Departure from flux-gradient relation 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 flux-gradient relation, but such a 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 flux–gradient relation assumes 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., these vectors are aligned. Our observations do not support this assumption, either onshore or offshore. Here, we present analyses of a misalignment between these vectors from a Doppler wind lidar observations and large-eddy simulations. We also use a real-time mesoscale model output for inter-comparison 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. The observations show this within the height range 100–500 m, β = −18◦ offshore and β = −12◦ onshore, on average. However, the large-eddy simulations show β ≈ 0◦ both offshore and onshore. We show that observed and mesoscale-simulated vertical profiles of mean wind speed and momentum fluxes agree well; however, the mesoscale results significantly deviate from the wind-turning observations.