ARTICLE

Large eddy simulation of forest canopy flow for wildland firemodelingEric Mueller, William Mell, and Albert Simeoni

Abstract: Large eddy simulation (LES) based computational fluid dynamics (CFD) simulators have obtained increasing attentionin the wildland fire research community, as these tools allow the inclusion of important driving physics. However, due to thecomplexity of the models, individual aspects must be isolated and tested rigorously to ensure meaningful results. As wind is adriving force that can significantly dictate the behavior of a wildfire, the simulation of wind is studied in the context of aparticular LES CFD model, the Wildland–urban interface Fire Dynamics Simulator (WFDS). As WFDS has yet to be testedextensively with regard to wind flow within and above forest canopies, a study of its ability to do so is carried out. First, threesimulations are conducted using periodic boundary conditions. Two of these assume a spatially heterogeneous forest and onemodels wind downstream of a canopy edge. Second, two simulations are conducted with specified “inflow” conditions using twoinflow profiles: one static and one dynamic (driven by a precursor simulation). Using periodic boundary conditions, the modelis found to generate profiles of mean velocity and turbulent statistics that are representative of experimental measurements. Thedynamic inflow scenario is found to perform better than the static case.

Key words: computational fluid dynamics, large eddy simulation, wildland fire, canopy, wind.

Résumé : Les simulateurs de dynamique des fluides numérique (CFD) basés sur la méthode de simulation de grands écoulementstourbillonnants (LES) sont l'objet d'une attention croissante de la part des chercheurs dans le domaine des feux de forêt étantdonné que ces outils permettent d'inclure des facteurs physiques déterminants. Cependant, a cause de la complexité desmodèles, des aspects particuliers doivent être isolés et testés rigoureusement pour s'assurer d'obtenir des résultats significatifs.Étant donné que le vent est un élément moteur important qui peut facilement déterminer le comportement d'un feu de forêt,la simulation du vent est étudiée dans le contexte d'un modèle LES CFD particulier : le simulateur de la dynamique des incendiesen milieu périurbain. Ce logiciel de simulation doit encore être testé de façon exhaustive en ce qui concerne l'écoulement du venta l'intérieur et au-dessus du couvert forestier; sa capacité a cet égard doit par conséquent être étudiée. Premièrement, troissimulations sont effectuées en utilisant des conditions aux limites périodiques. Deux de ces simulations assument que la forêtest spatialement hétérogène et une autre modélise le vent en aval de la lisière d'un couvert forestier. Deuxièmement, deuxsimulations sont effectuées dans des conditions d'écoulement déterminées. Des profils d'écoulement statique et d'écoulementdynamique (déterminé par une simulation préalable) sont utilisés. Avec l'utilisation de conditions aux limites périodiques, lemodèle génère des profils de vitesse moyenne et des statistiques de turbulence représentatifs des mesures expérimentales. Onobtient une meilleure performance avec le scénario d'écoulement dynamique que statique. [Traduit par la Rédaction]

Mots-clés : dynamique des fluides numérique, simulation de grands écoulements tourbillonnants, feu de forêt, couvert forestier,vent.

1. IntroductionNumerical simulation of wildland fire dynamics has shown

great potential as a tool, particularly for researchers, as the largerange of scales and conditions encountered in wildland fires aretypically difficult to capture experimentally. A variety of differentmodeling techniques have been developed over the years (Pastoret al. 2003; Sullivan 2009a, 2009b, 2009c). However, the commonlyused semi-empirical models, many of which are based on thework of Frandsen (1971) and Rothermel (1972), have limitationsdue to their inherent dependence on the experimental data fromwhich they were developed. More recently, models using a “de-tailed physical” computational fluid dynamics (CFD) based ap-proach have seen increasing attention. CFD models solve for theconservation of mass, energy, and momentum at discrete loca-tions over a computational grid. In particular, this study focuseson large eddy simulation (LES) CFD simulation, where LES refers

to the way in which turbulence is handled by the model. Fullyresolving all turbulent structures would be too computationallycostly for a wildfire simulation. Instead, only turbulent structureslarger than a prescribed filter width are resolved, and thosesmaller are modelled (Pope 2000). Such detailed physical modelshave the potential to explicitly represent more of the relevantdriving phenomena (Morvan 2011), giving them an advantage overthe semi-empirical approach. The trade-off to the complexity ofsuch models is that each different aspect and submodel must beexamined and tested carefully. The inclusion of a large number ofcoupled submodels means that errors or erroneous assumptionscan have a widespread effect on model outputs, which may bedifficult to trace back to the source. Therefore, it is advantageousto test these models with simple scenarios that limit the numberof driving physical phenomena to a particular subset of interest.

