Direct numerical simulation of stratified Ekman layers over a periodic rough surface

Abstract

Ekman layers over a rough surface are studied using direct numerical simulation. The roughness takes the form of periodic two-dimensional bumps whose non-dimensional amplitude is fixed at a small value and whose mean slope is gentle. The neutral Ekman layer is subjected to a stabilizing cooling flux for approximately one inertial period to impose the stratification. The Ekman boundary layer 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, Theor. Comput. Fluid Dyn., vol. 11, issue 3-4, 1998, pp. 263-279) 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 subcritical 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.