Boundary-layer development and gravity waves in conventionally neutral wind farms

Abstract

While neutral atmospheric boundary layers are rare over land, they occur frequently over sea. In these cases they are almost always of the conventionally neutral type, in which the neutral boundary layer is capped by a strong inversion layer and a stably stratified atmosphere aloft. In the current study, we use large-eddy simulations (LES) to investigate the interaction between a large wind farm that has a fetch of 15 km and a conventionally neutral boundary layer (CNBL) in typical offshore conditions. At the domain inlet, we consider three different equilibrium CNBLs with heights of approximately 300 m, 500 m and 1000 m that are generated in a separate precursor LES. We find that the height of the inflow boundary layer has a significant impact on the wind farm flow development. First of all, above the farm, an internal boundary layer develops that interacts downwind with the capping inversion for the two lowest CNBL cases. Secondly, the upward displacement of the boundary layer by flow deceleration in the wind farm excites gravity waves in the inversion layer and the free atmosphere above. For the lower CNBL cases, these waves induce significant pressure gradients in the farm (both favourable and unfavourable depending on location and case). A detailed energy budget analysis in the turbine region shows that energy extracted by the wind turbines comes both from flow deceleration and from vertical turbulent entrainment. Though turbulent transport dominates near the end of the farm, flow deceleration remains significant, i.e. up to 35 % of the turbulent flux for the lowest CNBL case. In fact, while the turbulent fluxes are fully developed after eight turbine rows, the mean flow does not reach a stationary regime. A further energy budget analysis over the rest of the CNBL reveals that all energy available at turbine level comes from upwind kinetic energy in the boundary layer. In the lower CNBL cases, the pressure field induced by gravity waves plays an important role in redistributing this energy throughout the farm. Overall, in all cases entrainment at the capping inversion is negligible, and also the work done by the mean background pressure gradient, arising from the geostrophic balance in the free atmosphere, is small.

Gravity Waves and Wind-Farm Efficiency in Neutral and Stable Conditions

“…Several other studies also found enhanced gravity-wave activity during nighttime when the surface heat flux was negative (Brinkmann 1974;Whiteman and Whiteman 1974;Doyle et al 2005;Valkonen et al 2010). In large wind farms, gravity waves impose significant pressure gradients in the boundary layer and play an important role in redistributing energy throughout the farm (Allaerts and Meyers 2017). The objective of the current study is to investigate the impact of stable stratification on wind-farm performance and boundary-layer flow, with a particular interest in gravity waves.…”

“…The subgrid-scale motions are modelled with the turbulent kinetic energy (TKE) model developed by Deardorff (1980), and classic Monin-Obukhov similarity theory is used to specify the boundary conditions near the surface. Following Allaerts and Meyers (2017), wind-farm entrance effects and boundary-layer development are included by using the concurrent-precursor method (Stevens et al 2014;Munters et al 2016), extended to include the effects of thermal stratification and Coriolis forces. Details of the LES methodology can be found in Appendix 1.…”

“…The set-up of the wind farm and the numerical domain is to a large extent inspired by the simulations of Allaerts and Meyers (2017). A summary and outline of the computational set-up are given in Table 1 and Fig.…”

“…With a turbine spacing of s x D = 7.5D and s y D = 5.33D, the wind farm covers an area of roughly 10 km × 4.8 km. We have chosen this size to be slightly smaller than the wind farm studied by Allaerts and Meyers (2017) in order to constrain the computational cost given the finer resolution required for stable boundary-layer simulations. Note that the amplitude of gravity waves is expected to depend on the flow blockage and therefore on the size of the wind farm.…”

“…Recently, Allaerts and Meyers (2017) showed using large-eddy simulations (LES) that in some situations large wind farms interact with the atmosphere on a much larger scale by exciting atmospheric gravity waves. Earlier, Smith (2010) considered this interaction and the impact on the wake efficiency with a simplified linear model.…”