Chapter Two: The turbulent wind in plant and forest canopies

John J. Finnigan ^{Research School of Biology, Australian National University, Canberra, ACT, Australia}

Abstract

Anyone who has walked in a tall forest on a windy day will have been struck by how effectively the trees shelter the forest floor from the wind. Tossing crowns and creaking trunks, and the occasional crash of a falling tree, attest to the strength of the wind aloft, but only an occasional weak gust is felt near the ground. An attentive observer will also notice that these gentle gusts seem to precede the most violent blasts aloft. Clearly, the presence of the foliage absorbs the strength of the wind very effectively before it can reach the ground. It is surprising, therefore, that only in the last 2 decades have we arrived at a satisfactory understanding of the way that interaction with the foliage changes the structure of the wind in tall canopies and leads to significant differences from normal boundary-layer turbulence. In this chapter I explore these differences, focusing especially on what the special structure of canopy turbulence implies for disturbance ecology. Gentle gusts at the ground foreshadowing the strong blasts aloft are but one example of the many curious and counterintuitive phenomena we will encounter.

Keywords

Atmospheric boundary layer; Turbulence; Plant canopy flows; Dispersion

Introduction

While we now have a consistent theory of the turbulent wind in uniform canopies, the translation of this understanding to disturbed canopy flows is still in its infancy. Nevertheless, important recent advances have yielded general principles for the effect of hills and the proximity of forest edges and windbreaks on the mean flow, although this new understanding does not yet have much to say about effects on turbulence structure. My focus will generally be on strong winds, for which the effects of buoyancy on the turbulence are negligible, at least at canopy scale (although buoyancy can have significant effects at large scale, generating destructive downslope winds and microbursts as detailed in Chapter 3). However, buoyancy can be relevant at canopy scale in two contexts.

The first is fire. The heat released by burning fuel, whether the fire is confined to the ground cover or becomes a crown fire, can generate strong anabatic flow, with fires burning vigorously to hilltops and ridge crests. The second is cold air drainage, where the presence of the canopy exacerbates and concentrates gravity currents, which strongly influence carbon dioxide concentrations and ambient temperature patterns at night. Both these areas are poorly understood, although I make a few remarks at the end of this chapter based on some very recent analysis.

Returning to the central topic of strong winds and the damage they cause, phenomena that generate exceptional winds, such as cyclones, tornados, downslope windstorms, and microbursts, occur on scales much larger than the canopy height. Their ability to break or blow down trees depends on the way their effects are manifested at the canopy scale. We find that even very strong winds rarely exert static loads large enough to break or uproot mature trees. Instead, we must address phenomena such as resonance and the interaction between plant motion and turbulent eddies that can generate peak loads sufficient to cause the damage we observe. These questions are intimately involved with understanding the turbulent structure of canopies.

Let us begin by setting the scene for this discussion of canopy flow by a brief survey of atmospheric boundary layer flow in general, in which tall canopies form only one kind of a range of rough surfaces commonly encountered on land.

Notation

Most symbols are introduced when they first appear. Standard meteorological notation is used throughout based on a right-handed rectangular Cartesian coordinate system, x_i {x, y, z}, with x₁,(x) aligned with the mean velocity, x₂,(y) parallel to the ground and normal to the wind, and x₃ (z) normal to the ground surface. Velocity components are denoted by u_i {u, v, w}, with u_i,(u) the streamwise, u₂,(v) the cross-stream horizontal, and u₃,(w) the vertical component. The time-average operator is denoted by an overbar and departures from the time-average by a prime, thus ct=c¯+c′t si9_e . Within the canopy it is also assumed that a spatial average has been performed over thin slabs parallel to the ground so that the large point-to-point variation in velocity and other properties caused by the foliage is smoothed out. This spatial averaging process is an important formal step in deriving conservation equations for atmospheric properties in a canopy, but I do not discuss it further here. The interested reader should refer to Finnigan (2000) and references therein.

The structure of the atmospheric boundary layer over land

Throughout most of its depth and for most of the time, the atmosphere is stably stratified with the virtual potential temperature increasing with height. The virtual potential temperature θ_v is the temperature corrected for the natural expansion of the atmosphere as pressure falls with increasing height and for the effect on buoyancy of the water vapor content of the air (Garratt, 1992). If the rate of change of θ_v with height is zero, then the atmosphere is neutrally stratified and a parcel of air displaced vertically will experience no buoyancy forces. For ∂ θ_v/∂ z > 0, the air is stably stratified and displaced parcels will tend to return to their origins. For ∂ θ_v/∂ z < 0, the air is unstably stratified and parcels will spontaneously accelerate vertically, generating convective turbulence.

Only in the atmospheric boundary layer during daytime is this state of stable stratification regularly overturned through the heating of the layers of air that are in contact with the surface. Conventionally, we divide the atmospheric boundary layer (ABL) into a relatively shallow surface layer (ASL) around 50 to 100 m deep and a convective boundary layer (CBL) extending some kilometers in height, depending on time of day. In the ASL, the wind and turbulence structure directly reflect the character of the surface, while in the CBL the main role of surface processes is to provide a buoyancy flux that determines the depth of the CBL and is the source of the kinetic energy of the turbulent eddies within it.

The ABL is turbulent for most of the time, and the source of this turbulence in the CBL is the flux of buoyancy produced at the warm surface. Heated parcels of air rise until they reach a level in the atmosphere at which they experience no further vertical accelerations. This level, z_i, increases rapidly from a few hundred meters or less at sunrise to 1 to 2 km or more around noon on sunny days when the growth in z_i slows and ceases. The top of the CBL at z_i is usually marked by a sharp discontinuity in temperature or “capping inversion” (Fig. 2.1A and B). At sundown there is a rapid collapse in z_i (Fig. 2.1B). The key scaling parameters in the CBL are z_i and the velocity scale, w*,

w⁎=gT0w′θv′¯zi1/3

si10_e (2.1)

where g is the acceleration of gravity, T₀ is a reference temperature in degrees K, and w′θv′¯ is the kinematic turbulent flux of buoyancy. The over-bar denotes a time average, and the prime denotes a turbulent fluctuation around this average so that the kinematic buoyancy flux is the average covariance between turbulent fluctuations in θ_v and the vertical wind component, w. These scales remind us that the typical size of convectively-driven eddies in the CBL is its depth, z_i, while their velocity is set by the flux of buoyancy from the surface.

Fig. 2.1 Atmospheric boundary layer structure and profiles: (A) velocity and temperature profiles in the daytime convective boundary layer; (B) daily evolution of boundary layer structure; and (C) velocity and temperature profiles in the night-time stable boundary layer. From Kaimal, J. C., Finnigan, J. J., 1994. Atmospheric Boundary Layer Flows: Their Structure and Measurement. Oxford University Press, New York, reprinted with permission from Oxford University Press © 1994.

The vigorous mixing generated by convective turbulence in the CBL ensures that the average velocity and scalar gradients in the CBL are small as we see in Fig. 2.1A. In the daytime, strong wind shear and large gradients in potential temperature are confined to the ASL, which typically occupies 10% of the fully developed ABL. There, the turbulent eddies derive their energy from both the unstable stratification and the wind shear. In fact, the wind shear can maintain the ASL in a turbulent state even when the stratification is stable at night (Fig. 2.1C). These two contributions to turbulence are captured in the gradient Richardson number, Ri, the parameter we use to characterize the local stability of the atmosphere,

Ri=-gT0∂θ¯v∂z∂u¯/∂z2

si12_e (2.2)

Positive values of Ri denote stable stratification and negative, unstable. When Ri reaches positive values between 0.2 and 0.25, turbulence will decay and the boundary layer will become laminar except in some special circumstances. When Ri is negative, turbulence generated by the unstable stratification augments the “mechanical” turbulence produced by shear (Finnigan et al., 1984).

Within the ASL, the atmosphere responds much more directly to surface conditions than in the CBL, and this is reflected in the length and velocity scales used to describe the turbulence there. The appropriate length scale is the height z so that the distance to the ground controls the eddy size. The velocity scale is u*, a parameter called the friction velocity, which is formed from the frictional force τ exerted by the wind on the ground.

u⁎=τ/ρ=−u′w′¯

si13_e (2.3)

where ρ is air density, and over flat ground in steady winds, the kinematic surface stress, τ/ρ, is equal to (minus) the average covariance between streamwise, u′, and vertical, w′, wind fluctuations in the ASL, τ/ρ=−u′w′¯. Combining the two scales above and introducing a further lengthscale, the Obukhov length, L_MO, to represent the effects of buoyancy in the surface layer, a comprehensive similarity theory that describes profiles of wind, temperature, and other scalars, as well as their turbulent moments, has been developed for the ASL. This is the eponymous Monin-Obukhov scaling.With

LMO=-u⁎3κgT0w′θv′¯

(2.4)

Monin-Obukhov theory predicts that the velocity and scalar profiles in the surface layer will be logarithmic, taking the form:

u¯z=u⁎κlnz−dzθ−ψmz−dLMO

(2.5)

θ¯z−θ¯0=θ⁎κlnz−dzθ−ψθz−dLMO

(2.6)

where κ ≈ 0.4 is an empirical constant called von Karman's constant, d is an effective origin for the logarithmic profile that must be included when Monin-Obukhov theory is applied over tall vegetation, and z₀ and z_θ are the “roughness lengths” for momentum and scalar θ, respectively. They characterize the exchange properties of the surface for the particular species. The reference concentration of the scalar at the canopy surface is θ¯0 si18_e , while the “no-slip” condition ensures that the surface reference value for velocity is zero. The empirical functions ψ_m and ψ_θ of the dimensionless stability parameter (z − d)/L_MO embody the influence of stability on the velocity and scalar profiles, respectively. The effect on the logarithmic velocity profile of stable and unstable stratification can be seen in Fig. 2.2.

