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, μ = 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 μ, thereby validating the GDL’s applicability to NSBLs _over a very wide μ range. We show that the boundary-layer height h scales with L_f L_s, while both the streamwise and spanwise wind gradients scale with u²_∗/(h²f), where u_∗ represents the friction velocity and f 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.