Direct and large eddy simulations of a bottom Ekman layer under an external stratification

A steady Ekman layer with a thermally stratified outer flow and an adiabatic boundary condition at the lower wall is studied using direct numerical simulation (DNS) and large eddy simulation (LES). An initially linear temperature profile is mixed by turbulence near the wall, and a stable thermocline forms above the mixed layer. The thickness of the mixed layer is reduced by the outer layer stratification. Observations from the DNS are used to evaluate the performance of the LES model and to examine the resolution requirements. A resolved LES and a near-wall model LES (NWM–LES) both compare reasonably well with the DNS when the thermal field is treated as a passive scalar. When buoyancy effects are included, the LES mean velocity and temperature profiles also agree well with the DNS. However, the NWM–LES does not sufficiently account for the overturning scales responsible for entrainment at the top of the mixed layer. As a result, the turbulent heat flux and the rate of change of the mixed layer temperature are significantly underestimated in the NWM–LES. In order to accurately simulate the boundary layer growth, the motions responsible for entrainment must either be resolved or more accurately represented in improved subgrid-scale models.