From shear to veer: theory, statistics, and practical application

Abstract. In the past several years, wind veer – sometimes called “directional shear” – has begun to attract attention due to its effects on wind turbines and their production, particularly as the length of manufactured turbine blades has increased. Meanwhile, applicable meteorological theory has not progressed significantly beyond idealized cases for decades, though veer's effect on the wind speed profile has been recently revisited. On the other hand the shear exponent (α) is commonly used in wind energy for vertical extrapolation of mean wind speeds, as well as being a key parameter for wind turbine load calculations and design standards. In this work we connect the oft-used shear exponent with veer, both theoretically and for practical use. We derive relations for wind veer from the equations of motion, finding the veer to be composed of separate contributions from shear and vertical gradients of crosswind stress. Following from the theoretical derivations, which are neither limited to the surface layer nor constrained by assumptions about mixing length or turbulent diffusivities, we establish simplified relations between the wind veer and shear exponent for practical use in wind energy. We also elucidate the source of commonly observed stress–shear misalignment and its contribution to veer, noting that our new forms allow for such misalignment. The connection between shear and veer is further explored through analysis of one-dimensional (single-column) Reynolds-averaged Navier–Stokes solutions, where we confirm our theoretical derivations as well as the dependence of mean shear and veer on surface roughness and atmospheric boundary layer depth in terms of respective Rossby numbers. Finally we investigate the observed behavior of shear and veer across different sites and flow regimes (including forested, offshore, and hilly terrain cases) over heights corresponding to multi-megawatt wind turbine rotors, also considering the effects of atmospheric stability. From this we find empirical forms for the probability distribution of veer during high-veer (stable) conditions and for the variability in veer conditioned on wind speed. Analyzing observed joint probability distributions of α and veer, we compare the two simplified forms we derived earlier and adapt them to ultimately arrive at more universally applicable equations to predict the mean veer in terms of observed (i.e., conditioned on) shear exponent; lastly, the limitations, applicability, and behavior of these forms are discussed along with their use and further developments for both meteorology and wind energy.