Wind farm global blockage as an adverse pressure gradient problem: turbulence amplification and spectral modification in the induction region of a model wind farm

Abstract

The induction region of a model wind farm is investigated experimentally as an adverse pressure gradient (APG) turbulent boundary layer problem, using hot-wire anemometry. An array of porous discs, with diameter $D=50$\,mm representing the farm, in multiple configurations across two turbulent boundary layers of different depths, with farm-present and farm-absent configurations compared throughout. The farm imposes a spatially developing adverse pressure gradient in the approach flow. Spanwise-averaged measurements reveal systematic farm-scale global blockage extending to at least $10D$ upstream in all cases. The farm-induced turbulence intensity increase, which reaches up to $7\%$ relative to the farm-absent reference for the shallowest boundary layer, is shown by cumulative variance decomposition to be carried predominantly by large-scale motions of the boundary layer, whilst the small-scale turbulence intensity is only weakly affected. This selective large-scale energisation is consistent with the outer-layer amplification driven by an adverse pressure gradient. The concentration of farm-induced turbulence energy at scales comparable to or larger than the rotor diameter has direct implications for turbine fatigue loading, preferentially exciting coherent rotor-scale load fluctuations at the frequencies most damaging under fatigue. The results establish a quantitative link between wind farm global blockage and APG boundary layer physics.