Fig. 2.2 Changes to the logarithmic velocity profile in the surface layer caused by stable and unstable stratification. From Kaimal, J. C., Finnigan, J. J., 1994. Atmospheric Boundary Layer Flows: Their Structure and Measurement. Oxford University Press, New York, reprinted with permission from Oxford University Press © 1994.

The canonical state of the daytime ABL in light to moderate winds is taken to be a convective well-mixed CBL with negligible gradients in wind and scalars above an ASL where profiles obey the logarithmic Monin-Obukhov forms of Eqs. (2.5) and (2.6). In reality, we rarely observe a truly well-mixed CBL, and measured wind and scalar profiles in the CBL usually have some vertical structure but, on average, the gradients there are much smaller than within the ASL. When synoptic winds are very strong, however, significant shear can exist through most of the boundary layer while the vertical variation in θ_v is small. The influence of the surface buoyancy flux then becomes secondary, and a balance between surface friction and Coriolis effects sets the depth of the ABL (Garratt, 1992). Similarly, at night, as the ground cools by radiation and the boundary layer is stably stratified, turbulent mixing is weak and the nocturnal boundary depth is seldom more than 200 m.

Over rough surfaces, which for our purposes are all land surfaces, we distinguish a further subdivision of the lowest part of the ASL into the canopy layer and the roughness sublayer (RSL); in the “canopy” category we include all tall roughness. The RSL extends from the ground to around two to three canopy heights, while the canopy layer itself occupies the bottom half or third of the RSL. What distinguishes the RSL from the ASL as a whole is that, within the RSL, the vertical and horizontal distributions of sources and sinks of scalars and momentum affect the average profiles, causing them to depart from the Monin-Obukhov forms (Fig. 2.3). For example, as the canopy is approached from above even in neutral conditions, the velocity and scalar profiles adopt forms similar to those found above the RSL in unstable conditions, where the shear-generated turbulence is augmented by buoyancy.

Fig. 2.3 Modifications to the logarithmic velocity profile in the roughness sublayer and the canopy. From Kaimal, J. C., Finnigan, J. J., 1994. Atmospheric Boundary Layer Flows: Their Structure and Measurement. Oxford University Press, New York, reprinted with permission from Oxford University Press © 1994.

Above the roughness sublayer, boundary layer turbulence over any kind of flat rough surface is essentially indistinguishable from that over a smooth surface (Raupach et al., 1991). Within the RSL and canopy layers, however, the differences are profound. Those differences are the main concern of the rest of this chapter. Detailed accounts of the behavior of the ABL, its turbulent structure, and the characterization of its several states may be found in many textbooks. To sample some different perspectives, see Kaimal and Finnigan (1994), Garratt (1992), Panofsky and Dutton (1984), or Fleagle and Businger (1963).

Characteristics of turbulent flow in and above plant canopies

The first theories of canopy turbulence supposed that the high turbulence intensities measured amid and just above the foliage were simply the result of the superposition of eddies shed from leaves and stalks onto standard boundary layer turbulence. However, this did not explain the observations that were available from the earliest two-point turbulence measurements (e.g., Allen, 1968) that canopy turbulence was correlated over distances similar to the canopy height—a much larger lengthscale than any associated with eddies shed from the foliage. Through the 1970s and 1980s, solid evidence accumulated to show that canopy turbulence was dominated by large, energetic eddies of whole-canopy scale and that the turbulence structure and dynamics were distinctly different from those of boundary layer turbulence.

This evidence was a mixture of the circumstantial, such as the failure of diffusive models of turbulent transport in the canopy (Denmead and Bradley, 1987), and the direct, such as that obtained from the application of conditional sampling techniques borrowed from wind tunnels to measurements in the field. These revealed the strongly intermittent nature of eddy activity in the canopy (Finnigan and Mulhearn, 1978; Finnigan, 1979a, b; Shaw et al., 1983) and showed that momentum transfer was accomplished by the infrequent penetration of strong gusts into the foliage from the ASL above. Time-height reconstructions of the turbulent velocity field in the x-z plane, obtained from multiple sensors in forests (e.g., Gao et al., 1989; Gardiner, 1994), were the first to link directly the spatial structure of the eddies with their temporal intermittency and confirmed earlier inferences from space–time correlations (Shaw et al., 1995).

Finally, a phenomenological theory—the “mixing layer” hypothesis—that explained the origin and scale of these large eddies was advanced by Raupach et al. (1996) and has since been more fully developed by Finnigan et al. (2009). Since 1996, a range of measurements in uniform canopies has strengthened its predictions, while limits to its range of validity have been explored by measurements in sparse canopies (Böhm et al., 2000, 2013; Novak et al., 2000). A comprehensive survey of canopy turbulence by Finnigan (2000) deals with its nature and dynamics in great detail. Here I concentrate on characteristics especially relevant to the forces exerted on plants in the canopy and hence to canopy damage and disturbance.

Velocity moments

Fig. 2.4A–I consists of a set of “family portraits” of single-point turbulence statistics measured in near-neutral flow in 12 canopies on flat ground. These plots are taken from Raupach et al. (1996) and range from wind tunnel models through cereal crops to forests. Details of the various canopies included in these plots are given in Table 2.1. The canopies span a wide range of roughness density λ (defined as the total frontal area of canopy elements per unit ground area) and a 500-fold height range. The vertical axis and length scales are normalized with canopy height h and velocity moments with either Uh=u¯h si19_e , the value of the time averaged “mean” velocity at the canopy height, or the friction velocity u*, where u* is measured in the constant shear stress layer above the canopy. Details for each experiment are given in Table 2.1. The observations in Fig. 2.4 have many common features, their differences being mainly attributable to their differing foliage area distribution. Fig. 2.4J shows that the main differences in this parameter lie in the extent to which the foliage is clustered in a crown at the canopy top.

si1_e — Fig. 2.4 A “family portrait” of canopy turbulence for canopies A to L in Table 2.1, showing profiles with normalized height z/h of (A) U/Uh=u¯z/u¯h; (B) −u′w′¯/u⁎2; (C) σ_u/u^⁎; (D) σ_w/u^⁎; (E) −ruw=−u′w′¯/σuσw; (F) Sk_u; (G) Sk_w; (H) L_u; (I) L_w; (J) hα(z), where α(z) is leaf area per unit volume. Lu and Lw are integral length scales derived by applying Taylor's hypothesis to the point-valued integral time scales of the fluctuating velocity (Finnigan, 2000). From Raupach, M. R., Finnigan, J. J., Brunet, Y., 1996. Coherent eddies in vegetation canopies—the mixing layer analogy. Bound.-Lay. Meteorol. 78, 351–382, reprinted with permission of Springer Science and Business Media.

Table 2.1

Physical and aerodynamic parameters of the canopies in Fig. 2.4.
Canopy	Identifier	h (m)	λ	Uh/u	Ls/h	References
WT strips	A	0.06	0.23	3.3	0.85	Raupach et al. (1986)
WT wheat	B	0.047	0.47	3.6	0.57	Brunet et al. (1994)
WT rods	C	0.19	1	5.0	0.49	Seginer et al. (1976)
Shaw corn	D	2.6	1.5	3.6	0.39	Shaw et al. (1974)
Wilson corn	E	2.25	1.45	3.2	0.46	Wilson et al. (1982)
Moga eucalypt	F	12	0.5	2.9	0.58	Unpublished
Uriarra pine	G	20	2.05	2.5	0.29	Denmead and Bradley (1987)
Amiro aspen	H	10	1.95	2.6	0.58	Amiro (1990)
Amiro pine	I	15	1	2.2	0.50	Amiro (1990)
Amiro spruce	J	12	5	2.4	0.44	Amiro (1990)
Gardiner spruce	K	12	5.1	4.0	0.30	Gardiner (1994)
Baldocchi deciduous	L	24	2.5	2.8	0.12	Baldocchi and Meyers (1988a, b)

The roughness density or frontal area index, λ, is assumed to be half the single-sided leaf area index for field canopies.

All normalized mean velocity profiles u¯z/Uh si20_e shown in Fig. 2.4A have a characteristic inflection point at z = h. The shear is maximal at z = h, and its strength can be described by the length scale, Lh=u¯h/∂u¯h/∂z si21_e . Above the canopy, we observe a standard boundary layer profile; within the canopy space, the profile can be described as roughly exponential. As we shall see later, the inflection point plays a critical role in canopy dynamics.

In Fig. 2.4B, the downward momentum flux −u′w′¯ si6_e normalized by u*, we see a standard constant stress layer above the canopy^a and then the rapid decay of −u′w′¯ si6_e as streamwise momentum is absorbed as aerodynamic drag on the foliage. Note that in all the cases of Fig. 2.4, −u′w′¯ si6_e is practically zero by ground level, indicating that all the horizontal momentum has been absorbed by the canopy elements and does not reach the ground, even though some of the canopies in the ensemble are not particularly dense. The normalized standard deviations of streamwise and vertical fluctuations, pictured in Fig. 2.4C and D, are more scattered than −u′w′¯ si6_e within the canopy but are also strongly inhomogeneous in the vertical. Values of σ_u/u^⁎ seem to group around 0.75 in the lower canopy, indicating that there is a good deal of horizontal “sloshing” motion there but that this motion is inactive in the sense that it transfers little momentum.

