Direct Numerical Simulation of the Turbulent Ekman Layer: Evaluation of Closure Models

A direct numerical simulation (DNS) at a Reynolds number of 1000 was performed for the neutral atmospheric boundary layer (ABL) using the Ekman layer approximation. The DNS results were used to evaluate several closure approximations that model the turbulent stresses in the Reynolds averaged momentum equations. Two first-order closure equations proposed by O'Brien and by Large, McWilliams, and Doney were tested; both models approximate the eddy diffusivity as a function of height using cubic polynomials. Of these two models, the O'Brien model, which requires data both at the surface layer and at the top of the boundary layer, proved superior. The higher-order k-epsilon model also agreed well with DNS results and more accurately represented the eddy diffusivity in this rotational flow.