On the Formulation and Universality of Monin–Obukhov Similarity Functions for Mean Gradients and Standard Deviations in the Unstable Surface Layer: Results from Surface-Layer-Resolving Large-Eddy Simulations

Abstract

Abstract Surface-layer-resolving large-eddy simulations (LESs) of free-convective to near-neutral boundary layers are used to study Monin–Obukhov similarity theory (MOST) functions. The LES dataset, previously used for the analysis of MOST relationships for structure parameters, is extended for the mean vertical gradients and standard deviations of potential temperature, specific humidity, and wind. Also, local-free-convection (LFC) similarity is studied. The LES data suggest that the MOST functions for mean gradients are universal and unique. The data for the mean gradient of the horizontal wind display significant scatter, while the gradients of temperature and humidity vary considerably less. The LES results suggest that this scatter is mostly related to a transition from MOST to LFC scaling when approaching free-convective conditions and that it is associated with a change of the slope of the similarity functions toward the expected value from LFC scaling. Overall, the data show slightly, but consistent, steeper slopes of the similarity functions than suggested in literature. The MOST functions for standard deviations appear to be unique and universal when the entrainment from the free atmosphere into the boundary layer is sufficiently small. If entrainment becomes significant, however, we find that the standard deviation of humidity no longer follows MOST. Under free-convective conditions, the similarity functions should reduce to universal constants (LFC scaling). This is supported by the LES data, showing only little scatter, but displaying a systematic height dependence of these constants. Like for MOST, the LFC similarity constant for the standard deviation of specific humidity becomes nonuniversal when the entrainment of dry air reaches significant levels.