O'brien cubic polynomial

O'Brien cubic polynomial

An approximation for the eddy diffusivity K as a function of height z in a boundary layer of depth h with surface layer (SL) of depth z_SL:

where the tunable parameters in the equation are eddy diffusivities at the top of the surface layer and at the top of the boundary layer, K(z_SL) and K(h), respectively, the heights of those two layers, and the gradient of eddy diffusivity at the top of the surface layer ∂K/∂z.

Above the top of the boundary layer the eddy diffusivity is assumed to be constant at K(h), while at the surface it is assumed to be zero.
See K-theory, gradient transport theory, first-order closure, closure assumptions.

O'Brien, J. J. 1970. A note on the vertical structure of the eddy exchange coefficient in the planetary boundary layer. J. Atmos. Sci.. 27. 1213–1215.

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1. The layer of fluid near a boundary that is affected by friction against that boundary surface, and possibly by transport of heat and other variables across that surface.