No viewer Trajectories in a Plant Canopy



In a crop or forest canopy, a substantial proportion of the scalar concentration (eg. of heat and water vapour) is contributed by the non-diffusive "near field" wakes of the nearby leaves, shedding heat and vapour to the airstream. By simultaneous measurement of mean profiles and eddy fluxes, T. Denmead and F. Bradley (CSIRO Environmental Mechanics, Canberra) have demonstrated the routine occurrence of counter-gradient heat and vapour fluxes in a pine forest. It is natural, then, to turn to a Lagrangian description, when wishing to quantify turbulent transport in a canopy.

But turbulent velocity statistics within a canopy are non-Gaussian, and extremely vertically-inhomogeneous. Much of the vertical exchange is accomplished by intermittent large eddies, whose origination possibly owes to an instability with respect to the inflexion-point in the wind profile. The pdf of the vertical velocity PE(w) is highly skewed, Skw -1, and in much of the canopy space, turbulence intensity is large (standard deviations of velocity fluctuations u',v' are NOT small with respect to the mean velocity U).

w-skewness is the signature of the intermittent large gusts, and since accounting for skewness had improved LS predictions of the CBL, one naturally expected an LS model properly derived from the skew Eulerian pdf ought to best handle canopy dispersion: a multi-dimensional trajectory model based on non-Gaussian velocity statistics seemed in order. Flesch and Wilson (1992) constructed such a model, for vertical and the alongwind fluctuations (U', W'). Two problems arose: (a) even given the joint pdf PE(u,w), Thomson's criteria do not provide a unique multi-dimensional LS model; and (b) given only the low-order moments of u and w, what is the p.d.f.? Concerning (a), non-uniqueness was resolved by postulating that Thomson's should act to conserve the direction of the Lagrangian velocity fluctuation vector. Concerning (b), following an idea of Baerentsen and Berkowizc, Flesch and Wilson superposed two joint Gaussians. Means and covariances of the individual joint-Gaussians were tailored to reproduce the lowest five moments of w, the lowest four moments of u, and the covariance . This was quite arbitrary, and entailed the hazard that correctly fitting the low moments might constrain other moments to unrealistic values.

Flesch and Wilson simulated experiments in which heat was released as a tracer, from line and area sources, within a model crop in a turbulent wind tunnel boundary layer. The surprising outcome of the work was that the more-complex LS model which accounted for the known skewness and kurtosis of the canopy velocity statistics performed worse than Thomson's (1987) multi-dimensional model based on Gaussian Eulerian statistics! Perhaps the cause was our adoption of an ad hoc pdf: the "best" (or least biased) choice would have been the mmi pdf. However it may also be that the extreme vertical inhomogeneity of canopy flow (in contrast to CBL flow) implies a less critical dependence (of canopy dispersion) on the velocity skewness. It is pertinent here to quote Dr. J. Hunt: "I believe that inhomogeneity will dominate over the niceties of third and fourth moments."


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Last Modified: 27 June 1995