A parametric large-eddy simulation study of wind-farm blockage and gravity waves in conventionally neutral boundary layers

Abstract

We present a suite of large-eddy simulations (LES) of a wind farm operating in conventionally neutral boundary layers. A fixed 1.6 GW wind farm is considered for 40 different atmospheric stratification conditions to investigate effects on wind-farm efficiency and blockage, as well as related gravity-wave excitation. A tuned Rayleigh damping layer and a wave-free fringe-region method are used to avoid spurious excitation of gravity waves, and a domain-size study is included to evaluate and minimize effects of artificial domain blockage. A fully neutral reference case is also considered, to distinguish between a case with hydrodynamic blockage only, and cases that include hydrostatic blockage induced by the air column above the boundary layer and the excitation of gravity waves therein. We discuss in detail the dependence of gravity-wave excitation, flow fields and wind-farm blockage on capping-inversion height, strength and free-atmosphere lapse rate. In all cases, an unfavourable pressure gradient is present in front of the farm, and a favourable pressure gradient in the farm, with hydrostatic contributions arising from gravity waves at least an order of magnitude larger than hydrodynamic effects. Using respectively non-local and wake efficiencies $\eta _{nl}$ and $\eta _{w}$ , we observe a strong negative correlation between the unfavourable upstream pressure rise and $\eta _{nl}$ , and a strong positive correlation between the favourable pressure drop in the farm and $\eta _{w}$ . Using a simplified linear gravity-wave model, we formulate a simple scaling for the ratio $(1-\eta _{nl})/\eta _{w}$ , which matches reasonably well with the LES results.