Flow within the canopy

Real terrestrial surfaces are rarely horizontally extensive, and are most often characterized by frequent changes in vegetation type and height. Particularly in naturally vegetated lands, the terrain commonly exhibits a complexity in slope and elevation that has major influences on the aerodynamics of plant canopies. Nevertheless, it is an essential first step to establish an understanding of flow through uniform canopies as a basis from which to study flows in even more complicated situations. 

The dimensionless drag coefficient cd (in meteorological practice the usual factor of 1/2 is omitted) is treated as isotropic and includes the influence of leaf and branch orientation, since the quantity a is the one-sided plant area density (m2/m3), not the cross-section exposed to the wind. Here, U is the scalar wind speed, while ui is the velocity vector in the -direction. 

Plant canopies exhibit remarkable turbulence statistics, which makes canopy aerodynamics a topic of substantial scientific interest. Of particular note are the degree to which vertical and streamwise velocities are correlated, and the high degree of skewness in these two velocity components. The correlation coefficient that relates stream-wise and vertical velocities, defined as 

Field observations have shown that pressure perturbations are also closely connected to coherent structures. Large-eddy simulations (LES) have been extremely useful in this regard and it is now recognized that a relatively large, positive pressure perturbation is centred at the scalar microfront and the top of the canopy. This pressure 

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We believe the major shortcoming of these models is inadequate meteorological input. In particular we need better descriptions of flow within the canopy and vertical flow profiles generated by drainage flow rather than mesoscale winds. We also need a fully operational three dimensional, complex terrain winds model. 

Vertical profiles of wind, temperature and scalar concentration within the canopy differ markedly from those found above the canopy. If above-canopy flow can be approximated as logarithmic, flow within the canopy is to be characterized as exponential (see upper left portion of Figure 4.1). The rate of depletion of wind with depth into the vegetation is directly related to the density of the canopy, which is usually expressed as the leaf surface area plus the cross-sectional area of cylindrical plant parts, such as branches and trunks, per unit volume that the material occupies. The curvature of the profile reverses in sign and creates an inflection point, which occurs close to the top of the stand when the canopy is sufficiently dense. If the stand is relatively open in its lowest levels, as is often the case in the trunk space of a forest, the wind profile can exhibit a secondary maximum before diminishing to zero at the ground surface. 

As described above, the flow within the canopy is heterogeneous at the scales d and AS. While this flow structure must be resolved to understand processes that occur at the scale of individual stems, such resolution is not needed, and in fact is quite cumbersome, when describing the flow over larger spatial scales. An averaging scheme is applied to reduce the complexity to tractable equations. The averaging method is nicely described in [522, 523], Following their notation, the velocity (a, v, w) and pressure p) field is first decomposed into a time average (overbar) and deviations from the... 

For continuity with flow within the canopy, the velocity is taken as a spatial and temporal average, (n), although above the canopy this spatial average is not needed. The effective momentum boundary is the vertical position within the canopy below which momentum from the overflow does penetrate. That is, for flow above the canopy, z = zm is an effective lower boundary and (H - zm) is the effective depth of the overflow. Friction velocity for the overflow may then be estimated as... 

Apart from the economic significance of such loss there are potentially adverse effects on the environment arising from acidification of rain and soil. Ammonia may react with hydroxyl radicals in the atmosphere to produce NOx contributing to the acidification of rain (4). Wet and dry deposition of NH3/NH4+ inevitably contributes to soil acidification through their subsequent nitrification. This effect can be accentuated in woodland by absorption of aerosols containing NH4+ within the canopy followed by transport to the soil in stem flow (5). In more extreme cases, NH3 emission from feedlots, pig and poultry... 

The drag force /, = fu,fv on the right-hand side of equations (1.4) or (1.5) parameterizes the influence of the canopy it equals zero outside it but depends on the local velocity and on the density within the canopy. All the individual obstructions that produce drag forces onto the flow in a unit volume Q, smeared into an average... 

Another vitally important question is how to model the turbulence within the canopy. It is clear by intuition that a number of vortices exists there, each shed from an individual obstruction. Figure 1.18 provides an experimental evidence to this. The known possible approach would be to introduce the effective turbulent viscosity v, and to model it as a function of coordinates and flow field quantities. The simplest case of a constant effective viscosity vf = const is known as the quasilaminar flow model. It will precede, in the Chapter 3, to more sophisticated models of turbulence considered in the Chapters 2, 4-8. 

As shown in Table 2.4, and reviewed by Britter and Hanna 2003 [81], most FAM s for the neighbourhood scale tend to focus on equilibrium flows within and just above the canopy. In a porous canopy (Figure 2.2), the mean velocity within the canopy Uc(z) is driven by the turbulent shear stresses generated in the intense shear layer just above the canopy. Here the ratio of Uc/U(z ), where U(z ) is the velocity at the top of... 

Figure 2.20 Porous canopy. Net air flow through the canopy with average velocity (Uc) (e.g. 0.3-0.5 Uh)- Plume has double structure within and above canopy structure, and also downwind.

We conclude that over the continuum scale the determining parameters are the wind speed Uh and turbulence initial parameters of the cloud/plume when it reaches the top of the canopy or, equivalently, the virtual source at the level of the canopy. Using suitable fast approximate models for the flow field over urban areas (e.g. RIMPUFF, FLOWSTAR), the variation of the mean velocity and turbulence above the canopy can be calculated. The FLOWSTAR code (Carruthers et al., 1988 [105]) has been extended to predict how (Uc) varies within the canopy. Dispersion downwind of the canopy can also be estimated using cloud/plume profiles, denoted by Gc,w,GA,w which are shown in Figures 2.20 and 2.22. 

The first attempts to model flow and transport in plant canopies that accommodated (i) the distinct microclimates of different stands of vegetation (ii) the separation of soil surface and layers of canopy as distinct sources and sinks of heat and mass and (iii) the influence of atmospheric stability or advection effects, applied gradient transfer to diffusion within the canopy space ([493]). In this procedure, a flux density is expressed as the product of a diffusion coefficient (turbuient or eddy diffusivity) and the gradient of the time average of the quantity of interest, as in the following examples ... 

One final prediction made by the theory of Finnigan and Belcher, [189] must be mentioned as it turns out to have important consequences for scalar transport. This is that even on hills of low slope, H/L 1 a region of reversed flow will appear within the canopy on the lee side of the hill, if the canopy is sufficiently deep and dense. This is... 

With Fr 1 globally, the flow in the Wind Tunnel model study divided into two distinct flow regimes. Above the canopy the flow remained fully turbulent but stably stratified with a gradient Richardson number Ri 0.1. Within the canopy, the flow was laminar with Ri 10 and flowed downhill as gravity currents on both the windward... 

The flow within a canopy is driven by the combination of turbulent stress generated by the overflow and by potential gradients associated with the hydrostatic pressure gradient and bed slope. The relative importance of these drivers depends on the depth of submergence (H/h) and the canopy momentum absorption, aCo The pressure-potential-) driven component is given in equation (6.6). A simple model for the stress-driven, in-canopy flow has been given for terrestrial canopies by Raupach and Thom [522] and applied to aquatic canopies by Abdelrhman [1], see also discussion in Chapter 4. With Uh the velocity at the top of the canopy (at z = h), the profile within the canopy is... 

Both of the above types of canopy are characterized by a very small fraction of the total canopy volume, so that canopy modelers can generally neglect this volume not occupied by the fluid. The same concept relates to many other types of obstructed geometries such as droplet layers, Sections 1.4 and 3.2, windmills, Section 1.4 and bubble flows, Section 7.5. Despite their diversity, many of these flows may, nevertheless, be united by the fact that one needs to account for both the internal decelerated flow within the obstructed geometry and for the external free flow over it. Field experiments in natural forests or in agricultural canopies, in wind tunnels with simulated forests of urban settlements and in water flumes with simulated aquatic vegetation have discovered many common features of these flows. These features are formalized in mathematical models. 

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