Vertical Eddy Diffusion Coefficient Ka

The expressions available for Kzz are based on Monin-Obukhov similarity theory coupled with observational or computationally generated data. It is best to organize the expressions according to the type of stability. 

We note that for stable and neutral conditions fy(z,/L) is identical to that for momentum transfer, given by (16.75). For unstable conditions, (z/L) = (c m(z/L))2 

Since we generally need expressions for Kzz that extend vertically beyond the surface layer, we now consider some available correlations for the entire Ekman layer. 

Unstable Conditions In unstable conditions there is usually an inversion base height at z = Zi that defines the extent of the mixed layer. The two parameters that are key in determining Kzz are the convective velocity scale wr and Zi- We expect that a dimensionless profile Kzz = Kzz/w,z., which is a function only of z/z., should be applicable. This form should be valid as long as Kzz is independent of the nature of the source distribution. Lamb and Duran (1977) determined that Kzz does depend on the source height. With the proviso that the result be applied when emissions are at or near ground level, Lamb et al. (1975) and Lamb and Duran (1977) derived an empirical expression for Kzz under unstable conditions, using the numerical turbulence model of Deardorff (1970)  

Other expressions for Kzz in unstable conditions exist, notably those of O Brien (1970) and Myrup and Ranzieri (1976), that are similar in nature to (18.121). 

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