Validation and extension of an analytical momentum availability model for the two-scale momentum theory of wind farm flows

A key parameter in the two-scale momentum theory of wind farm flows is the momentum availability, which quantifies the supply of momentum to a wind farm from various different momentum transport mechanisms (advection, pressure gradient, Coriolis, turbulence and unsteadiness). In this study, the contribution of each of these mechanisms to the momentum availability is evaluated directly from large-eddy simulation data in order to validate an analytical momentum availability model (Kirby, Dunstan & Nishino 2023 J. Fluid Mech. , vol. 976 , A24). Analysis of six wind farm cases, three with different atmospheric boundary-layer (ABL) heights and three with different turbine layouts, reveals that advection, pressure gradient forcing and turbulence are the dominating mechanisms in all cases, as is also assumed in the analytical model. The Coriolis effect however still has an important indirect influence through shear stress veering. Despite the fact that the individual submodels of the various mechanisms show varying accuracy, the combined analytical momentum availability model consistently performs well across all cases, except for the ‘half-farm’ case, where the inherent large-scale wind farm assumptions of the theory are less valid. The linearised version of the model increasingly overpredicts the momentum availability for increasing ABL heights and it is found that this is related to the ABL Rossby number. Based on this observation, we propose an extension of the original linear model, which improves its accuracy for the considered cases and makes it more generally applicable, in particular to cases with tall ABL heights or large Coriolis frequencies.