Canopy flow

Bridge, B.J., Mott, J.J., Winter, W.H. Hartigan, R.J. (1983). Improvement in soil structure resulting from sown pastures on degraded areas in the dry savanna woodlands of northern Australia. Australian Journal of Soil Research, 21, 83-90. Cionco, R.M. (1972). A wind profile index for canopy flow. Boundary Layer Meteorology, 3, 255-63. 

There are several theoretical approaches to the canopy flows considered by meteorologists, [17, 155, 187, 522], In the simplest one-dimensional mathematical model, the canopy is of an infinite extent along the axis Ox of the flow direction. The following mathematical model with coupled ordinary differential equations is the usual approximation in this case [155] ... 

The results obtained by meteorologists for forest canopies are the most advanced. They are widely applied now by other scientists who deal with canopies of other kinds. The theoretical investigations of the forest canopy flows stimulated their laboratory investigations, to which a special paragraph has been devoted. 

Bennovitsky suggested and validated the experimental evidence that velocity profiles followed the logarithmic law just over the vegetation in the free stream [56], So the approximation (1.1) may be employed in this problem again. Three empirical parameters required were adopted from the theory of atmospheric canopy flows [155], For instance, the relation d = 0.65h was found [56]. 

This paper is mainly a general review of turbulent atmospheric flows through canopy flows and the various mathematical and computational modelling approaches that are available. The review which is mostly non-mathematical in its presentations, is particularly relevant to urban areas because of the urgency of developing methods for dealing with accidental releases in urban areas. The dispersion of contaminants flow studies is also included in this review. We focus on dispersion from localised sources released suddenly, or over longer periods. 

Figure 2.1 Characteristic features of canopy flows (especially urban canopies). Lo is outer-or meso- (regional) scale on which the canopy affects the dispersion. Lc and L/ are the canopy and inner length scales, respectively. Note that UG is the approach geostrophic wind speed above the boundary layer, UB is the typical wind speed associated with local buoyancy effects, e.g. downslope winds from nearby mountains. Hc is the canopy height and Hc is the standard deviation of building height.

Table 2.2 Main types and features of canopy flows on the mesoscale (urban, forests).

Several models of the droplet easily penetrable roughness were suggested to demonstrate that the Eulerian mathematical description of a canopy flow can be generalized to represent the more complex structures met in practice. Linking the numerical methods with the analytical solutions of simplified models, one examines the correctness of the models and obtains the analytical estimations useful for engineering purposes. 

The so-called 0°-canopy consisted of Up -orientated trees rotated to the wind direction a = 0° (that is, parallel to it). Hence, the resistance to the flow was mainly caused by the pressure drag force acting within the stem space and, within the crown space, by the surface shear stress on the triangular surfaces. No significant features of this canopy flow were found at the location X=10 rows to distinguish it from the flow associated with the canopy consisting only of stems . 

In particular, a hypothesis was recently formulated for canopy flows [186, 187] that, because of an inflexion point on the mean velocity profile U(z) between the internal and external flows, an instability occurs over the PR s leading edge that creates coherent vortices. This hypothesis and its explanation is discussed in Chapters 4 and 5. 

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. 

The canopy flow itself breaks down into upper and lower canopy layers. In the upper canopy the linearised momentum balance to 0[H/L is,... 

Figure 6.1 Three regimes of canopy flow. Three scales of turbulence are present. The smallest scale (black circles) is set by the canopy morphology, specifically the diameter of and spacing between individual canopy elements, such as stems and branches. Drag discontinuity at the canopy interface generates a shear-layer that produces vortices via Kelvin-Helmholtz (K-H) instability (shown as solid, black ovals). Boundary layer vortices are present above the canopy (dashed gray). When H/h is small the water surface constrains the boundary layer eddy scale.

Figure 6.9 Velocity profile in and above a submerged canopy. In the upper portion of the canopy flow is predominantly driven by turbulent stress, which penetrates downward into the canopy over attenuation scale (aCD) l. Below this flow is driven by potential gradients due to bed- or pressure gradients. At the top of the canopy the discontinuity in drag generates a mixing-layer. Above this the profile transitions to a logarithmic boundary layer profile.

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... 

The expressions are functionally similar to those derived from under canopy flow. Artificial plastic trees were selected by Meroney [410] to reproduce the median behavior of measurements made about live trees (Colorado Blue Spruce, Juniper, Pine, and... 

The fraction of the total canopy volume that is not occupied by the fluid cannot be neglected for urban building array geometries. However, extensive investigations and measurements have shown many common features with the other canopy flows. Therefore, some of the discoveries made in canopy flow studies have also been successfully applied to urban canopies . 

A consistent theory for the phenomenon of canopy flows has been developed over the last twenty five to thirty years. It arose from studies of flows around single isolated obstacles and now accounts for the effects of groups of obstructions and with models for particular canopy types. 

Ayotte, K.W., Finnigan, J.J., and Raupach, M.R. (1998) A second order closure for neutrally stratified vegetative canopy flows, Boundary-Layer Meteorol 90, 189-216. 

Gross, G. (1993) Numerical Simulation of Canopy Flows, Berlin - Heidelberg, Springer Verlag. 

Wilson, N.R., and Shaw, R.H. (1977) A higher-order closure model for canopy flow, J. Appl. Meteorol. 16, 1197-1205. 

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