In Fig. 2.4E, the correlation coefficient ruw=u′w′¯/σuσw si26_e can be interpreted as the efficiency of momentum transport. Well above the canopy, r_uw assumes its standard ASL value of about − 0.32, corresponding to σ_u/u^⁎ = 2.5, σ_w/u^⁎ = 1.25, values typical of a constant stress surface layer (Garratt, 1992). At the canopy top, in contrast, the stress ratios fall to σ_u/u^⁎ = 2.0, σ_w/u^⁎ = 1.0, producing a value of r_uw = − 0.5. Although there is a good deal of scatter in the data, it is clear that the turbulence around the canopy top transports substantially more momentum per unit variance than in the surface layer above, suggesting that, in some way, the character of the turbulence has changed.

Moving from second to third moments, we observe in Figs. 2.4F and G that the skewnesses of streamwise and vertical velocity fluctuations are of order + 1 and − 1, respectively, in the canopy space, in sharp contrast to the near-zero values these statistics assume in the ASL. Positive skewness tells us that large positive excursions in velocity (gusts) are much more likely than negative excursions (lulls). Gaussian velocity distributions have skewnesses of zero. Large positive Sk_u and negative Sk_w values are associated with the intermittent penetration of the canopy by strong streamwise gusts from the ASL.

Length and time scales

In Figs. 2.4H and I, the streamwise L_u and vertical L_w Eulerian integral length scales obtained from integral time scales using Taylor's “frozen turbulence” hypothesis are plotted,

Lu=u¯σu2∫0∞u1′tu1′t+τ¯dτ;Lw=u¯σw2∫0∞u3′tu3′t+τ¯dτ

si27_e (2.7)

Both these scales are much larger than the size of individual canopy elements, reaching L_u ≅ h; L_w ≅ h/3 in the upper canopy. Other measures of the scale of turbulent eddies, both indirectly from spectra (Kaimal and Finnigan, 1994) and directly from two-point velocity measurements (Shaw et al., 1995), confirm that typical sizes of turbulent eddies in tall canopy flows are of order the canopy height.

Large Eddy structure in canopy turbulence

Until the 1960s, the limitations of turbulence sensors in wind tunnels and in the field meant that we had only a sketchy idea of the detailed structure of turbulent flows. Turbulence was assumed to be a superposition of “eddies”—coherent patterns of velocity and pressure—spanning a wide range of space and time scales. More sophisticated measurement and visualization techniques applied from the mid 1960s onward, however, began to reveal that different turbulent flows were dominated by eddies of quite different character and that the average properties of the different flows, such as their ability to transport momentum and scalars, were linked to these differences in eddy structure. In shear flows, such as boundary layers, it quickly became clear that large coherent eddies that spanned the whole width of the shear layers contained most of the kinetic energy of the turbulence and were responsible for most of the transport.

Most of the early information on large eddy structure in canopy turbulence was circumstantial inasmuch as what was really being observed was intermittency in time series measured at single points. Conditional sampling techniques, such as “quadrant-hole” analysis, revealed that transport of momentum and heat to the canopy is primarily accomplished by sweeps (downward incursions of fast-moving air) in contrast to the surface layer above, where transfer is dominated by ejections (upward movement of slow-moving air). Moreover, transfer by these sweeps is very intermittent. For example, Finnigan (1979b) found in the upper levels of a wheat crop that more than 90% of the momentum transfer occurred only 5% of the time. More sophisticated techniques, such as wavelet analysis (e.g., Collineau and Brunet, 1993; Lu and Fitzjarrald, 1994), clarified the sequence of ejections and sweeps in a typical transfer event, but these point measurements alone could not shed light on the spatial structure of the eddies responsible.

Time-height plots of data from vertical arrays of anemometers were the first to show unequivocally that the transfer events were coherent through the roughness sublayer and that the sweep events corresponded to displacement of canopy air by the coherent airmass of a canopy scale eddy. Fig. 2.5, from Gao et al. (1989), shows a time-height plot from an 18-m tall mixed forest in southern Canada. Both velocity vectors and temperature contours are shown. The velocity vectors demonstrate that an ejection precedes the sweep event and that it is weaker than the sweep within the canopy but stronger above. The compression of temperature contours into a microfront at the leading edge of the sweep is also characteristic and in a time series is signaled by a “ramp” structure, where a slow increase in temperature over periods of minutes is followed by a sudden temperature drop that takes only seconds.

Time-height plots such as that shown in Fig. 2.5 are usually composites of many events, with the sharply changing front of the ramp structure being used as a sampling trigger so that individual events can be aligned. Since they also rely on the wind to advect the turbulent field past the sensor [so that minus time can be taken as a surrogate for the streamwise (x) space axis], they reveal only a slice through the eddy on the x-z plane and not its three-dimensional structure. An extension and refinement of the time-height compositing technique by Marshall et al. (2002) has used wavelet transforms to produce pseudo-instantaneous flow maps coincident with the maximum bending force on a model tree in a wind tunnel. The use of the maximum force on the tree as a sampling trigger is more directly relevant to the subject of tree damage, of course, and it also confirms that the sweep events are indeed those responsible for exerting the maximum bending moment, thereby establishing a direct connection that allows earlier information on large eddy structure to be interpreted in terms of tree damage.

A more objective approach to deducing the spatial structure of the dominant eddies has been taken by Finnigan and Shaw (2000) and Shaw et al. (2004), who have applied the techniques of empirical orthogonal function (EOF) analysis to a wind tunnel model canopy and to the output of a large eddy simulation model of canopy flow. EOF analysis in the context of turbulent flows was introduced by Lumley (1967, 1981). It consists of finding the sequence of orthogonal eigenfunctions and associated eigenvalues that converges optimally fast when the variance or kinetic energy of the turbulent flow is represented as the sum of this sequence. The spatial structure of the turbulent field is contained in the eigenfunctions, and the rate of convergence of the sequence of eigenvalues is a sensitive indicator of the presence and relative importance of coherent structures. In shear flows dominated by coherent motions, a large fraction of the variance or turbulent kinetic energy is captured in just the first few eigenmodes, whereas in flows with no dominant structure the rate of convergence is slower. A great strength of the method is that only trivial assumptions about the form of the dominant structure need be made a priori so that we obtain essentially objective knowledge about the spatial structure of the coherent motion. Lumley (1981), in introducing the application of the technique to turbulent flows, thoughtfully discusses the relative merits and drawbacks of conditional sampling and the EOF method.

Despite the advantages of the EOF method, it has not been widely used in turbulent flows because the required empirical eigenfunctions are those of the two-point velocity covariance tensor Rijxx′=ui′xuj′x′¯ si28_e with spatial separation in three dimensions, a data set whose collection requires a particularly intensive experiment. The technique has been applied to numerical simulations as much as to real data. Moin and Moser (1989), for example, performed an EOF analysis of a numerical simulation of channel flow; their paper is an excellent introduction to the technique. Finnigan and Shaw (2000) used as their data set a two-point covariance field obtained in a wind tunnel model canopy as described by Shaw et al. (1995). Shaw et al. (2004) applied the method to a large eddy simulation^b of the velocity and scalar fields of a canopy with the same physical characteristics as the wind tunnel model.

With some simple and plausible assumptions about the distribution of the coherent eddies in space, EOF analysis enables us to reconstruct the instantaneous velocity and scalar fields of a “typical” large eddy without any a priori assumptions, such as the coincidence of the eddy with the scalar microfront or the maximum tree bending moment. Fig. 2.6 shows the velocity field of the characteristic eddy deduced from wind tunnel data by Finnigan and Shaw (2000) projected onto the (x,0,z) plane so it can be compared with the time-height composite reconstructions of Gao et al. (1989) shown in Fig. 2.5. If anything, the dominance of the sweep motion is clearer in the EOF reconstruction than in the time-height plot. Fig. 2.7, also from Finnigan and Shaw (2000), shows a cross-section of the eddy at its midpoint (x/h = 0 in Fig. 2.6) projected onto the y-z plane. This vector plot reveals information that cannot be found in time-height plots. It shows that: the eddy consists of a double roller vortex pair, with the strong downward sweep motion being concentrated on the plane of symmetry; the blocking action of the ground produces strong lateral outflows in the upper canopy; and the recirculation around the vortex centers, which are situated at about z/h ≈ ± 1.5; y/h ≈ ± 1, occurs in the upper part of the roughness sublayer.

Fig. 2.6 The u′, w′ vector field of the characteristic eddy projected onto the (rx,0,z) plane, where the horizontal coordinate rx is relative to the notional center of the eddy. (A) Arrow lengths are proportional to the magnitude of the velocity vector. (B) Arrow lengths in regions of low velocity are magnified to show the flow direction more clearly. From Finnigan, J. J., Shaw, R. H., 2000. Turbulence in waving wheat: an empirical orthogonal function analysis of the large-eddy motion. Bound.-Lay. Meteorol. 96, 211–255, reprinted with permission of Springer Science and Business Media.

Fig. 2.7 The v′, w′ vector field of the characteristic eddy projected onto the (ry,0,z) plane, where the horizontal coordinate ry is relative to the notional center of the eddy. (A) Arrow lengths are proportional to the magnitude of the velocity vector. (B) Arrow lengths in regions of low velocity are magnified to show the flow direction more clearly. From Finnigan, J. J., Shaw, R. H., 2000. Turbulence in waving wheat: an empirical orthogonal function analysis of the large-eddy motion. Bound.-Lay. Meteorol. 96, 211–255, reprinted with permission of Springer Science and Business Media.

