Effects of wind-farm blockage and gravity waves on large-scale wind farms operating in conventionally neutral boundary layers

Conventionally neutral boundary layers (CNBLs) often develop offshore as a result of land-sea transitions. These conditions have been studied in measurement campaigns and numerical simulations. However, the cost and complexity of wind-farm large-eddy simulations (LESs) in the presence of thermal stratification above the atmospheric boundary layer (ABL) have limited the number of studies to a handful of atmospheric states. To fulfil this gap, we perform 40 LESs of a large-scale wind farm which operates in various atmospheric states, including different capping inversion heights and strengths, as well as lapse rates in the free atmosphere. We use this suite of LESs to investigate wind-farm induced gravity-wave effects on farm efficiency and blockage, as well as the flow behaviour in and around the farm. The numerical domain length and width are determined by a sensitivity study which reveals that atmospheres with shallow ABLs necessitate a wider domain to limit artificial domain blockage. A tuned Rayleigh damping layer and a wave-free fringe region method are used to avoid spurious excitation of gravity waves. To distinguish between a case with hydrodynamic blockage only, a fully neutral reference case is also considered. These results are compared with cases that include hydrostatic blockage excited by gravity waves. 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 and favourable pressure gradients are present in front and within the farm, respectively, with hydrostatic contributions arising from gravity waves at least an order of magnitude larger than hydrodynamic effects. We extend our analysis to the farm efficiencies, where we observe a strong negative correlation between unfavourable upstream pressure gradient and non-local efficiency, and a strong positive correlation between the favourable pressure drop in the farm and the wake efficiency. Using a simplified linear gravity-wave model, we formulate a scaling for the non-local to farm-efficiency ratio, which matches reasonably well with the LES results. Finally, we compare the LES results against several gravity-wave linear-theory models found in the literature, finding overall a very good agreement.