where L and l are the spacing parameters for uniform roughness and are the results of spatially averaging the roughness effects. In addition to the usual turbulence modeling closure requirements for - pu v , u '2, and - pv h , the roughness model has closure requirements for CD and Nud .

The turbulence model is not modified to include roughness effects since the physical effects of the roughness on the flow are explicitly included in the differential equations. The Prandtl mixing length with van Driest damping is used for turbulence closure. Hence

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