Similarity Statistics from a Direct Numerical Simulation of the Neutrally Stratified Planetary Boundary Layer

The turbulent flow in the unstratified Ekman layer over a smooth surface for the case of no horizontal rotation has been simulated. All relevant scales of motion are resolved so that no subgrid-scale parameterization is needed. The Reynolds number Re, while much smaller than those found in the atmosphere, is large enough that the flow exhibits a distinct logarithmic surface layer and yields shear-stress statistics that, to a good approximation, satisfy Reynolds number similarity. Agreement with shear-stress profiles from large eddy simulations is good, especially when latitude and geostrophic wind direction are taken into account. Results are used to estimate the ratio of the boundary layer depth to the Ekman scale u∗/f and the similarity constants needed to determine the geostrophic drag coefficient u∗/G and surface-stress angle α0 in the Re → ∞ limit characteristic of the neutral planetary boundary layer.