Turbulent Transfer in the Atmospheric Layer with Small Wind Shear

Abstract

The equation of eddy diffusivity K given by the product of the square of mixing length l and wind shear is not valid in the flow with small wind shear. If the wind shear used in the equation of K is replaced by a value averaged over relevant finite time Tl, the equation may become valid in the flow with small shear. The wind shear averaged over Tl can be written as the summation of the expected value and the deviation. Assuming that the probability distribution of the deviation is Gaussian, and that the structure function of wind velocity averaged over Tl obeys the 2/3 power law, we have
K=max(l2|dV/dz|, αl4/3). The value of a is estimated as 0.l≤α≤0.2 (MKS units).