(formerly paper 5.5) Dispersive fluxes and canopy flows: Just how important are they?

Dispersive fluxes result from spatial correlations between regions where local means differ from the spatial mean. They combine with turbulent and molecular fluxes to produce the horizontally averaged total flux in the spatially averaged plant-canopy flow and conservation equations.

Dispersive fluxes are potentially significant in flows distorted by roughness elements, however they are rarely measured in the field because of the cost and difficulty of erecting numerous towers within a plant canopy or urban area. In wind tunnel experiments they are easier to measure, although constructing a true spatial average is often compromised by probe and traverse gear dimensions.

We compare dispersive fluxes of momentum and a scalar with area-averaged turbulent fluxes in a sparse wind-tunnel-model plant canopy. The Black Forest model was constructed of small light globes with a distinct crown and trunk region. Heat was used as a passive scalar that was independently introduced to the flow at ground and crown heights. Four scalar source distributions were generated, ranging from ground-only to canopy-only. Hotwire anemometery with simultaneous coldwire measurements were used to sample vertical profiles at eleven locations throughout the canopy area.

Comparisons of momentum fluxes show that the dispersive fluxes are much smaller in the upper canopy than the turbulent fluxes. At h, the area-averaged dispersive flux is of order 0.001 m2s-2 whereas the area-averaged turbulent flux is -0.558 m2s-2. These results support conclusions by other workers that dispersive momentum fluxes are insignificant in the upper canopy and for z > h. In contrast, for z < 0.5h, the dispersive flux is the same order of magnitude as the turbulent flux.

Over much of the canopy height, vertical gradients in dispersive momentum flux are 2-3 times smaller than those for turbulent momentum flux. Above 0.6h, however, dispersive flux divergence increases rapidly to a maximum of almost (minus) one half of the turbulent flux divergence. Neglect of the dispersive flux divergence term in this region of the canopy layer would lead to a 50% overestimation of the canopy drag.

Comparisons of scalar fluxes show that dispersive fluxes and turbulent fluxes are of similar magnitude within the model plant canopy. The greater importance of scalar dispersive fluxes relative to those for momentum follows because both w" and c" are asymmetrically disposed about each canopy element in contrast to the dispersive momentum flux where u" is symmetric and w" asymmetric about an element so that the spatial integral of their product is small (" denotes departures from the spatial mean). The role played by dispersive fluxes increases as the source distribution moves from canopy-only to ground-only.

The sum of dispersive and turbulent fluxes matches source distributions inferred from electrical loading only approximately. While some of this mismatch may be attributed to spatial undersampling, an important component of scalar turbulent flux is carried by eddies that cannot be resolved by the heat flux sensor. Spectral analysis confirms this.