Reynolds-number independent modelling of low-order statistics in turbulent Ekman flow

Modelling of low-order statistics, in particular of the mean profiles of wind speed and direction, is a crucial task for many applications in the boundary layer. We present here a formulation of the profiles of wind speed and direction in turbulent Ekman flow based on asymptotic theory and data from direct numerical simulation. The profile of the stream-wise component follows the classical viscous, logarithmic and wake scaling. In the outer layer, the velocity component proles 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-ow 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.