Direct Numerical Simulation of Neutrally Stratified Ekman Boundary Layer

Abstract

Direct numerical simulations (DNSs) are performed for the turbulent Ekman boundary layer over a smooth surface. The Reynolds numbers Ref are set to be Ref = 400, 510, 600, 775, 1140 and 1393 where Ref is based on the geostrophic wind G, the kinematic viscosity ν and Coriolis parameter f. The simulations of Ref = 1140 and 1393 have been carried out on the Earth Simulator. In the cases of the higher Reynolds numbers, the mean velocity profiles show good agreement with the experimental data of Caldwell et al. (1972) and the DNS data of Coleman (1999). A low-speed large-scale structure is found in the upper region, whereas the well-known streaky structure appears in the vicinity of the wall. This large-scale structure is observed in a motion of a material line. The inclination of this structure does not coincide with the direction of the mean flow velocity. The reason is discussed based upon the motion of a material line whose initial position is horizontal in a vicinity of the wall. In addition, the eddy-viscosity model proposed by Blackadar (1962, 1965) is examined with respect to the obtained DNS data base. The improved model gives good agreement with the results by the present DNS. Keywords: