Some Problems on Edding Diffusion

Abstract

If we assume that the mixing lengths of x, y-components (x-axis coincides with the direction of gradient wind) are not equal, and write the components of eddy velocity in the form following Prandtl's treatment, we can readily derive the coefficient of eddy viscosity along x-and y-direction in the form:
As the value of U and V, we adopted Ekman's spiral which has been observed by Mr. Fedor Schwandke at Hall/Leipzig and Hannover during the year from 1930 to 1933, and determined the value of ∂U/∂z, ∂V/∂z at each height by graphical method.
First we adopted Taylor's equipartition theory of edding energy, and discussed the value l₁, l₂ at each height. Thus we found that in the lower atmosphere the relation l2>l1 holds, which, with the approach to the height of gradient wind, tends to the relation l₂=l₁.
Next we rely on F. J. Scrase's observation. Assuming the relation l₁=l₂, we discussed the distribution of eddy velocity at each height. The value u'/v' thus obtaind gives a maximum value at a height of 100m and decreases with height.
Assuming rather a general case in which neither the condition v'²=u'² nor l₁=l₂ exists, wealso obtaind approximately the relation l₂_??_l₁, in the lower atmosphere. On account of the above discussion, we may conclude that the coefficient of eddy viscosity has a large value in the perpendicular direction to the general flow.
Adopting the coefficient of eddy viscosity k₁, k₂ we solved the equation of eddy motion. As the relation between surface wind and gradient wind, we have the following form.
which, of course, in case of k₁=k₂ reduces to Taylor's relation.