Of particular interest in the context of forces on the plants is the spatial distribution of momentum transfer by the characteristic eddy, which is shown in Fig. 2.8 as a contour plot on the y-z plane at x/h = 0. Here we see that the sweep motion, which is the part of the eddy responsible for strong aerodynamic forces on the plants, is confined to a width of y/h ≈ ± 0.5 while the circulation of the pair of vortices that make up the eddy ensure that the sweep is flanked laterally by two ejection regions as the upward motion of the vortices carries low momentum (and warmer/colder air in the daytime/night-time) out of the canopy. Combining Figs. (2.6), (2.7), and (2.8) indicates that although the characteristic canopy eddies are coherent over about 8 h in the streamwise and 4 h in the lateral directions, the intense sweep region is much smaller, being about 3 h in the streamwise and 1 h in the lateral directions. This three-dimensional information has obvious relevance when we come to consider windthrow and crop lodging later in this chapter.

Fig. 2.8 Spatial contours of u′w′¯ in the characteristic eddy. (A) Projection onto the (rx,0,z) plane (contour interval, 0.5; minimum value, − 7.34). (B) Projection onto the (0,ry,z) plane (contour interval, 0.5; minimum value, − 7.55). Solid contour lines denote positive covariance, dotted lines negative covariance.

si4_e — Fig. 2.8 Spatial contours of u′w′¯ in the characteristic eddy. (A) Projection onto the (rx,0,z) plane (contour interval, 0.5; minimum value, − 7.34). (B) Projection onto the (0,ry,z) plane (contour interval, 0.5; minimum value, − 7.55). Solid contour lines denote positive covariance, dotted lines negative covariance.

A dynamic model for the large eddies—The mixing layer hypothesis

It is evident not only that the statistics of turbulence in the RSL are quite different from those in the surface layer above but the large-eddy structure deduced by conditional sampling and EOF analysis also has distinct differences. A decade ago, Raupach et al. (1986, 1996) proposed that these differences might be explained by taking the plane-mixing layer rather than the boundary layer as a pattern for RSL turbulence.

The plane-mixing layer

The plane-mixing layer is the free shear layer that forms when two airstreams of different velocity, initially separated by a splitter plate, merge downstream of the trailing edge of the plate. Flows of this kind are common in engineering applications and have been intensively studied. Conventionally, the splitter plate occupies the horizontal half plane (x < 0; z = 0) and the difference between the free stream velocities above and below the plate is ΔU. The width of the mixing layer can be characterized by the vorticity thickness δω=ΔU/∂u¯/∂zmax si29_e as shown in Fig. 2.9. Even if the boundary layers on each side of the splitter plate are laminar at x = 0, the mixing layer rapidly becomes turbulent and “self-preserving” whereupon δ_ω ∝ (x − x₀), where x₀ is a virtual origin (Townsend, 1976).

si5_e — Fig. 2.9 Composite plot defining the parameters and flow statistics in the self-preserving region of a plane mixing layer. Variables are normalized with vorticity thickness δ_ω and velocity difference ΔU. (A) U=u¯; (B) σ_u, σ_v, σ_w, and −u′w′¯; (C) the budget of turbulent kinetic energy: P_b is shear production, ɛ is viscous dissipation, A is advection, T is turbulent transport, and T_p is pressure transport (for further explanation, see Finnigan, 2000); (D) Sk_u, Sk_w; (E) inverse turbulent Prandtl number, Pr_t^− 1. From Raupach, M. R., Finnigan, J. J., Brunet, Y., 1996. Coherent eddies in vegetation canopies—the mixing layer analogy. Bound.-Lay. Meteorol. 78, 351–382, reprinted with permission of Springer Science and Business Media.

In Fig. 2.9A–E, various properties of fully developed, self-preserving mixing layers are plotted with the vertical coordinate z scaled by δ_ω and the velocity moments by ΔU. In Fig. 2.9A we see the inflection point in the mean velocity profile that is characteristic of mixing layers. The turbulent velocity variances σ_u², σ_v², σ_w² and the shear stress −u′w′¯ si6_e (Fig. 2.9B) all peak at the position of maximum shear, z = 0, and then decay toward the edge of the layer. Finally, in Fig. 2.9D we observe that streamwise and vertical skewnesses are of order one in the outer parts of the mixing layer, reversing sign as the centerline is crossed. If we compare these single-point moments with their counterparts in the RSL that were plotted in Fig. 2.4A–D, we see close correspondence between the canopy layer and the low speed side of the mixing layer.

Mixing layers are also populated with coherent motions that span the depth of the layer. The inflected velocity profile of the mixing layer is inviscidly unstable to small perturbations and growing, unstable modes of Kelvin-Helmholtz type emerge in the early stages of mixing layer development. The initial Kelvin-Helmholtz waves rapidly evolve into distinct transverse vortices or rollers connected by “braid” regions. Streamwise vorticity initially present in the flow is strongly amplified by strain in the braid regions while, at the same time, the transverse rollers become kinked and are less organized. As the mixing layer develops further, the transverse vorticity weakens and most of the total vorticity becomes concentrated in streamwise vortices in the braid regions and the streamwise component of kinked rollers (Rogers and Moser, 1992). The streamwise wavelength of the initial Kelvin-Hemholtz instability, Λ_X, is preserved through the stages of transition to fully developed turbulence and becomes the effective average spacing of the ultimate coherent structures. In a fully developed turbulent mixing layer, observations of Λ_x/δ_ω range from 3.5 to 5. A more detailed account of this process can be found in Raupach et al. (1996).

The canopy-mixing layer analogy

The obvious feature of plane-mixing layers that first prompted the comparison between them and canopy flows was the inflected mean velocity profile. Since it was known that this was inviscidly unstable to small perturbations, unlike the uninflected boundary layer profile (which becomes unstable only if viscosity is present), it was seen as a possible source of the high turbulence intensities in the RSL. Given the fact that the unstable eigenmodes were the same scale as δ_ω, a bulk measure of the profile also seemed to offer a clue to the origin of the large eddies in the RSL. I have already noted the similarities among first, second, and third velocity moments in mixing layers and the RSL. Comparing integral length scales, terms in the turbulent kinetic energy budgets and other properties, such as the turbulent Prandtl number, confirm that RSL turbulence shares the character of mixing layer rather than boundary layer turbulence to a compelling degree (Raupach et al., 1996; Finnigan, 2000).

We can go further and make a direct comparison between features of the coherent structures in the RSL and the mixing layer if we first state the relationship between the shear scale L_S and the vorticity thickness, δ_ω,

LS=u¯h∂u¯/∂zz=h≅12δω=12ΔU∂u¯/∂zmax

si31_e (2.8)

Equation (2.8) is exact if the maximum shear is at z = h (which can serve as a dynamic definition of h) and if we take the velocity deep within the canopy, where the shear is small (see Fig. 2.4A), as equivalent to the free stream velocity on the low-speed side of the mixing layer. Observations of the spacing of coherent eddies in fully developed mixing layers then fall in the range 10 > Λ_x/L_S > 7. Raupach et al. (1996) compared estimates of Λ_x obtained from nine of the canopies in Fig. 2.4 against the shear length scale L_S. They found that the data over a very wide range of canopy types and scales closely fit the relationship Λ_x = 8.1L_S, which falls in the middle of the range for fully developed mixing layers. This is compelling evidence that the process controlling the generation of large coherent structures in the RSL is very similar to that in the plane-mixing layer; further supporting argument can be found in Raupach et al. (1996).

We can summarize the canopy-mixing layer analogy by reference to the schematic diagram, Fig. 2.10:

1. The first stage is the emergence of the primary Kelvin-Helmholtz instability. We suppose that this occurs when a large-scale gust or sweep from the boundary layer well above the canopy raises the shear at z = h above some threshold level at which the instability can grow fast enough to emerge from the background before it is smeared out by the ambient turbulence. The growth rate of the mixing layer instability is proportional to the magnitude of the shear at the inflection point whereas, in the high Reynolds number canopy flow, the scale of the shear L_S and therefore the scale of the instability is independent of windspeed, depending only on canopy height and aerodynamic drag.
2. The second stage is the clumping of the vorticity of the Kelvin-Helmholtz waves into transverse vortices or rollers connected by braid regions of highly strained fluid. The spacing of the rollers is similar to the wavelength of the initial instability.
3. Finally, secondary instabilities in the rollers lead to their kinking and pairing, while any ambient streamwise vorticity in the braid regions is strongly amplified by strain, resulting in coherent structures whose transverse and streamwise dimensions are of the same order and most of whose vorticity is aligned in the streamwise direction just as found for the “characteristic eddy” revealed by EOF analysis in Fig. 2.7. Note that the schematic “coherent structure” shown as the third panel of Fig. 2.10 is based on diagrams in Rogers and Moser (1992).

This conceptual picture has some further consequences. Because we expect that the primary instability will emerge from the background only when the shear at the canopy top exceeds some threshold, the convection velocity of the ultimate coherent structures will be larger than the mean velocity. We imagine that the footprint of the sweep that raises the shear above the threshold will be of larger scale than Λ_x, so we should expect to see some streamwise periodicity in canopy eddies. Short sections of periodicity are revealed by short-time two-point space-time correlations, and by using this technique in a wheat canopy, Finnigan (1979b) found that canopy eddies arrived in groups of three or four. Each group has a common convection velocity Uc≈1.8u¯h si32_e that presumably corresponds to the velocity of the large sweep that initiated the instability. The mixing layer analogy also has obvious consequences for scaling and modeling canopy flow. A single length scale δ_ω and single velocity scale u* or u¯h si33_e determine the primary instability and ultimate coherent structures in the RSL. Within the RSL, δ_ω or L_S replace (z − d), the height-dependent length scale of the surface layer. There has been substantial development of this picture of canopy turbulence in the last 10–15 years. These are summarized in Patton and Finnigan (2012) and Shaw et al. (2013).

