Asymmetric behaviour of turbulence in the wake of wind farms caused by the Coriolis force

TL;DR

This study addresses the asymmetric wake behavior of offshore wind farms in shallow atmospheric boundary layers by combining SAR observations with PALM-LES simulations. It systematically isolates veer and wake-deflecting Coriolis effects across hemispheres and fictitious ABLs to identify the mechanism behind a persistent TKE streak. The key finding is that veer in the incoming flow is the dominant cause of the streak, with the left-edge manifestation in the Northern Hemisphere and a right-edge manifestation in the Southern Hemisphere; the Coriolis-induced wake deflection plays a secondary role, and symmetry is restored when Coriolis effects are removed. The work links LES-derived TKE streaks to SAR NRCS patterns and highlights implications for wake recovery and downstream wind-farm interactions in veered flows, while noting limitations in near-wall modeling and sea-surface physics.

Abstract

Large offshore wind farm wakes in shallow atmospheric boundary layers (ABL) exhibit often an asymmetric behaviour when observed through Synthetic-Aperture-Radar or simulated through Large-Eddy Simulations (LES). In previous LES of wind farms in the northern hemisphere, the asymmetry manifests as a streak at the left side of the wake, looking downstream, where the turbulence kinetic energy (TKE) is greater than the surrounding flow. This work aims at clarifying the physical mechanism that leads to the formation of such a phenomenon. Identifying the Coriolis force as one possible source of asymmetry in the resolved physics, we simulate a real wind farm located in the German Bight operating under different ABLs: one representative of the northern hemisphere; one of the southern hemisphere; and three fictitious ABLs where the Coriolis effects on the inflow and wake, i.e. veer and the wake deflecting force, are removed individually or altogether. Our results show that the TKE streak appears on the opposite side of the wake, i.e. the right one, in the southern hemisphere, and it is primarily caused by veer in the incoming flow, a result of the Coriolis force in a marine ABL. The process involves a larger TKE production which originates from a larger vertical shear promoted where the undisturbed veer profile converges towards the wake in the top part of the ABL. We find that the TKE streak improves the farm wake recovery modestly. Finally, we compare the asymmetry modelled by LES with those observed in several on-field measurements, finding striking similarities.

Figures (15)

• Figure 1: Normalized Radar Cross Section (NRCS) for several situations captured by Copernicus satellite Sentinel-1A/B when passing over the German Bight, acquired on 21 March 2018 at 05:48 UTC (a), 20 March 2019 at 17:15 UTC (b), 13 August 2020 at 05:49 UTC (c), and 19 May 2017 at 05:48 UTC (d). In cases of westerly winds, the wakes generated by the wind farms display a streak of enhanced NRCS along the northern wake boundary (panels a,b). On the other hand, under easterly winds, a similar streak occurs along the southern boundary (panels c,d). Red arrows point at the most striking feature in each scene. The magnifying window in panel (a) highlights the wind farm and situation we aimed at replicating in the numerical set-up.
• Figure 2: Schematics of how the Coriolis force in the crosswise direction $F_{\textrm{c},y}$ induces changes in the crosswise velocity $V$. Panel (a) represents the veer present at the wind farm or turbine inflow that is the direct consequence of the Coriolis force arising from the boundary layer deceleration of an undisturbed streamwise velocity $U_\textrm{g}$. Panel (b) showcase the further change in $V$ localized in the turbine wake, again imposed by the Coriolis force arising from the streamwise velocity deficit inside the wake region.
• Figure 3: Occurrence of asymmetric cluster wake behaviour in relation to atmospheric conditions. The scatterplot shows boundary layer height and air/sea-surface temperature differences, both derived from ERA5, for colocated SAR cases in which wakes were observed behind offshore wind farms in the German Bight during 2018 and 2019. Marker colour indicates the velocity at 10 m as calculated from ERA5. Cases exhibiting asymmetric behaviour, defined as a streak of enhanced NRCS confined to the left side of the wake relative to the wind direction, are indicated by triangular symbols.
• Figure 4: Precursor run vertical domain size (a). Main run horizontal domain size (b). Main run and precursor share the vertical direction. The region where the Rayleigh damping layer is applied is displayed as a grey shaded area in the precursor domain. In the main run, we showcase the precursor horizontal extent, the turbines, and the plane at which turbulent fluctuations are calculated to be recycled at the inlet.
• Figure 5: Mean vertical profiles of streamwise velocity (a), crosswise velocity (b), TKE (c), and potential temperature (d) averaged across the crosswise direction for the empty box main run simulation at $x=30$ Km. These represents the inflow profiles to the wind farm in the 5 different simulation considered. The grey horizontal lines represent the turbine rotor vertical extent and the dash-dotted line the hub height.