Departure from K-theory in the planetary boundary layer

Abstract. It is well known that when eddies are small, the eddy fluxes can be directly related to the mean vertical gradients, the so-called K-theory, but such relation becomes weaker the larger the coherent structures. Here, we show that this relation does not hold at heights relevant for wind energy applications. The relation implies that the angle (β) between the vector of vertical flux of horizontal momentum and the vector of the mean vertical gradient of horizontal velocity is zero, i.e., the vectors are aligned. This is not what we observe from measurements performed both offshore and onshore. We quantify the misalignment of β using measurements from a long-range Doppler profiling lidar and large-eddy simulations. We also use mesoscale model output from the New European Wind Atlas project to compare with the lidar-observed vertical profiles of wind speed, wind direction, momentum fluxes, and the angle between the horizontal velocity vector and the momentum flux vector up to 500 m both offshore and onshore, hence covering the rotor areas of modern wind turbines and beyond. The results show that within the range 100–500 m, β = −18° offshore and β = 12° onshore, on average. However, the large-eddy simulations show β ≈ 0°, partly confirming previous modeling results. We illustrate that mesoscale model output matches the observed mean wind speed and momentum fluxes well, but that this model output has significant deviations with the observations when looking at the turning of the wind.