Anisotropy of globally intermittent flows in the Ekman boundary Layer

The characteristics of the planetary boundary layer drastically depend on its density stratification. In the stable boundary layer (SBL), strong stratification can lead to the absence of turbulence. Quasi-laminar patches develop locally and can extend across the entire boundary layer, leading to a globally intermittent flow. Multiple studies have also shown that small-scale turbulence becomes more anisotropic with increasing stratification, with frequent occurrence of a one-component Reynolds stress tensor (i.e., kinetic energy along a main direction) that also characterizes the large scales, such as gravity waves or other submeso motions. Turbulence intermittency and anisotropy challenge traditional boundary-layer theories, which are based on homogeneous, isotropic turbulence. 

Direct numerical simulations (DNSs) of stably stratified turbulent Ekman flows over a smooth wall have shown that globally intermittent flows are well organized at both the large and the small scales. Quasi-laminar and turbulent patches, even near the surface, are aligned along a distinct direction comparable with the orientation of large-scale coherent structures that develop further above in the outer layer. Within the turbulent patches, small-scale hairpin vortices are oriented along a similar direction. Whether the flow organization contributes to the occurrence in the SBL of one-component states of anisotropy at both large and small scales is the object of the present contribution.

We analyze the spectra of kinetic energy and the anisotropy of the stress tensor at multiple heights and across scales from the previously mentioned DNSs. Comparison with the better-known setup of a neutrally stratified Ekman flow, where continuous and isotropic turbulence develops, is performed.

Large-scale coherent structures in the outer layer are found to be one-component and to influence the spectra of kinetic energy down to the surface. While in the neutral case only one peak of kinetic energy is observed, occurring at small scales, a second peak at large scales is found in the stably stratified case, with an energy-containing length scale consistent across the entire boundary layer. This suggests that the large-scale organization near the surface is related to the one-component structures further above. The anisotropy of the large scales near the surface, however, has a two-component signature (i.e., kinetic energy along two main directions), typical of sheared flow, instead of a one-component signature. This feature is observed only in the stable case, characterized by a shallower spiral than in the neutral case, pointing to directional wind shear as the driver of large-scale anisotropy. Patches of organized hairpins do not have a one-component contribution to the flow anisotropy, suggesting that the one-component structures in the outer layer do not influence the small-scale anisotropy near the surface. Instead, directional wind shear appears to influence the hairpins’ orientation, which is height-dependent.