Wind Veer and Speed in Turbulent Ekman Flow Part I: Scaling Analysis and Velocity Profile Model

Abstract

The profiles of wind speed and direction in turbulent Ekman flow are formulated based on asymptotic theory and data from direct numerical simulation. The profile of the streamwise component, considered in a wall-stress-aligned reference frame, follows the classical viscous, logarithmic and wake scaling. In the outer layer, the velocity component profiles can be described by an Ekman-spiral with adapted boundary conditions that result in a reduction of the spiral-like rotation. The span-wise component poses a conceptual challenge to the channel-flow analogy in the context of asymptotic matching; it exhibits a mixed scaling in the surface layer, but follows outer scaling for most of the outer layer. Viscous stress scales universally across the boundary layer in inner units while the total stress becomes universal as a function of the outer height, commonly denoted as . This implies a mixed scaling for the turbulent stress and eddy viscosity across the inner layer and convergence to a scaling as function of the outer height across the outer layer for increasing scale separation, i.e., for increasing Reynolds number. The extrapolation to these scaling to atmospheric scale separation is confirmed via large-eddy simulation in part II of this manuscript.