Anisotropic turbulence in the Ekman boundary Layer

The Ekman boundary layer is driven by the triadic balance of pressure gradient, Coriolis, and friction force. Under strongly stable stratification, the flow can become globally intermittent, with large-scale motions controlling the spatial organisation of quasi-laminar patches of fluid that extend from the outer layer down to the surface layer. Stable stratification additionally affects the Ekman spiral, making it shallower and characterized by a faster veering of the wind vector compared to neutral stratification, resulting in stronger directional wind shear.

In the present contribution, a dataset from direct numerical simulations (DNS) of a turbulent Ekman flow over a smooth and flat wall is used to investigate how the spatial organization of a globally intermittent flow and the modified Ekman spiral shape the anisotropy of the stress tensor. Multiple studies have shown that small-scale turbulence becomes more anisotropic with increasing stratification, with frequent occurrence of one-component anisotropic stress tensors (i.e. kinetic energy distributed along one dominant direction) that also characterizes the large scales. Previous analyses of small-scale coherent vortical structures in these DNS revealed that hairpin vortices within a turbulent patch of a globally intermittent flow are aligned along the same direction, which may contribute to shaping the anisotropy of the stress tensor at the large and small scales.

Scale-wise analyses of the flow and its stress anisotropy under strongly stable stratification and neutral stratification are performed to investigate these features. Results show that large-scale motions found in the outer layer are associated with a dominant energy-containing length scale that extends down to the inner layer. As a result, the energy spectrum in the inner layer has two dominant length scales, with shear-driven turbulence associated with the smaller length scale. Directional wind shear contributes to large-scale anisotropy as the surface is approached. Due to the strong coupling arising from global intermittency, information on anisotropy is transferred from the outer layer down to the surface layer.