Baroclinicity and directional shear explain departures from the logarithmic wind profile

Abstract

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.

Using observed and modelled heat fluxes for improved extrapolation of wind distributions

“…Here we are studying the effects of atmospheric stability only and therefore the impact of baroclinicity is ignored. We note that the inŕuence of baroclinicity on the wind proőle can be pronounced and the model can correct for this using A and B values that vary with respect to the mean geostrophic wind shear vector (Floors et al 2015;Ghannam and Bou-Zeid 2021).…”

“…In Eq. ( 13), the őrst three terms in the large brackets are the same as in Troen and Petersen (1989) and the last term is adapted from the wind proőle model from Ghannam and Bou-Zeid (2021). The latter model reduces to the logarithmic wind proőle in the limit Ro → ∞, but accounts for the effect of the boundary-layer height and baroclinicity.…”

A pressure-driven atmospheric boundary layer model satisfying Rossby- and Reynolds number similarity

“…This can seen as approximation whereby the minor effect of lateral winds provides a perturbation to the streamwise gradients, when considering the full wind shear dS/dz and gradient of mean kinetic energy dS 2 /dz. Ghannam and Bou-Zeid (2020) considered the effect of veer on ABL profiles, and derived an approximate model for such; the neglected terms in Eq. 6 Analytic solutions of the wind speed profile can be derived from Eq.…”

Review of wes-2020-130

“…This can seen as approximation whereby the minor effect of lateral winds provides a perturbation to the streamwise gradients, when considering the full wind shear dS/dz and gradient of mean kinetic energy dS 2 /dz. Ghannam and Bou-Zeid (2020) considered the effect of veer on ABL profiles, and derived an approximate model for such; the neglected terms in Eq. ( 6), with the above equation, can be compared to magnitudes implied by their model.…”