In the context of large off-shore wind farms, power production is influenced greatly by the turbine array's interaction with the atmospheric boundary layer. One of the most influencing manifestations of such complex interaction is the increased level of shear stress observed within the farm. This leads to higher momentum fluxes that affect the wind speed at the turbine locations and in the cluster wake. At the wind farm entrance, an internal boundary layer (IBL) grows due to the change in effective roughness imposed by the wind turbines, and for large enough clusters, this can reach the unperturbed boundary layer height in what is referred to as the fully developed regime. Downwind, a second IBL starts growing, while the shear stress profile decays exponentially to its unperturbed state. In the present study, we propose a simple analytical model for the vertical profile of the horizontal shear stress components in the three regions identified above. The model builds upon the top-down model of Meneveau (J. Turbul., vol. 13, 2012, N7), and assumes that the flow develops in a conventionally neutral boundary layer. The proposed parametrization is verified successfully against large-eddy simulations, demonstrating its ability to capture the vertical profile of horizontal shear stress, and its evolution both inside and downwind of the wind farm. Our findings suggest that the developed model can prove extremely useful to enhance the physical grounds on which new classes of coupled wind farm engineering models are based, leading to a better estimation of meso-scale phenomena affecting the power production of large turbine arrays.@en

The interaction of large wind farm clusters with the thermally stratified atmosphere has emerged as an important physical process that impacts the productivity of wind farms. Under stable conditions, this interaction triggers atmospheric gravity waves (AGWs) in the free atmosphere due to the vertical displacement of the atmospheric boundary layer (ABL) by the wind farm. AGWs induce horizontal pressure gradients within the ABL that alter the wind speed distribution within the farm, influencing both wind farm power generation and wake development. Additional factors, such as the growth of an internal boundary layer originating from the wind farm entrance and increased turbulence due to the wind turbines, further contribute to wake evolution. Recent studies have highlighted the considerable computational cost associated with simulating gravity wave effects within large-eddy simulations (LESs), as a significant portion of the free atmosphere must be resolved due to the large vertical spatial scales involved. Additionally, specialized boundary conditions are required to prevent wave reflections from contaminating the solution. In this study, we introduce a novel methodology to model the effects of AGWs without extending the LES computational domain into the free atmosphere. The proposed approach addresses the wave reflection problem inherently, eliminating the need for these specialized boundary conditions. We utilize the recently developed multi-scale coupled (MSC) model of Stipa et al. (2024b) to estimate the vertical ABL displacement triggered by the wind farm, and we apply the deformation to the domain of an LES that extends only to the inversion layer. The accuracy in predicting the AGW-induced pressure gradients is equivalent to the MSC model. The AGW modeling technique is verified for two distinct free-atmosphere stability conditions by comparing it to the traditional approach in which AGWs are fully resolved using a domain that extends several kilometers into the free atmosphere. The proposed approach accurately captures AGW effects on the row-averaged thrust and power distribution of wind farms while demanding 12.7 % of the computational resources needed for traditional methods. Moreover, when conventionally neutral boundary layers are studied, there is no longer a need to solve the potential temperature equation, as stability is neutral within the boundary layer. The developed approach is subsequently used to compare the global blockage and pressure disturbances obtained from the simulated cases against a solution characterized by zero boundary layer displacement, which represents the limiting case of very strong stratification above the boundary layer. This approximation, sometimes referred to as the “rigid lid”, is compared against the full AGW solution using the MSC model. This is done for different values of inversion strength and free atmosphere lapse rate, evaluating the ability of the “rigid lid” to predict blockage, wake effects, and overall wind farm performance.

@en

As offshore wind farms grow in size, the blockage effect associated with the atmospheric gravity waves they trigger is expected to become more important. To model this, recent research has produced an Atmospheric Perturbation Model (APM), which simulates the mesoscale flow in the atmospheric boundary layer at a low computational cost compared to traditional methods. However, as a simplified reduced-order model, it can not resolve individual turbine wakes, and has to be coupled to an engineering wake model to predict farm power output. Over the years, three coupling methods have been developed, and been combined into the open-source framework WAYVE. This paper compares them, discussing both their theoretical validity and their performance. For the latter, we validate the velocities and power outputs predicted by WAYVE against 27 LES simulations. We find that the velocity matching (VM) and the pressure-based (PB) methods perform the best. Of these two, the VM method is more consistent with the APM output, while the PB method has a significantly lower computational cost.

@en

In recent years, the relevance of the interaction between neighboring wind farms has grown steadily. As one farm extracts energy from the wind, a downstream one can systematically experience lower wind speeds which threatens the economic viability of the farm. Significant progress has been made in understanding these farm-farm wake interactions, but we still lack methodologies to mitigate their undesired effects. In this study, we introduce Active Cluster Wake Mixing (ACWM). This novel method aims to accelerate the recovery of the cluster wake using dynamic control actions: By exciting the thrust of the individual turbines depending on their relative location, we generate non-uniform patterns of energy extraction. Phase offsets between the individual excitation signals propagate these regions through the wind farm. This results in large-scale velocity gradients inside the farm, which also affect the flow in the cluster wake region. An in-depth exploration and optimization of ACWM requires significant computational effort. Therefore, we compare three different wind farm modeling approaches in Large Eddy Simulations (LES) that differ in their computational costs regarding their suitability for further exploration of ACWM. For this purpose, we use an unoptimized ACWM scheme with two different excitation frequencies. For the first time ever we successfully show that ACWM manipulates the flow inside the wind farm with favorable effects on the wake velocity. We also demonstrate that the modeling of cluster wakes is challenging and has a significant effect on the potential gain.

@en