Turbulent boundary region, eddy motion

Equation 11.12 does not fit velocity profiles measured in a turbulent boundary layer and an alternative approach must be used. In the simplified treatment of the flow conditions within the turbulent boundary layer the existence of the buffer layer, shown in Figure 11.1, is neglected and it is assumed that the boundary layer consists of a laminar sub-layer, in which momentum transfer is by molecular motion alone, outside which there is a turbulent region in which transfer is effected entirely by eddy motion (Figure 11.7). The approach is based on the assumption that the shear stress at a plane surface can be calculated from the simple power law developed by Blasius, already referred to in Chapter 3. 

The eddies which give rise to short laminar motions along the wall are generated in the vicinity of the boundary in a region, located at the distance y0 from the interface, dominated by turbulence. The intensity of these eddies can be characterized by their kinetic energy E0 at that distance. The path length x is expected to depend on E0 and on the physical constants r and p. Consequently, dimensional analysis leads to... 

Here, H = 8500 m denotes the atmospheric scale height. Radon obviously would be a good tracer for turbulent mixing in the troposphere. Unfortunately, it is hard to measure. It should be noted that the assumption of a constant Kz in the troposphere is a reasonable approximation only for the region outside the planetary boundary layer (zs=2km). The air motions close to the earth surface are greatly influenced by friction, which causes the eddy coefficients to decrease from their values in the free troposphere. 

---