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

TL;DR

This paper validates and extends an analytic model for momentum availability in wind farm flows, using LES data to improve predictions across different atmospheric conditions and turbine layouts.

Contribution

It evaluates the original model's accuracy with LES data and proposes an extension to improve predictions for tall boundary layers and strong Coriolis effects.

Findings

The full model performs well across various cases.

The linearized model overpredicts with increasing ABL height.

The extension improves model accuracy for tall ABLs and strong Coriolis effects.

Abstract

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 (LES) data in order to validate an analytic momentum availability model (Kirby, Dunstan, & Nishino, J. Fluid Mech., vol. 976, 2023, A24). Application of the model to six wind farm cases, three with different atmospheric boundary-layer (ABL) heights and three with different turbine layouts, shows that the full model performs well across all cases, but that its linearized version increasingly overpredicts the momentum availability for increasing ABL heights. It is found that the overprediction is related to the ABL Rossby number, and 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 strong Coriolis forcing.