The global properties of nocturnal stable atmospheric boundary layers

Accurate prediction of the global properties of wall-bounded turbulence holds significant importance for both fundamental research and engineering applications. In atmospheric boundary layers, the relationship between friction drag and geostrophic wind is described by the geostrophic drag law (GDL). We use carefully designed large-eddy simulations to study nocturnal stable atmospheric boundary layers (NSBLs), which are characterized by a negative potential temperature flux at the surface and neutral stratification higher up. Our simulations explore a wider range of the Kazanski-Monin parameter, mu=L-f/L-s=[16.7,193.3], with L-f the Ekman length scale and L(s )the surface Obukhov length. We show collapse of the GDL coefficients onto single curves as functions of mu, thereby validating the GDL's applicability to NSBLs over a very wide mu mu range. We show that the boundary-layer height hh scales with root LfLs, while both the streamwise and spanwise wind gradients scale with u(& lowast;)(2)/(h(2)f), where u(& lowast;) represents the friction velocity and ff the Coriolis parameter. Leveraging these insights, we developed new analytical expressions for the GDL coefficients, significantly enhancing our understanding of the GDL for turbulent boundary layers. These formulations facilitate the analytical prediction of the geostrophic drag coefficient and cross-isobaric angle.