The vertical profiles of the wind speed and direction in atmospheric boundary layers are strongly controlled by turbulent friction. Some global weather forecast and climate models parameterize the turbulent momentum fluxes by means of a downgradient eddy diffusion approach, in which the same stability-dependent eddy viscosity profile is applied to both horizontal wind components. In the present study we diagnose eddy viscosity profiles from large-eddy simulations of a stable, a neutral and six convective boundary layers. Each simulation was forced by the same geostrophic wind of 15 ms$^{-1}$, but with a different surface heat flux. The stably stratified boundary layer sustains the largest friction and largest ageostrophic wind turning, due to its shallow depth, which leads to a steep slope (large vertical divergence) of the momentum fluxes. For convective cases we find that the eddy viscosity profiles for the two horizontal wind components are very different, in particular, we find negative eddy viscosities for the cross-isobaric wind component, indicating that its turbulent transport is counter the mean gradient. This implies that a purely downgradient diffusion approach for turbulent momentum fluxes is inadequate. To assess the consequence of applying an anisotropic diffusion approach, a modified solution of the Ekman spiral is presented. It is found that an anisotropic diffusion approach allows for a different vertical profile of the wind in terms of the height of maximum wind speed and the turning of the wind.

Motivated by an observed relationship between marine low cloud cover and surface wind speed, this study investigates how vertical wind shear affects trade-wind cumulus convection, including shallow cumulus and congestus with tops below the freezing level. We ran large-eddy simulations for an idealised case of trade-wind convection using different vertical shears in the zonal wind. Backward shear, whereby surface easterlies become upper westerlies, is effective at limiting vertical cloud development, which leads to a moister, shallower and cloudier trade-wind layer. Without shear or with forward shear, shallow convection tends to deepen more, but clouds tops are still limited under forward shear. A number of mechanisms explain the observed behaviour: First, shear leads to different surface wind speeds and, in turn, surface heat and moisture fluxes due to momentum transport, whereby the weakest surface wind speeds develop under backward shear. Second, a forward shear profile in the subcloud layer enhances moisture aggregation and leads to larger cloud clusters, but only on large domains that generally support cloud organization. Third, any absolute amount of shear across the cloud layer limits updraft speeds by enhancing the downward-oriented pressure perturbation force. Backward shear — the most typical shear found in the winter trades — can thus be argued a key ingredient at setting the typical structure of the trade-wind layer.

Momentum transport by boundary-layer turbulence causes a weak synoptic-scale vertical motion. The classical textbook solution for the strength of this Ekman pumping depends on the curl of the surface momentum flux. A new solution for Ekman pumping is derived in terms of the curl of the geostrophic wind and a term that depends in a non-trivial way on the vertical profile of the turbulent momentum flux. The solution is confined to a boundary-layer regime that is vertically well mixed and horizontally homogeneous. The momentum flux is computed from a commonly used bulk surface drag formula and a flux-jump relation to capture the entrainment flux of momentum at the top of the boundary layer. It is found that the strength of Ekman pumping is bounded. The weakening of Ekman pumping for enhanced turbulent surface friction can be explained from the fact that it will reduce the magnitude of the horizontal wind. It is demonstrated that entrainment of momentum across the top of the boundary layer tends to diminish the large-scale divergence of the wind. As momentum transport is parameterized in large-scale models, the analysis is relevant for the understanding and interpretation of the evolution of synoptic-scale vertical motions as predicted by such models.

Numerical simulations of the tropical mesoscales often exhibit a self-reinforcing feedback between cumulus convection and shallow circulations, which leads to the self-aggregation of large cloud structures. We investigate whether this basic feedback can be adequately captured by large-eddy simulations (LESs). To do so, we simulate the non-precipitating, cumulus-topped boundary layer of the canonical ‘BOMEX’; case over a range of numerical settings in two models. Since the energetic convective scales underpinning the self-aggregation are only slightly larger than typical LES grid spacings, aggregation timescales do not converge even at rather high resolutions (less than 100m). Therefore, high resolutions or improved unresolved scales models may be required to faithfully represent certain forms of trade-wind mesoscale cloud patterns and self-aggregating deep convection in large-eddy and cloud-resolving models, and to understand their significance relative to other processes that organise the tropical mesoscales.

A new generation of operational atmospheric models operating at horizontal resolutions in the range 200 m ~ 2 km is becoming increasingly popular for operational use in numerical weather prediction and climate applications. Such grid spacings are becoming sufficiently fine to resolve a fraction of the turbulent transports. Here we analyze LES results of a convective boundary layer obtained by coarsening horizontal grid spacings up to 800 m. The aim is to explore the dependency of the mean state and turbulent fluxes on the grid resolution. Both isotropic and anisotropic eddy diffusion approaches are evaluated, where in the latter case the horizontal and vertical eddy diffusivities differ in accord with their horizontal and vertical grid spacings. For coarsening horizontal grid sizes entrainment at the top of the boundary layer tends to get slightly enhanced for isotropic diffusion. An analysis of the energy spectrum shows that anisotropic diffusion causes relatively more dissipation of variance at smaller length scales. This leads, in turn, to a shift of spectral energy towards larger length scales. This can also be clearly seen from the different kinds of spatial organization. The present study therefore suggests that details with regards to the representation of processes at small scales might impact the organization at length scales much larger than the smallest scales that can be resolved by the model.