One aspect of detailed physical models that requires investiga-tion is their ability to simulate wind-driven flows, both within and

Received 6 April 2014. Accepted 11 July 2014.

E. Mueller and A. Simeoni. University of Edinburgh, BRE Centre for Fire Safety Engineering, Edinburgh, UK.W. Mell. USDA Forest Service, Pacific Wildland Fire Sciences Laboratory, Seattle, WA, USA.Corresponding author: Eric Mueller (e-mail: e.mueller@ed.ac.uk).

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Can. J. For. Res. 44: 1534–1544 (2014) dx.doi.org/10.1139/cjfr-2014-0184 Published at www.nrcresearchpress.com/cjfr on 15 July 2014.

around vegetative fuel, as well as over various terrain. Wind is animportant driving factor in the behaviour of any outdoor fire,including those in the wildland and the wildland–urban interface.Wind impacts fire behavior on a range of scales, from ventilationconditions within and around the flame, to convective and radia-tive heat transfer ahead of the fire front, to plume dynamics andfirebrand transport. Confidence in a model's representation of firebehavior depends on its ability to simulate accurate wind flows. Itshould be noted that this study focuses on the interaction of theflow with vegetation, and the role of terrain is not currently con-sidered.

The particular model studied here is the Wildland–urban inter-face Fire Dynamics Simulator (WFDS) (Mell et al. 2007, 2009), anLES CFD fire spread model that is currently under joint devel-opment by the United States Forest Service and the NationalInstitute of Standards and Technology (NIST). The model is imple-mented within the framework of the NIST Fire Dynamics Simula-tor (FDS) version 6 (beta, svn 9977). FDS has been developed over anumber of years (McGrattan et al. 2013a), but it was created withthe intention of simulating fires in the built environment. In suchscenarios, buoyancy is considered to be the dominant driver ofmomentum. Although FDS includes a relatively detailed descrip-tion of fire behaviour and heat transfer, outdoor conditions arenot typically simulated. Other LES models have been examinedfor the simulation of wind within both homogeneous canopies(Aumond et al. 2013; Dupont and Brunet 2008a; Pimont et al. 2009;Shaw and Schumann 1992; Su et al. 1998) and nonhomogeneouscanopies (Aumond et al. 2013; Cassiani et al. 2008; Dupont andBrunet 2008b, 2008c; Dupont et al. 2011; Pimont et al. 2009; Yanget al. 2006a, 2006b). However, these were developed specificallyfor atmospheric applications, as well as one purely for large-scalewildland fires (Pimont et al. 2009). Such a study in the context ofWFDS is warranted, as the adaptation of FDS to this type of appli-cation remains relatively untested.

The objective of this work was to determine the basic capabilityof WFDS to simulate flow above and within a forest canopy. Thiswas done through a series of simulations, five of which are pre-sented here. The first three were designed as an evaluation of theformulation specific to WFDS, in terms of both physical assump-tions and numerical techniques. Idealized (periodic) boundaryconditions were used for these. However, this study also aims toaddress the fact that for the intended application, such flows needto be simulated in a manner that is conducive to the transient,localized nature of fire spread. Therefore, the final two simula-tions tested boundary conditions that are more appropriate to thesimulation of fire. The simulations in this paper all represent“cold” flows (without fire), because it is ideal to first test simplifiedcases, as was mentioned previously. The inclusion of strong localbuoyancy forces will serve to complicate the scenario, and so theanalysis of wind fields in the presence of fire should be carried outafter this work.

The first simulation presented was intended to evaluate theperformance of the model when simulating a simple homoge-neous canopy. The experimental data of Shaw et al. (1988) (aspresented in Su et al. 1998) were used to model the canopy archi-tecture and for experimental comparison, as has been done byseveral others (Aumond et al. 2013; Dupont and Brunet 2008a;Pimont et al. 2009). In the second and third simulations, a morecomplex canopy (with a dense crown and sparse trunk space) wasconsidered as a homogeneous layer and as canopy edge, respec-tively. The experimental data presented by Dupont et al. (2011)were used to model the canopy architecture and for experimentalcomparison.

