Logarithmic profiles of velocity in stably stratified atmospheric boundary layers

Abstract

The universal velocity log law first proposed by von K\'arm\'an in the near-wall region of turbulent shear 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 in the atmospheric boundary layer. In contrast to MOST, we propose new 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 change the logarithmic nature of velocity profiles but instead modifies the slope of the log law in stably stratified conditions.