Baroclinicity and directional shear explain departures from the logarithmic wind profile

Similarity and scaling arguments underlying the existence of a logarithmic wind profile in the atmospheric surface layer (ASL) rest on the restrictive assumptions of negligible Coriolis effects (no wind turning in the ASL) and vertically-uniform pressure gradients (barotropic atmospheric boundary layer, ABL). This paper alleviates these asymptotic arguments to provide a realistic representation of the ASL where the common occurrence of baroclinicity (height-dependent pressure gradients) and wind turning, traditionally treated as outer-layer attributes, take part in modulating the ASL. The approximation of a constant-stress ASL is first replaced by a refined model for the Reynolds stress derived from the mean momentum equations to incorporate the cross-isobaric angle (directional shear) and a dimensionless baroclinicity parameter (geostrophic shear). A model for the wind profile is then obtained from first-order closure principles, correcting the log-law with an additive term that is linear in height and accounts for the combined effects of wind turning and baroclinicity. Both the stress and wind models agree well with a suite of large-eddy simulations in the barotropic and baroclinic ABL. The findings provide a methodology for the extrapolation of near-surface winds to some 200 m in the near-neutral ABL for wind energy applications, the validation of the surface cross-isobaric angle in weather and climate models, and the interpretation of wind turning in field measurements and numerical experiments of the Ekman boundary layer.