Logarithmic profile of temperature in sheared and unstably stratified atmospheric boundary layers

The impact of buoyancy on the mean velocity, temperature, and scalar concentration profiles in the lower atmosphere is typically investigated within the framework of MoninObukhov similarity theory (MOST). MOST is the theoretical foundation for parametrizing surface-atmosphere exchanges in nearly all weather, climate, and hydrological models. According to MOST, the classic logarithmic profiles of mean velocity and temperature break down as the buoyancy effects become important. However, recent studies on turbulent Rayleigh-Benard convection and natural convection along vertical walls suggest that the mean temperature in the near-surface region still follows a logarithmic profile. Motivated by these new results, we study the mean potential temperature profile in sheared and unstably stratified atmospheric boundary layers using direct numerical simulations and field observations. We find that the mean potential temperature profile remains logarithmic across a wide range of stability parameters, which characterizes the relative importance of buoyancy versus shear effects. Compared to MOST, our results suggest that the buoyancy force does not modify the logarithmic nature of the mean potential temperature profile, but instead modulates its slope, which is no longer universal and differs from 1/kappa, where kappa is the von Karman constant. This study provides another perspective on scalar turbulence in the atmospheric boundary layer.