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Surface layer
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==Assumptions about the mixing length== From the figure above, we can see that the size of a turbulent eddy near the surface is constrained by its proximity to the surface; turbulent eddies centered near the surface cannot be as large as those centered further from the surface. From this consideration, and in neutral conditions, it is reasonable to assume that the [[Mixing length theory|mixing length]], <math>\xi'</math> is proportional to the eddy's depth in the surface: :<math>\xi' = kz</math>, where <math>z</math> is the depth and <math>k</math> is known as the [[Theodore von Kármán|von Kármán]] constant. Thus the gradient can be integrated to solve for <math>\overline{u}</math>: :<math>\overline{u} = \frac{u_*}{k}\ln\frac{z}{z_o}</math>. So, we see that the mean flow in the surface layer has a [[logarithm]]ic relationship with depth. In non-neutral conditions the mixing length is also affected by buoyancy forces and [[Monin-Obukhov similarity theory]] is required to describe the horizontal-wind profile.
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