Logarithmic profiles of velocity in stably stratified atmospheric boundary layers

The universal velocity log law proposed by von Kármán in wall-bounded turbulent flows is one of the cornerstones of turbulence theory. When buoyancy effects are important, the universal velocity log law is typically believed to break down according to Monin-Obukhov similarity theory (MOST), which has been used in almost all global weather and climate models to describe the dependence of the mean velocity profiles on buoyancy near the earth's surface and to characterize the surface-atmosphere exchange of momentum, heat, water vapor, and carbon dioxide. In contrast to MOST, we propose logarithmic profiles of near-wall mean velocity in the stably stratified atmospheric boundary layers based on direct numerical simulations and field observations across a wide range of buoyancy effects. We find that buoyancy does not seem to change the logarithmic nature of velocity profiles but instead modifies the slope of the log law in stably stratified conditions. This paper provides a perspective on wall turbulence and can be applied to numerical simulations of turbulence, weather, and climate.