Effects of topography and heterogeneity

If we take the horizontally homogeneous quasi-steady flow described previously as the canonical state, then in the context of disturbance ecology the most important kinds of perturbations that we need to consider are those caused by hilly terrain and by forest edges or clearings. In trying to draw general conclusions about the way that canopy flows depart from horizontally homogeneous behavior, it is useful to break the problem into two parts: the nature of the forcing and the response of the canopy. We can identify two kinds of forcing. The first occurs when we accelerate the canopy flow by applying a pressure field p¯xyz that varies over a horizontal scale L much larger than the canopy height (i.e., L ≫ h). This is the kind of pressure field that results when the canopy is on a hill. Alternatively, such a pressure field could be generated diabatically by a strong contrast in surface energy balance, such as occurs in a true sea breeze or an “inland sea breeze.” The second case occurs when the scale of the pressure gradient is comparable to the canopy height and this kind of forcing occurs around local obstructions, such as clearings or forest edges. Diabatic forcing can also occur on this scale, as in the case of anabatic and katabatic flows, where density gradients and accompanying pressure gradients develop initially at the scale of the canopy height. The most obvious case of this that interests us is fire.

A key measure of the response of the canopy is the distance needed to reestablish horizontally homogeneous flow within the canopy after a sudden change in the external forcing. By considering the idealized case of a one-dimensional canopy flow, it is easy to show that the flow responds exponentially to a change in the driving pressure gradient with a distance constant L_C (Finnigan and Brunet, 1995; Finnigan and Belcher, 2004) and that,

LC=Cda−1

si35_e (2.9)

where C_d is the dimensionless drag coefficient of the foliage and a is the foliage area per unit volume of space, so we can write the aerodynamic drag force as F_D = u ∣ u ∣ /L_C. Most of the canopy drag is transmitted as a pressure force on the foliage, so the drag is proportional to the square of the windspeed while the modulus sign recognizes that the drag force is always directed in the instantaneous wind direction. L_C is the fundamental lengthscale of adjustment of the within-canopy flow to external forcing and appears in many contexts, such as in the changes that must be made to Kolmogorov inertial sublayer spectral forms within canopies (Finnigan, 2000). In the discussion below, we will see in each case that the flow response is a balance between the strength of the forcing and the tendency of the within-canopy flow to return to equilibrium with a response distance L_C.

Flow over hills

Before considering canopy flows in complex topography, it is useful to set the scene by describing flow over rough hills without canopies. I will confine this discussion to hills sufficiently small that the flow perturbations they cause are confined within the boundary layer. In practice, this means that the hill height H and the hill horizontal lengthscale L satisfy H ≪ z_i and L ≪ h*, where h* is the “relaxation length” of the boundary layer defined as h ⁎ = z_iU₀/u_⁎ or z_iU₀/w_⁎ according to whether the flow is neutrally stratified or convectively unstable. U₀ is the velocity characteristic of the ABL above the surface layer; thus, in the case of the convective boundary layer portrayed in Fig. 2.1A, it would be the constant windspeed above z/z_i ≈ 0.2. The horizontal length scale L is defined as the distance from the hillcrest to the half-height point. In continuously hilly terrain it can be more appropriate to use a characteristic wavelength l as the horizontal length scale and in sinusoidal terrain, L = λ/4.

Fig. 2.11 shows the main features of the velocity field about an isolated hill. The figure could represent flow approaching an axisymmetric hill or a two-dimensional ridge at right angles. Close to the surface, the flow decelerates slightly at the foot of the two-dimensional ridge before accelerating to the summit. In the case of an axisymmetric hill, the deceleration is replaced by a region of lateral flow divergence at the foot of the hill. The wind reaches its maximum speed above the hilltop and then decelerates on the lee side. If the hill is steep enough, a separation bubble forms in which the mean flow reverses direction. Whether the flow separates or not, a wake region forms behind the hill with a marked velocity deficit extending for at least 10H downwind. The same information is made more concrete in Fig. 2.12, which plots velocity profiles well upwind, over the hilltop and in the wake. The vertical coordinate z measures height above the local surface. In Fig. 2.12, it is made dimensionless with the inner layer height, l, defined below. Upwind we have a standard logarithmic profile (Eq. 2.5), but on the hill top the profile is accelerated with the maximum relative speed-up occurring quite close to the surface at z/l ∼ 0.3. In the wake we see a substantial velocity deficit extending to at least z = H.

Fig. 2.12 Profiles of mean velocity observed upwind, on the crest, and in the wake region of a hill. The vertical scale is made dimensionless with the inner layer depth, l. Note the position of the maximum speed-up above the crest at z ~ l/3. From Kaimal, J. C., Finnigan, J. J., 1994. Atmospheric Boundary Layer Flows: Their Structure and Measurement. Oxford University Press, New York, reprinted with permission from Oxford University Press © 1994.

Much of the understanding we now have about the dynamics of flow over hills derives from linear theory, which assumes that the mean flow perturbations caused by the hill are small in comparison to the upwind flow. Although linear theory is limited to hills of low slope, H/L ≪ 1, its insights are applicable to much steeper hills. Linear theory supposes a division of the flow field into two main regions, an inner region of depth l and an outer region above, which are distinguished by essentially different dynamics (Fig. 2.13). The flow dynamics are governed by the balance between advection, streamwise pressure gradient, and the vertical divergence of the shear stress. Over low hills this balance can be expressed in an approximate linearized momentum equation,

UBz∂Δu¯∂x+∂Δp¯∂x∼∂Δτ∂z

si36_e (2.10)

where Δu¯ si37_e , Δp¯ si38_e , Δτ are the perturbations in mean streamwise velocity, kinematic pressure, and shear stress induced by the hill and U_B(z) denotes the undisturbed flow upwind of the hill or, in the case of a range of hills, the horizontally averaged wind. Well above the surface in the outer region, perturbations in stress gradient are small and advection and pressure gradient, the first two terms in Eq. (2.10), are essentially in balance. Closer to the surface, an imbalance develops between these terms as the perturbation stress gradient grows. The inner layer height is defined as the level at which the left side of Eq. (2.10) equals the right side (Hunt et al., 1988; henceforth, HLR).

Fig. 2.13 The different regions of the flow over an isolated hill, comprising inner, middle, outer, and wake layers and their associated length scales. From Kaimal, J. C., Finnigan, J. J., 1994. Atmospheric Boundary Layer Flows: Their Structure and Measurement. Oxford University Press, New York, reprinted with permission from Oxford University Press © 1994.

If the undisturbed upwind profile is taken as logarithmic, U_B(z) = u ⁎ /κ ln (z/z₀), this definition for the inner layer depth leads to an implicit expression for l (HLR):

lLlnlz0=2κ2

si39_e (2.11)

The pressure field that develops over the hill deflects the entire boundary flow over the obstacle. Its magnitude is determined, therefore, by the inertia of the faster-flowing air in the outer region and is also related to the steepness of the hill, so we expect:

Δp¯∼HLU02

(2.12)

Scaling arguments (HLR) reveal that when the winds are strong so that the logarithmic law describes the wind profile to heights much larger than H, the appropriate definition of U₀ is

U0=Uhm;hmLln1/2hmz0∼1

(2.13)

The middle layer height h_m divides the outer region into a middle layer between l and h_m, where shear in the approach flow exerts an important influence on the flow dynamics, and an upper layer, where shear in the approach flow is negligible. In contrast to the inner layer, the perturbations in the outer layer are controlled by inviscid flow dynamics, obeying the equations of rotational inviscid flow in the middle layer and irrotational or potential flow equations in the upper layer. For a hill with L = 200 m, u_⁎ = 0.3 m s^− 1 and z₀ = 0.02 m, typical sizes of the key parameters are l = 10 m, h_m = 70 m, U₀ = 6 m s^− 1 and U_B(l) = 4.5 m s^− 1. Note that in the linear theory the vertical extent of the regions influenced by the hill depend only on the hill length, L. The hill height enters only through the influence of the steepness H/L on the pressure perturbation that drives all other changes in the flow field.

The pressure perturbation falls to a minimum at the hilltop and then rises again behind the hill. It varies in both the horizontal and vertical directions over distances of order L. Hence, because l is much smaller than L, the horizontal pressure gradient ∂Δp¯/∂x si42_e is essentially constant with height through the inner layer. The scaling of the pressure perturbation field gives a strong clue as to why the velocity speed-up peaks in the inner layer. Referring again to Eq. (2.10), in the outer layer the momentum balance is dominated by the pressure gradient and the advection so that UBzΔu¯xz/L∼H/LU02/L si43_e . Within the inner layer, as the background flow U_B(z) becomes much smaller than U₀, the velocity perturbation Δu¯ si44_e must grow to compensate. Eventually, at the bottom of the inner layer the shear stress gradient dominates the momentum balance and reduces Δu so that the peak in speed-up is found at about z ~ l/3 (Fig. 2.12).

