large-eddy simulations

Abstract. The size of newly installed offshore wind farms increases rapidly. Planned offshore wind farm clusters have a rated capacity of several gigawatts and a length of up to 100 km. The flow through and around wind farms of this scale can be significantly different than the flow through and around smaller wind farms on the sub-gigawatt scale. A good understanding of the involved flow physics is vital for accurately predicting the wind farm power output as well as predicting the meteorological conditions in the wind farm wake. To date there is no study that directly compares small wind farms (sub-gigawatt) with large wind farms (super-gigawatt) in terms of flow effects or power output. The aim of this study is to fill this gap by providing this direct comparison by performing large-eddy simulations of a small wind farm (13 km length) and a large wind farm (90 km length) in a convective boundary layer, which is the most common boundary layer type in the North Sea. The results show that there are significant differences in the flow field and the energy budgets of the small and large wind farm. The large wind farm triggers an inertial wave with a wind direction amplitude of approximately 10∘ and a wind speed amplitude of more than 1 m s−1. In a certain region in the far wake of a large wind farm the wind speed is greater than far upstream of the wind farm, which can be beneficial for a downstream located wind farm. The inertial wave also exists for the small wind farm, but the amplitudes are approximately 4 times weaker and thus may be hardly observable in real wind farm flows that are more heterogeneous. Regarding turbulence intensity, the wake of the large wind farm has the same length as the wake of the small wind farm and is only a few kilometers long. Both wind farms trigger inertial gravity waves in the free atmosphere, whereas the amplitude is approximately twice as large for the large wind farm. The inertial gravity waves induce streamwise pressure gradients inside the boundary layer, affecting the energy budgets of the wind farms. The most dominant energy source of the small wind farm is the horizontal advection of kinetic energy, but for the large wind farm the vertical turbulent flux of kinetic energy is 5 times greater than the horizontal advection of kinetic energy. The energy input by the gravity-wave-induced pressure gradient is greater for the small wind farm because the pressure gradient is greater. For the large wind farm, the energy input by the geostrophic forcing (synoptic-scale pressure gradient) is significantly enhanced by the wind direction change that is related to the inertial oscillation. For both wind farms approximately 75 % of the total available energy is extracted by the wind turbines and 25 % is dissipated.