A prediction model for vertical turbulence momentum flux above infinite wind farms

Abstract

Large wind farms can significantly change the vertical layered structures and some of the statistical characteristics of the atmospheric boundary layer (ABL). The vertical turbulence momentum flux (VTMF) above a wind farm, which quantifies the vertical transport of the ABL, is important to meteorological simulation and power absorption of the wind farm. However, we still lack a fast prediction model for the VTMF. To this end, a suite of large-eddy simulations (LESs) is performed for infinite wind farms with various turbine positionings. We show that, in the outer layer above a wind farm, the VTMF normalized by the wind farm's equivalent frictional velocity exhibits a linear relationship with height, which agrees well with the linear law for the canonical rough wall. In contrast, in both the wake layer and the inner layer, the VTMF is significantly dependent on the turbine positionings. Consequently, a prediction model for the VTMF in the outer layer of the ABL is proposed only using the mean velocity in the inner layer of the ABL (below the wind rotors). The kinetic energy transport downward to wind farms is also calculated using the proposed model.