Before considering how the presence of a canopy modifies this picture, we must note that strong stable stratification can have a large influence on the perturbation pressure field and the subsequent velocity and stress perturbations. In particular, it moves the position of maximum velocity from the hilltop to the downwind slope (see Kaimal and Finnigan (1994) and references therein). This is important because the pressure field around large hills, defined as hills that occupy a large fraction of the boundary layer, is often dominated by the displacement of the stable troposphere above the boundary layer rather than processes within the boundary layer itself. A consequence of this can be severe “downslope” windstorms on the lee slopes of forested mountains. The front range of the Rocky Mountains, west of Denver, Colorado, has provided many destructive examples of this phenomenon (Duran, 1990).

Canopies on hills

Even though so many of the forests and other canopies in which we are interested are on hills, we have very few comprehensive measurements of the way topography alters the homogeneous canopy turbulence described previously. Measurements in the field almost all come from single towers so that the streamwise development of the windfield is not recorded. The expense of multiple tower studies in forests is one reason for their rarity, but even in wind tunnels only a few published model studies are available. That of Finnigan and Brunet (1995) still provides the only comprehensive data set of within-canopy velocity statistics, although Ruck and Adams (1991) and Neff and Meroney (1998) have made measurements above the model canopy.

We can turn instead to theoretical models for insight, but even there few signposts are available. The numerical model study by Wilson et al. (1998) reproduced the data of Finnigan and Brunet (1995), but it did not make major strides in unraveling the basic physics. A recent analytical linear model of flow in a tall canopy on a low hill by Finnigan and Belcher (2004) has, however, provided some insights comparable to the linear analytic models of flow over rough hills that followed the pioneering work of Hunt et al. (1988). Like that of Hunt et al., the analysis of Finnigan and Belcher divides the flow in the canopy and that in the free boundary layer above into a series of layers with essentially different dynamics. The dominant terms in the momentum balance in each layer are determined, and the complete solution for the flow field is achieved by asymptotically matching the solutions for the flow in each layer. The model applies in the limit of “tall” canopies, by which we mean that almost all the momentum is absorbed as aerodynamic drag on the foliage and not as shear stress on the underlying surface. We can see from Fig. 2.4B that this condition is satisfied in most continuous natural canopies.

Finnigan and Belcher calculate the perturbations to a background flow U_B(z) that now consists of a logarithmic velocity profile above the canopy merging smoothly with an exponential profile in the canopy. These formulae are easier to state if we take the origin of coordinates at the canopy top rather than the ground surface so that:

UBz=u⁎κlnz+dtz0;z>0UBz=Uheβzl;z≤0

si45_e (2.14)

where U_h = U_B(0) is the mean wind speed at the top of the canopy, u* is the friction velocity, l = 2β³L_c is the mixing length in the canopy l = κu ⁎ (z + d_t) is the mixing length above the canopy and β = u ⁎ /U_h quantifies the momentum flux through the canopy. For closed uniform natural canopies, β ≈ 0.3 (Raupach et al., 1996). Note that with the change of z origin we have also introduced the redefined displacement height d_t, where d_t = h − d [compare with Eqs. (2.5) and (2.6). Matching both mean wind and shear stress at the canopy top also fixes the following relationships:

Uh=u⁎κlndtz0;d=l/κ;z0=lκe−k/β

si46_e (2.15)

The essential features of canopy flow on low hills under neutral stratification can now be summarized as follows. Above the canopy, the flow behaves as described previously. The magnitude of the driving perturbation pressure gradient is essentially invariant with height through the canopy as it is through the inner layer. The canopy flow itself divides naturally into an upper and a lower layer. In the upper canopy layer, the dominant terms in the momentum balance are the streamwise pressure gradient induced by the hill, the shear stress divergence, and the aerodynamic drag on the foliage. In comparison to these three terms, advection is small. In the lower canopy layer, the shear stress divergence becomes small compared to the pressure gradient and the aerodynamic drag. The depths of the upper and lower canopy layers are defined in Finnigan and Belcher (2004).

In the air layers above the canopy, the velocity perturbation caused by the hill is in phase with (minus) the pressure perturbation so that the maximum velocity perturbation (speed-up) occurs over the hilltop:

OuterLayer:Δu¯xz∝−Δp¯SgnΔp¯

si47_e (2.16)

In the lower canopy layer, in contrast, the velocity perturbation is in phase with (minus) the gradient of the pressure perturbation, which attains its maximum value on the upwind slope of the hill and reverses on the lee side (Fig. 2.14):

LowerCanopyLayer:Δu¯x=−Lc∂Δp¯/∂xSgn∂Δp¯/∂x

si48_e (2.17)

Fig. 2.14 The pressure perturbation and its gradient induced by a hill. Curves of static pressure measured along a streamline within the canopy (dashed line) and the kinematic static pressure gradient averaged over the height range 1.5 > z/h > 0. Data from the wind tunnel model experiment of Finnigan, J. J., Brunet, Y. (1995). Turbulent airflow in forests on flat and hilly terrain. In Wind and Trees (Coutts, M. P., and Grace, J., Eds.), pp. 3–40. Cambridge University Press, Cambridge, UK. Reprinted with permission from Cambridge University Press © 1995.

Matching the solutions in the different layers tells us that the shear stress layer and upper canopy layer together form a region of adjustment across which the mean flow perturbations change from being in phase with (minus) the pressure well above the surface (Eq. 2.16) to being in phase with (minus) the pressure gradient deep in the canopy (Eq. 2.17). This adjustment strongly modulates the shear across the canopy top. These features are clearly illustrated in Fig. 2.15, from Finnigan and Belcher (2004), where the perturbations in mean streamwise velocity at a series of stations across one of a range of sinusoidal ridges are plotted. Included for comparison are solutions for a rough surface with the same z₀ from the theory of Hunt et al. (1988). The extra turbulent mixing generated by the canopy reduces the sharp speed-up peak on the hillcrest predicted by Hunt et al. and moves it from around z ≈ h_i/3 to z ≈ h_i.

Fig. 2.15 Profiles of velocity perturbations caused by a low hill. Comparison of velocity perturbation Δu/U_SC over a hill covered with a tall canopy with the no-canopy Hunt et al. (1988) solution (dotted line). Note the Hunt et al. solution is only valid to z = − d + z₀. Profiles are plotted at a series of X/L values between X/L = − 2 (upwind trough) and X/L = 2 (downwind trough). The units of Z are meters and the vertical range is 2l_i > Z > L_C. From Finnigan, J. J., Belcher, S. E., 2004. Flow over a hill covered with a plant canopy. Part 1 analytical model for the flow. Q. J. R. Meteorol. Soc. 130, 1–29, reprinted with permission from the Quarterly Journal of the Royal Meteorological Society, Volume 130, © 2004.

Fig. 2.16 shows consecutive vertical profiles of total mean velocity, UBz+Δu¯xz si49_e , from the wind tunnel model study of Finnigan and Brunet (1995). Although this hill is too steep to satisfy the H/L ≪ 1 limits of linear theory, upwind of the hillcrest we can still see the main features predicted by the Finnigan and Belcher model. The maximum velocity in the lower canopy occurs well before the crest and is falling by the hilltop. The difference between lower canopy and outer layer velocities is greatest at the hilltop and maximizes the canopy-top shear at that point, with consequences for the magnitude and scale of turbulence production. Conversely, the difference is at a minimum halfway up the hill, where the lower-canopy velocity is maximal but the outer layer flow has not yet increased much. This effect is so marked that the inflection point in the velocity profile at the top of the canopy has disappeared. Note also that on this steep hill we observe a large separation bubble behind the hillcrest.

si7_e — Fig. 2.16 Consecutive profiles of u¯z at consecutive x locations over a wind tunnel model of a tall canopy on a hill. From Finnigan, J. J., Brunet, Y., 1995. Turbulent airflow in forests on flat and hilly terrain. In Wind and Trees (Coutts, M. P., and Grace, J., Eds.), pp. 3–40. Cambridge University Press, Cambridge, UK., reprinted with permission from Cambridge University Press © 1995.

The vertical profiles of streamwise velocity variance, u′2¯ si8_e , from the same experiment of Finnigan and Brunet (1995) are shown in Fig. 2.17. Two features are noteworthy, particularly so since they affect fluctuating forces on the plants, a point I return to later in this chapter. The first thing to note is that the peak in u′2¯ si8_e that is seen at the canopy top upwind of the hill is substantially reduced halfway up the hill, the position where the shear across the upper canopy and inner layers is reduced by the phase difference in the velocity perturbations above and below the canopy, as seen in Figs. 2.15 and 2.16. The second is the strong peak in u′2¯ si8_e at the top of the canopy over the hilltop. This peak coincides with the strong shear region of Figs. 2.15 and 2.16. Behind the hill the peak in u′2¯ si8_e follows the separated shear layer that bounds the separation bubble.

A series of consequences flows from these dynamics. First is a marked increase in the aerodynamic drag even on low hills covered with tall canopies because the negative velocity perturbation behind the crest displaces streamlines away from the surface, increasing the asymmetry of flow around the hill and thereby the pressure drag. This increased drag of the hills on the airflow can affect predictions of wind speeds at larger scale around a region of forested hills, and many meteorological models in current use have poor parameterizations of this effect. Equally important is the interaction of the negative velocity perturbation and the mean flow behind the hillcrest. Positive mean flow behind the hillcrest is maintained by turbulent transport of momentum from the faster-moving fluid above the vegetation, but this mechanism is ineffective deep in a canopy. The pressure field, in contrast, passes essentially unimpeded through the canopy; thus, the pressure gradient that is acting to decelerate the flow can easily overwhelm the turbulent transport. The result is reversal of the total velocity and flow separation. Hence, even on low hills, if the canopy is deep enough we can expect reversed flow and separation near the ground.

