Prediction of the Monin-Obukhov Similarity Functions from an Invariant Model of Turbulence

Abstract

The second-order, invariant modeling technique for turbulent flows as developed by Donaldson is applied to the atmospheric surface layer. The steady, high-Reynolds number equations reduce to a universal set when the variables are scaled by the shear stress and vertical heat flux as suggested by Monin and Obukhov. Numerical integration of these equations yields results for the mean velocity gradient, mean temperature gradient, Richardson number, rms vertical velocity and temperature fluctuations, and horizontal heat flux which agree favorably with experimental observations over the complete range of stability conditions.