Universal Functions with Ekman Spiral and Monin–Obukhov Surface Layers

Today, computational fluid dynamics (CFD) is widely used for atmospheric dispersion at building scale. This type of simulation requires boundary conditions for wind, turbulence, and temperature. A classical way of imposing representative flow at open boundaries is to derive (universal) functions corresponding to idealised situations (e.g. constant shear stress, constant heat flux, such as in the Monin–Obukhov theory). In this paper, we first propose an analysis of universal functions for the surface layer and compare them to a 5-year data base of measurement on the SIRTA observatory (France). The conclusion is that these functions are in good agreement with the experimental data for moderate ratios of (distance to the ground divided by Obukhov length), but most of them do not fulfil asymptotic behaviours in the very stable or convective limit. We also compare the measurements with the extensions proposed by Gryning et al. (Bound Layer Meteorol 124(2):251–268, 2007), which take into account the height of the atmospheric boundary layer. Then, following the work of Nieuwstadt (Noct Bound Layer J Atmos Sci 41(14):2202–2216, 1984. https://doi.org/10.1175/1520-0469(1984)041$lt$2202:TTSOTS$gt$2.0.CO;2), we propose universal functions able to reproduce the Ekman spiral and consistent with moment-turbulence closures for stably stratified atmospheres.