Characterisation of vorticity generation in the wake of different wind farms

The expansion in offshore wind energy leads to more large wind farms being built in close proximity to each other. The wakes of upstream wind farms can influence downstream wind farms, even if they are tens of kilometres apart, exposing them to reduced wind speeds that result in lower power production. To mitigate this effect, it is desirable to reduce the extent and intensity of wind farm wakes by enhancing wake recovery. Suitable mitigation strategies could include adaptations in the wind farm layout, turbine type or operation strategy. However, knowledge on the wake recovery mechanisms of large wind farms is still limited. In particular, the influence of the wind farm setup and operation on different recovery mechanisms is unclear. In this study, we aim to understand the formation of circulation zones inside and in the wake of large wind farms, which can contribute to wake recovery by advecting momentum. We set up idealised large-eddy simulations with a conventionally neutral boundary layer with common offshore characteristics for three different wind farm setups: First, a baseline setup of an aligned wind farm, second, a vertically staggered wind farm with alternating columns of low and high turbine hub heights, and third, a wind farm with alternating columns of positive and negative turbine yaw misalignment. We analysed the budget of the streamwise vorticity to understand which terms are relevant for creating circulation zones. Based on that we identified two different types of circulation zones, inside the wind farm wake area and at the farm wake edges. Inside the wind farm, vorticity is mainly generated because of the rotation of the wind turbines and partly because of spatial variations in Reynolds stresses and buoyancy. At the left and right farm wake edge, vorticity is mainly created by the buoyancy term. The vorticity at the left wake edge is stronger than at the right edge, which is related to the wind farms geographical location on the northern hemisphere. The wind farm setup has a considerable influence on the magnitude of the vorticity. Both, the vertical staggering and organised yaw misalignment cause stronger vorticity inside the wind farm compared to the baseline setup. This enhanced vorticity persists multiple tens of kilometres downstream and contributes to heterogeneities in the wind farm wake. Irrespective of the setup, the dominating mechanism for enhancing and maintaining vorticity in the far-wake of the wind farm is buoyancy. Overall, the results show that wind farms with heterogeneous setups can enhance vortex structures in wind farm flows, which results in a more heterogeneous wake and influences the wake recovery. Given the intrinsic relation between buoyancy and the vertical temperature profile, future work should characterize the effect of atmospheric stratification on the circulations.