Symmetry Analysis of Mean Velocity Distribution in Stratified Atmospheric Surface Layers

The mean velocity distributions of unstably and stably stratified atmospheric surface layers (ASLs) are investigated here using the symmetry approach. Symmetry groups for the mean momentum and the Reynolds stress equations of ASL are searched under random dilation transformations, which, with different leading order balances in different flow regions, lead to a set of specific scalings for the characteristic length l13 (defined by Reynolds shear stress and mean shear). In particular, symmetry analysis shows that in the shear-dominated region, l13 scales linearly with the surface height z, which corresponds to the classical log law of mean velocity. In the buoyancy-dominated region, l13/L similar to z/L4/3 for unstably stratified ASL and l13/L similar to const for stably stratified ASL, where L is the Obukhov length. The specific formula of the celebrated Monin-Obukhov similarity function is obtained, and hence an algebraic model of mean velocity profiles in ASL is derived, showing good agreement with the datum from the QingTu Lake observation array (QLOA) in China.

Automated summary

The mean velocity distributions of unstably and stably stratified atmospheric surface layers (ASLs) are investigated using the symmetry approach. The study derived an algebraic model for mean velocity profiles in ASL and validated it with observational data.