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.

Flow blockage by large wind farms leads to an upward displacement of the boundary layer, which may excite atmospheric gravity waves in the free atmosphere aloft and on the interface between the boundary layer and the free atmosphere. In the current study, we assess the sensitivity of wind-farm gravity-wave excitation to important dimensionless groups and investigate the feedback of gravity-wave induced pressure fields on wind-farm energy extraction. The sensitivity analysis is performed using a fast boundary-layer model that is developed to this end. It is based on a three-layer representation of the atmosphere in an idealised barotropic environment, and is coupled with an analytical wake model to account for turbine wake interactions. We first validate the model in 2D–mode with data from previous large-eddy simulations of “infinitely” wide wind farms, and then use the model to investigate the sensitivity of wind-farm induced gravity waves to atmospheric state and wind-farm configuration. We find that the inversion layer induces flow physics similar to shallow-water flow and that the corresponding Froude number plays a crucial role. Gravity-wave excitation is maximal at a critical Froude number equal to one, but the feedback on energy extraction is highest when the Froude number is slightly below one due to a trade-off between amplitude and upstream impact of gravity waves. The effect of surface friction and internal gravity waves is to reduce the flow perturbation and the related power loss by dissipating or dispersing perturbation energy. With respect to the wind-farm configuration, we find that gravity-wave induced power loss increases with wind-farm size and turbine height. Moreover, we find that gravity-wave effects are small for very wide or very long wind farms and attain a maximum at a width-to-depth ratio of around 3/2.

Under conventionally neutral conditions, the boundary layer is frequently capped by an inversion layer, which counteracts vertical entrainment of kinetic energy. Very large wind farms are known to depend on vertical entrainment to transport energy from above the farm towards the turbines. In this study, large eddy simulations of an infinite wind-turbine array in a conventionally neutral atmospheric boundary layer are performed. By carefully selecting the initial potential-temperature profile, the influence of the height and the strength of a capping inversion on the power output of a wind farm is investigated. Results indicate that both the height and the strength have a significant effect on the boundary layer flow, and that the height of the neutral boundary layer is effectively controlled by the capping inversion. In addition, it is shown that the vertical entrainment rate decreases for increasing inversion strength or height. In our infinite wind-farm simulations, varying the inversion characteristics leads to differences in power extraction on the order of 13% ± 0.2% (for increasing the strength from 2.5 to 10 K), and 31% ± 0.4% (for increasing the height from 500 to 1500 m). A detailed analysis of the mean kinetic-energy equation is included, showing that the variation in power extraction originates from the work done by the driving pressure gradient related to the boundary layer height and the geostrophic angle, while entrainment of kinetic energy from the free atmosphere does not play a significant role. Also, the effect of inversion strength on power extraction is energetically not related to different amounts of energy entrained, but explained by a difference in boundary layer growth, leading to higher boundary layers for lower inversion strengths. We further present a simple analytical model that allows to obtain wind-farm power output and driving power for the fully developed regime as function of Rossby number and boundary layer height.

We use large-eddy simulations (LES) to investigate the impact of stable stratification on gravity-wave excitation and energy extraction in a large wind farm. To this end, the development of an equilibrium conventionally neutral boundary layer into a stable boundary layer over a period of 8 h is considered, using two different cooling rates. We find that turbulence decay has considerable influence on the energy extraction at the beginning of the boundary-layer transition, but afterwards, energy extraction is dominated by geometrical and jet effects induced by an inertial oscillation. It is further shown that the inertial oscillation enhances gravity-wave excitation. By comparing LES results with a simple one-dimensional model, we show that this is related to an interplay between wind-farm drag, variations in the Froude number and the dispersive effects of vertically-propagating gravity waves. We further find that the pressure gradients induced by gravity waves lead to significant upstream flow deceleration, reducing the average turbine output compared to a turbine in isolated operation. This leads us to the definition of a non-local wind-farm efficiency, next to a more standard wind-farm wake efficiency, and we show that both can be of the same order of magnitude. Finally, an energy flux analysis is performed to further elucidate the effect of gravity waves on the flow in the wind farm.

Mesoscale-to-microscale coupling (MMC) aims to address the limited scope of traditional large-eddy simulations by driving the microscale flow with information concerning largescale weather patterns provided by mesoscale models. We present a new offline MMC technique for horizontally homogeneous microscale flow conditions, in which internal forcing terms are computed based on mesoscale time-height profiles of mean-flow quantities.The advantage of such an approach is that it can be used to drive a microscale simulation with either mesoscale or observational data, and that it does not rely on specific terms in the mesoscale budget equations, which are typically not part of the default output of a mesoscale solver. The performance of the proposed profile assimilation technique is assessed based on the simulation of a typical diurnal cycle over the Scaled Wind Farm Technology site in west Texas. Results indicate that simple data assimilation techniques lead to unphysically high levels of shear and turbulence caused by the algorithm's inability to cope with inaccuracies in the mesoscale time-height profiles. Modifying the algorithm to account for vertical coherence in the mesoscale source terms gives the microscale solver a greater ability to correct the provided mesoscale time-height profiles, leading to improved predictions of shear and turbulence statistics. The resulting turbulence statistics are in good agreement with meteorological tower observations and simulation results obtained with state-of-the-art coupling techniques using mesoscale budget components.