Finally, I need to point out that both the wind tunnel model and theoretical studies I have quoted were performed with the wind perpendicular to two-dimensional ridges. This configuration maximizes the speed-up and associated distortions of the wind and scalar fields. Isolated axisymmetric hills are likely to exhibit effects that are similar in kind but smaller in degree than ridges. Conversely, saddles between two isolated hills can exhibit even larger effects than ridges when the wind blows across the saddle.

Before moving on to consider situations with smaller scale forcing, I remind the reader that most of the features of the perturbed flow in a canopy on a hill should be observed in any large-scale pressure field, whether caused by a hill or not. Large-scale contrasts in surface energy balance are a ubiquitous source of such pressure fields, and with appropriate redefinition of coordinate frames, we can expect canopy flow dynamics similar to those described previously in such cases.

Forest edges and clearings

There has been a series of field studies of this situation, but in Fig. 2.18 we again have recourse to a wind tunnel study (Raupach et al., 1987) because of the far greater data density it affords. These results from a simulation of flow into a forest comprise a set of profiles of first, second, and third moments of velocity:u¯z si54_e , σuz=u′2¯ si55_e , σwz=w′2¯ si56_e , u′w′¯ si57_e , Sku=u′3¯/σu3/2 si58_e . They show several characteristic features. The flow near the surface decelerates and streamlines are displaced upward as the flow encounters the resistance offered by the aerodynamic drag of the canopy. Very close to the surface in the canopy we see deceleration for a distance x > 10 h. In contrast, just above the canopy top we see the flow accelerate. The accelerated flow above the top of the forest produces the characteristic inflection point velocity profile that we expect at the top of a canopy (see previous section on characteristics of turbulent flow in and above plant canopies), but the depth of this inflected shear layer and the scale of the energetic large eddies that develop within it are initially much smaller than the canopy height, h.

As we progress downwind, this shear layer deepens, eventually reaching its equilibrium width as the decelerated region of the within-canopy flow grows. The large eddies that are generated in this shear layer penetrate progressively deeper into the canopy as the shear layer grows with x, transferring momentum deeper into the foliage, and eventually, at downstream distances greater than ~ 10 h, lead to an acceleration of the flow lower in the canopy. The result is a reconvergence of the streamlines that were originally displaced upward (Morse et al., 2002). Since this process is governed by the canopy aerodynamic resistance and the adjustment of the within-canopy flow, we can expect it to scale on L_C rather than h so long as the ratio h/L_C is sufficiently small that almost all the streamwise momentum is absorbed as foliage drag rather than as shear stress on the surface beneath the trees. A value of h/L_C ≥ 1 is sufficient to ensure this. Both wind tunnel and field experiments suggest that the maximum streamline displacement and, therefore, the minimum velocity at mid canopy height (z/h ~ 0.5) occur in the region 10 > x/L_C > 5. These features are also in broad agreement with the recent analytical theory of Belcher et al. (2003), although that theory, which parameterizes momentum transfer through a mixing length, cannot reproduce flow features that depend on the character of the large turbulent eddies, as I discuss next.

Equilibrium flow within the canopy is almost re-established by x/L_C ~ 10, but turbulence statistics just above the canopy continue to develop in the growing internal boundary layer (Morse et al., 2002). Peaks in streamwise and vertical velocity variance and in shearing stress are observed in the region 10 > x/L_C > 5, suggesting that the turbulent eddies attain maximum energy when the inflected shear layer at the canopy top has reached an intermediate depth, sufficient for the inviscid instability process by which these large eddies gain energy from the mean flow to be well established but before the mechanisms that dissipate the energy in the coherent eddies have developed fully. The velocity moment in which this is most marked is the streamwise velocity skewness, Sk_u, which in the region 6 > x/L_C > 4 becomes two or three times larger than its canopy-top equilibrium value (compare Fig. 2.4I and Fig. 2.18). Such behavior is consonant with what is known of the development of plane-mixing layers (see preceding section on characteristics of turbulent flow in and above plant canopies).

For details of the structure of the wind blowing from a continuous canopy into a clearing, I again refer to a wind tunnel study by Chen et al. (1995). References to several other studies, both in wind tunnels and the field, are quoted there. The wind structure they observed was quite similar to what is found behind thin porous windbreaks. A sheltered region just behind the forest edge extends for around 3–5 h, at which point the inflection in the velocity profile at z = h has disappeared and a boundary layer profile is re-established at the ground, even though the overall mean velocity levels are much lower than further downwind. Over this “quiet zone,” mean windspeeds rise; the fastest increase is at z = h, while the turbulent intensities, σu/u¯ si59_e and σw/u¯ si60_e , rise below z = h and fall at and above z = h.

Behind the quiet zone, the effect of the upwind canopy is felt through a wake zone extending to at least 20 h. Mean velocities are suppressed in this region and turbulence levels enhanced compared to far downwind. Total readjustment of the flow to the downwind surface can require distances of as much as 50 h. The speed of adjustment is controlled by the roughness of-the downwind surface: the rougher the surface, the more rapidly the influence of the upwind canopy is lost (Kaimal and Finnigan, 1994).

Implications of this velocity structure for canopy disturbance

Windthrow and crop lodging

This subject is treated in much more detail in Chapter 4. Here I simply make the connection between the properties of the turbulent wind field in canopies and the key factors contributing to windthrow. Considerable work has been done in the last two decades on the detailed mechanisms by which individual trees or swathes of trees or crop plants are flattened by the wind. This research has treated the plants as aeroelastic cantilevers and utilized the considerable mathematical apparatus developed by aeronautical engineers to quantify their interaction with the turbulent canopy wind (e.g., Finnigan and Mulhearn, 1978; Baker, 1995; Marshall et al., 2002). Aeroelastic canopy models representing cereal crops (Finnigan and Mulhearn, 1978; Brunet et al., 1994) and conifer forests (Stacey et al., 1994) have been constructed and studied and the results compared with simultaneous measurements of bending and turbulence in real canopies. The several individual mechanisms leading to failure of stems, trunks, root plates, and the soil matrix have also been studied intensively (Coutts and Grace, 1995). We can conclude several things from this body of research.

The first is that the key parameter determining whether a tree or plant will blow down is the maximum bending moment at the plant's root. The root bending moment is defined as:

MR=∫0hzFzdz

si61_e (2.18)

where F(z) is the aerodynamic force on the plant at height z and h, the plant or canopy height. The rapid absorption of momentum by the canopy is demonstrated by the shear stress profiles of Fig. 2.4C and results in the characteristic exponential velocity profile seen in Fig. 2.4A. In horizontally homogeneous flow, the time-averaged aerodynamic force on the plants at a height z is simply Fz=∂ρu′w′¯/∂z si62_e , the vertical derivative of the shear stress, so that we see that aerodynamic force is concentrated in the upper canopy, maximizing the root bending moment. This is in contrast to the forces on an isolated tree, which for the same vertically integrated force will experience a much smaller root bending moment than its counterpart in a forest.

Two modes of failure are commonly seen in windthrow of plants: stem breakage and root plate failure. In tree stands, static failure by either mechanism is rare because the average wind speeds required to generate time-averaged root bending moments large enough to exceed the failure threshold are very large. Typical calculations show that steady wind speeds greater than 20 m s^− 1 would be required for static failure of trees (Baker, 1995). Cereal crops, in contrast, could fail at wind speeds about half this, particularly when rain adds weight to stalks displaced from the vertical (Baker, 1995). As we have seen in the earlier sections, however, the canopy wind is not steady and peak loads much higher than the average are readily generated. Furthermore, plants are dynamic elastic objects that interact with the wind as forced resonant cantilevers. The peak loads experienced by the plants are, therefore, a function of the turbulent wind, which determines the spectrum of forcing, and the elastic nature and resonant properties of the individual plants, including the damping of the motion of individual plants. In canopies, this is determined primarily by the mechanical interference of adjacent plants and the interaction of the roots and the soil matrix rather than by internal damping in the flexing stems (Finnigan and Mulhearn, 1978; Baker, 1995; Marshall et al., 2002).

When the aeroelastic nature of the plants is taken into account in this way, it is clear that it is possible to exceed the threshold for failure much more easily than the static load criterion would suggest. Marshall et al. (2002) have shown that if the peak root bending moment is used as a trigger for conditional sampling of the windfield, then wind patterns that correspond to the characteristic ejection-sweep sequence of the large canopy eddies are obtained. In other words, the peak overturning moments on the plants are associated directly with the coherent canopy eddies discussed previously. The intermittent loading by these eddies, however, is not the only mechanism causing the root bending moment to exceed the failure threshold.

Baker (1995) has suggested that the best way to view forcing by the turbulent wind is as a sequence of intermittent step changes in root bending moment, each triggered by the arrival of a canopy gust or large eddy. After being bent over by the gust, the plant executes several damped oscillations at its natural frequency until the next gust arrives. If these oscillations are of large enough amplitude, then the cohesion between soil and root plate can be reduced (especially in very wet soils) and the root bending moment required for failure reduced so that a later gust may cause the plant to fall. Gardiner (1994), in contrast, using measurements in a spruce plantation, has demonstrated an alternative mechanism whereby resonant interaction between the wind and plants can cause the failure threshold to be exceeded. A wind tunnel model study supported his conclusions. As noted previously, we expect the canopy eddies generated by the mixing layer instability process to come in groups of two, three, or four as the canopy-top instability is triggered by a large-scale gust from the boundary layer above so that resonant interaction is clearly possible. Indeed, Finnigan (1979b) speculated that the most spectacular cases of honami^c occur when this gust-arrival frequency coincides with the natural waving frequency of the plants.

