Boundary Layer, Urban Meteorology and Land-Surface Processes

A very basic model for velocity statistics of an Ekman-like neutral turbulent layer

Ethan Cook
OU School of Meteorology

24 April 2015, 3:00 PM

National Weather Center, Room 5600
120 David L. Boren Blvd.
University of Oklahoma
Norman, OK

The PDF transport equations are derived in fully incompressible form in Lungren (1967). With initial joint distributions of velocity components, the time evolution can be obtained. Closures can be obtained for steady state statistics as well, wherein physics from the Navier-Stokes equations is substituted for the acceleration expression. In Wenzel and Baldauf (1998) obtains a bivariate PDF for the vertical and (one) horizontal velocity component by parameterizing the two point joint velocity distribution which arises from the pressure gradient term in the N.S. equations. Substitution for the pressure gradient is accomplished by taking the gradient of the N.S. equations and employing the Green's function for the Laplacian to obtain an expression for pressure.
The process of approximating terms involving the two-point distributions involves several steps and is conceptually difficult. We will describe a different, if somewhat less sophisticated, method of obtaining the joint pdf of velocity components using a simple first-order closure, somewhat analogous to the Ekman solution.

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