Simulation and scaling analysis of small-scale roughness in neutrally and stably stratified turbulent Ekman flow

Atmospheric flows virtually always occur over rough surfaces, which enhances the drag, mixing and vertical transport of pollutants and moisture in the atmospheric boundary layer (ABL). During nighttime, when the absence of solar radiation leads to surface cooling, a stratified surface layer forms, and turbulence decreases in intensity and spatial extent, giving rise to large-scale intermittency. Roughness is known to counteract the buoyancy-induced reduction of turbulence in the stable regime by an increase of mixing, but the effects are lumped together in surface-layer similarity. To investigate the interaction of surface roughness and stable density stratification in the ABL at the process level, direct numerical simulation (DNS) of rough turbulent Ekman flow at Reynolds numbers well within the turbulent regime and for large domains is performed. Roughness is represented by an array of 56×56 roughness elements with a uniform width and height distribution on the lower wall. This small-scale three-dimensional surface roughness is fully resolved with an immersed boundary method (IBM) and has a packing density of 10%. For neutral stratification, we have obtained data in the transitionally rough regime and at the verge of the fully rough regime. Starting from the roughest neutral case with z₀⁺≈2, stable stratification is gradually increased with a constant-temperature (Dirichlet) boundary condition. The focus of this study is the direct effect of roughness on the stability regime, the rough-wall scaling in the logarithmic layer and the scaling for the roughness parameters z-nought for momentum and temperature, which is crucial for the Monin–Obukhov similarity theory.

* This work is funded by the ERC Starting Grant ”Turbulence-Resolving Approaches of the Intermittently Turbulent Atmospheric Boundary Layer [trainABL]” of the European Research Council (funding ID 851347). Simulations were performed on the resources of the High-Performance Computing Center Stuttgart (HLRS) on the Hawk cluster. The computing time and storage facilities were provided by the project trainABL with the project number 44187.