Effects of turbulent dispersion on the wind speed profile in the surface layer

New Reynolds mean momentum equations including turbulent viscosity and dispersion are used to analyze the vertical profile of wind speed in the surface layer it is demonstrated that the wind profile of the surface layer including turbulent dispersion has a logarithmic modification on the classical power law under the condition of unstable stratification, the effect of dispersion is stronger than under stable stratification under neutral stratification, the power law degenerates to the logarithmic law, but the von Karman constant is replaced by k(1) = (1+ k/4)(-1) k, which can also be obtained by similarity theory.