In summary, we see that windthrow is caused by the intermittent penetration of canopy eddies, interacting with the resonant swaying of plants. The largest overturning forces are caused by the intermittent canopy eddies generated by the mixing layer instability, and we expect these to arrive in groups leading to the possibility of resonant amplification of the peak loads. These eddies are of relatively small, cross-stream extent, as we have seen (Fig. 2.7), so that it is unlikely that wide cross-wind swaths of trees will be laid low by this mechanism, although entanglement of branches may spread the effect of failure. The rapid absorption of momentum in the upper canopy amplifies the bending moment relative to isolated trees, and this is as true for the impact of the large eddies as for the mean wind (Marshall et al., 2002 and Fig. 2.4C).

Rapid momentum absorption in the upper part of horizontally homogeneous canopies (Fig. 2.4A) is echoed by the peak in u′2¯ si8_e near the top of the foliage (Fig. 2.4C) so that both the mean and the fluctuating contributions to the root bending moment are enhanced for plants in canopies compared to the same plants in isolation. We can see from Figs. 2.16 and 2.17 that this picture is altered for canopies on hills. On the hilltop, not only are the mean wind and u′2¯ si8_e increased relative to values on flat ground, but their profiles are more sharply peaked around the canopy top, ensuring that for the same total force on the plant the mean and fluctuating root bending moments would be substantially increased. Halfway up the hill, in contrast, the profiles of u¯ si65_e and u′2¯ si8_e are both less peaked than on the flat, leading to reduced root M_R, other factors being equal. Hence, trees near the hilltop will suffer greater static and fluctuating bending moments than trees in the valley, and those on the upwind slope will have the smallest M_R. Of course, this does not mean that trees on the hilltop are the first to blow over, as they will have grown in this environment, but it does indicate where in the landscape any given threshold M_R will be exceeded first as overall wind speeds rise.

Spread of spores and pathogens

Long-distance dispersal of seeds, spores, and insects is central to species expansion following ecological disturbance. Recent work by Nathan et al. (2002) has shown that the particular nature of the turbulent wind structure determines whether a species will spread over significant distances in a canopy. The key to long-distance dispersal is ejection of the seed or spore from within the canopy to the ASL above. Objects diffusing within the canopy are typically intercepted by the ground or foliage elements within a distance of order h. Nathan et al. (2002) found that h was the modal distance of within-canopy travel for a variety of seeds in a deciduous forest. In contrast, seeds ejected from the canopy traveled tens to hundreds of canopy heights downwind (hundreds of meters to several kilometers). The most energetic ejection events are probably associated with the outer edges of the turbulent large structures generated by the mixing layer instability. To eject seeds or spores from the canopy, these ejection events must have vertical velocities greater than the terminal velocity of the particles. According to the calculations of Nathan et al. (2002), the probability of such events ranges between 1% and 5% for seeds ranging from 5 to 50 mg in weight.

No measurements are currently available to indicate how these probabilities are modified by topography or homogeneity. Nevertheless, we can infer from published and unpublished data from the wind tunnel experiment of Finnigan and Brunet (1995) that ejection from a canopy on a hill is most likely to occur halfway up the windward slope, where the inflection in the velocity profile is weakest, and that it is in this region also that spores or seeds from the lower canopy space have the greatest chance of being fully ejected from the canopy. Conversely, spores, seeds, or pathogens being intercepted by canopy plants are more likely to be transported all the way to the ground by turbulence in this region, while on the hilltop they will be intercepted by the overstory.

Fire

At first thought it seems reasonable to imagine that the character of the turbulent canopy airflow should strongly influence forest fires. However, a revealing similarity analysis of bushfire plumes by Raupach (1990) has shown that this can be true only for fires of very low intensity. By representing a fire front as a line source of buoyancy, Raupach showed how to relate the heat released by the fire in W m^− 1 to the characteristic vertical velocity in the ensuing buoyant plume. Classifying fires in terms of the heat released, he associated updraft velocities with fire strengths from a small burn at 10⁵ W m^− 1 to an inferno at 10⁸ W m^− 1 (see Table 2.2).

Table 2.2

Updraft velocity generated by wildfires of specified heat release.
Type of fire	Heat release H (W m^− 1)	Updraft velocity w_B (m s^− 1)
Small burn	10⁵	2.4
	10⁶	5.0
	10⁷	10.9
Inferno	10⁸	23.4

We can compare the updraft velocities, w_B in Table 2.2, with the mean and turbulent components of the horizontal wind speed at the canopy top to estimate the dynamic significance of the wind patterns generated by the canopy relative to those produced by the fire front. First, we note even moderate burns of 10⁶ W m^− 1 produce updraft velocities around 5 m s^− 1. Next we can calculate that to generate a velocity u¯h si33_e of 5 m s^− 1 over a forest canopy of moderate density (leaf area index ~ 4, say) requires windspeeds at z = 2 h of 10 to 15 m s^− 1. Finally, we recall from Fig. 2.4 that in the roughness sublayer the streamwise velocity variance σu≤u¯ si68_e . Hence, we see that only in very strong winds are the mean wind fields and turbulent velocities generated by the canopy comparable to the buoyant updrafts generated by fires of even moderate intensity.

Another measure of the windfield distortion calculated by Raupach (1990) was the effect of the buoyant plume on the horizontal wind. He showed by a mass conservation argument that the difference in horizontal mean velocity across the plume could be estimated as u¯in=u¯out≈0.2wB si69_e . This implies that the streamwise velocity difference across the fire front is small for small to moderate fires (H ≤ 10⁶W/m) but ranges up to about 5 m s^− 1 for intense fires with H ~ 10⁸ W m^− 1. In other words, the action of the fire line as a windbreak is weak except for very strong fires.

It is clear that the particular structure of the canopy windfield is likely to play only a minor role in determining fire dynamics, except in the case of rather cool burns confined to the under story. While this is itself a case of practical importance, because it corresponds to fuel reduction burns that are a part of fire management regimes, wildfires that cause major ecological disturbance probably have windfields totally dominated by the intense buoyant updrafts accompanying the fire front itself and the more diffuse buoyant plume generated over the heated burned region behind the front. Katabatic winds produced in this way typically result in fires burning fiercely to ridge tops on the windward slopes of hills and can result in near-sterilization of hill crests, with profound consequences for the structure of the reemerging canopy.

Summary

I have covered a great deal of ground in this chapter, so it might be useful to recall the approach taken. The chapter began by looking at the structure of the atmospheric boundary layer over land from a traditional micrometeorological point of view. It is worth noting that this point of view tends to be biased toward midlatitude conditions when it isn't raining. Not only do most meteorological instruments (rain gauges excepted) fail to work then, but there are theoretical grounds for believing that turbulent structure changes qualitatively when it is raining. This said, I followed the traditional division of the boundary layer into the mixed or convective boundary layer by day with the surface layer beneath and a shallower stable boundary layer at night.

Discussing the daytime surface layer allowed an introduction to Monin-Obukhov similarity theory, and the departures from this theory close to the canopy pointed to the distinctive nature of turbulence there. I began a closer dissection of canopy flows with a brief history of the development of ideas and followed this with a set of diagrams illustrating typical common features of turbulent and mean flow in uniform canopies. In particular, we saw how turbulence moments and integral scales departed from surface layer norms. Moving on to the cause of these differences, I showed that the flow structure in the canopy was dominated by large coherent eddies that owed their origin and behavior to a hydrodynamic instability of the mean flow that mimics a plane-mixing layer rather than a conventional boundary layer.

All these ideas had been developed for the simplest case of uniform canopies on flat ground, so next I considered heterogeneity in the form of clearings, forest edges, and canopies on hills. From a fluid mechanical point of view, the distinction between these situations is determined by the scale of the heterogeneous forcing rather than by the canopy response, which operates through the same mechanism in both cases. Canopies on hills are subject to forcing by a perturbation pressure field varying on the scale of the hill, a scale much larger than the canopy height. A series of consequences follows from this including, at the local scale, strong perturbations to the mean and turbulent flow fields in and just above the canopy and, at the global scale, phenomena such as increased topographic drag over ranges of hills. The effects of flow across a forest edge are qualitatively different. The pressure field that develops and drives the perturbations varies on the scale of the canopy height and the development of a velocity profile of mixing layer type in a streamwise distance of around 5 to 10 canopy heights plays a critical role in the adjustment of turbulence structure from field to forest.

Finally, I considered the implications of uniform and distorted flows for three kinds of disturbance: windthrow, seed or spore dispersal, and fire. The root bending moment necessary to blow a tree over is difficult to achieve with the drag force developed by the mean wind but is much more easily exceeded if we consider the resonant interaction of flexible plants and the turbulent wind. Seed and spore dispersal, which can govern the spread of weeds, pathogens, or even insect infestations, depends on the ejection of these vectors from the canopy. This, in turn, is directly dependent on the turbulence structure and is probably strongly modulated by topography. In the last example of the implications of canopy wind structure, I analyzed its impact on fire. I compared typical canopy mean and turbulent velocities with the updraft velocities developed around a fire front and also looked at the ability of the fire front to perturb the canopy flow. The conclusion was that in all but the least intense burns the detailed structure of the canopy wind plays little part in controlling the fire. Rather, the windfield is dominated by the buoyancy field of the fire itself.