Flux-gradient relation and atmospheric wind profiles — an exploration using WRF and lidars

A common closure for the planetary boundary layer in numerical weather models assumes a direct relation between turbulent fluxes and the mean wind vertical gradient, i.e., the flux-gradient relation or K-theory. This assumption implies that the angle β between the momentum stress vector and the mean gradient of the velocity vector are aligned, i.e., β = 0°. This is not what we observe from measurements. We quantify the misalignment of β in offshore conditions using measurements from a long-range Doppler profiling lidar and numerical simulations from the New European Wind Atlas mesoscale model output. We compare vertical profiles of wind speed, wind direction, momentum fluxes, and β up to 500 m, hence covering the rotor areas of modern offshore wind turbines and beyond. The results show that β ≈ −18° on average, with a lower, but still non-zero, value under stable stability conditions, ≈ −7°. We illustrate that the simulations describe well the mean wind speed and momentum fluxes within the observed levels, but the characterization of wind turning effects could be improved.