A Second-Order Closure for Neutrally Stratified Vegetative Canopy Flows

Abstract

An existing second-order closure model is modified to include the effects on mean and turbulent motions of form and viscous drag in vegetative canopies. The additional physical mechanisms represented by the closure are viscous and pressure drag on canopy elements, their role in momentum absorption, in the creation of fine scale turbulent eddies and in enhancing the total viscous dissipation in the canopy airspace. Viscous dissipation is split into a standard 'isotropic’ contribution associated with the spectral eddy cascade and a foliage contribution associated with work against pressure and viscous drag on the foliage. Changes in the turbulent time scale that result from these mechanisms are included in the standard parameterisations of third moments and of the eddy cascade contribution to dissipation. The model is tested against a wind- tunnel 'wheat’ canopy, a corn canopy and a eucalypt canopy, a height range from 50 mm to 12.6 m. Model results show that the parameterisations of foliage interaction used in the closure are sufficiently robust to reproduce second-moment profiles within and above vegetative canopies to a high degree of accuracy without resorting to 'tuning’ of the model constants. The model also shows the natural emergence of two length scales, one associated with the familiar eddy cascade isotropic contribution to total dissipation and the other associated with the length scales of the canopy elements.