Ekman layers over a rough surface are studied using direct numerical simulation (DNS). The roughness takes the form of periodic two-dimensional bumps whose non-dimensional amplitude is fixed at a small value (h+ = 15) and whose mean slope is gentle. The neutral Ekman layer is subjected to a stabilizing cooling flux for approximately one inertial period (2π/ f) to impose the stratification. The Ekman Boundary Layer (EBL) is in a transitionally rough regime and, without stratification, the effect of roughness is found to be mild in contrast to the stratified case. Roughness, whose effect increases with the slope of the bumps, changes the boundary layer qualitatively from the very stable (Mahrt, 1998) regime, which has a strong thermal inversion and a pronounced low-level jet, in the flat case to the stable regime, which has a weaker thermal inversion and stronger surface-layer turbulence, in the rough cases. The flat case exhibits initial collapse of turbulence which eventually recovers, albeit with inertial oscillations in turbulent kinetic energy.

The roughness elements interrupt the initial collapse of turbulence. In the quasi-steady state, the thickness of the turbulent stress profiles and of the near-surface region with sub-critical gradient Richardson number increase in the rough cases. Analysis of the turbulent kinetic energy (TKE) budget shows that, in the surface layer, roughness counteracts the stability-induced reduction of TKE production. The flow component, coherent with the surface undulations, is extracted by a triple decomposition, and leads to a dispersive component of near-surface turbulent fluxes. The significance of the dispersive component increases in the stratified cases. Motivated by the dynamics of the atmospheric boundary layer, we also examines the influence of Coriolis acceleration on wall-bounded turbulence. The large-scale structures of an Ekman boundary layer are compared to those of a channel. The distribution of energy across scales is studied by looking into the spectra of the velocity fluctuations. Linear stability analysis reveals the existence of an unstable range of wavenumbers which sustain the turbulence and lead to transverse “roll” structures observed in instantaneous snapshots of the flow. Finally, additional DNS has been performed to find the effect of the roughness geometry in counteracting the buoyancy. Changing the bump height without changing its aspect ratio has little influence. However, for sufficiently large surface cooling flux, roughness is unable to maintain a turbulent state. Comparison of all the simulated cases shows that the final value of Rib is sufficient to provide guidance on the overall state of the boundary layer and its characterization into the following regimes: (i) weakly stable, (ii) very stable with turbulence collapse and rebirth to a state of global intermittency, or (iii) very stable with turbulence collapse and no recovery.