Many canopy flow simulations such as those mentioned previ-ously (Aumond et al. 2013; Cassiani et al. 2008; Dupont and Brunet2008b, 2008c; Dupont et al. 2011; Pimont et al. 2009; Shaw andSchumann 1992; Su et al. 1998; Yang et al. 2006a, 2006b) and thefirst three simulations of this report utilize periodic boundary

conditions. This allows a model to be run until quasi-steady flow isreached. The advantage is that turbulent structures generated bythe canopy can be recycled upstream and do not need to be ex-plicitly defined at any boundary beforehand, allowing for a basicassessment of the model to be easily carried out. However, in thecase of a fire simulation, it is expected that the buoyant fire plumecan have a significant impact on the surrounding flow conditions,often far downstream. Unless a sufficiently (and potentially pro-hibitively) large domain is used, features of the flow, which aregenerated by the fire and advected downstream, will be recycledupstream by periodic boundary conditions. The result is that thefire will be influenced by a kind of feedback mechanism. There-fore, studies have aimed to explicitly specify the characteristics ofthe flow upstream (Linn et al. 2012, 2013; Pimont et al. 2011).

There are a number of potential methods for specifying thevelocity boundary conditions, each with pros and cons, and twohave been tested here. Most simply, a static (laminar) velocityprofile can be used. It is easy to implement and can be useful whenthere is no prior knowledge of the turbulent flow characteristics.This simple approximation was used for the fourth simulation.However, specifying dynamic (turbulent) velocity profiles willclearly have a superior result. Methods to prescribe such a condi-tion include running a precursor simulation to obtain the turbu-lent velocity data that will drive a fire simulation (Linn et al. 2013;Pimont et al. 2011), using a data assimilation technique to driveboundary conditions with experimental data (Linn et al. 2012), orpotentially using a purely numerical treatment to inject turbu-lence, e.g., the synthetic-eddy method (Jarrin et al. 2006) (thoughthis particular method does not appear to have been formallytested for wildfire simulations to date). Due to a lack of time-resolved experimental data, the first of these methods (precursor)was studied here. For both “inflow” simulations, spanwise anddownstream boundaries were set to “open”, unlike in previousfire simulations in which one or more of these boundaries werealso explicitly prescribed (Linn et al. 2012, 2013; Pimont et al. 2011).

2. Mathematical modelWFDS uses the methods of FDS when solving for the gas phase

fluid dynamics, heat transfer, and combustion (McGrattan et al.2013b). An LES technique is used to solve the Navier–Stokes equa-tions. FDS employs a low Mach number approximation to filterout pressure waves and decrease computational costs. As thisstudy is focused on nonreacting flow in which heat transfer wasconsidered to be of limited significance, the main equation ofinterest is the conservation of momentum (for more details onFDS, see McGrattan et al. 2013b):

(1)��ui

�t�

��uiuj

�xj� �

�p�xi

���ij

�xj� �gi � fd,i

where the tilde indicates Favre (mass-weighted) filter but will bedropped for clarity from herein. (For an explanation of symbolsused throughout, see List of symbols.) Note that FDS employsimplicit filtering, meaning that filter width is determined by gridsize and requires no additional computation. The deviatoric stresstensor is given as

(2) �ij � �2(� � �t)� 12��ui

�xj�

�uj

�xi� �

13

( ·u)ij�The turbulent eddy viscosity is modeled using the approach ofDeardorff (1980):

(3) �t � �Cv��ksgs

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where Cv = 0.1, � = (x y z)1/3, and ksgs is the subgrid-scale (SGS)turbulent kinetic energy (TKE), a measure of the energy containedin the small eddies of the flow.

Unlike other LES models that have been studied for similarflows, this particular formulation does not solve a conservationequation for SGS TKE. Instead, ksgs follows an algebraic modelbased on scale similarity (Bardina et al. 1980). This is of particularinterest because other models separate the TKE equations intodistinct bands for the SGS, wake scale (Shaw and Patton 2003), andfine scale (Pimont et al. 2009). Depending on the scale, these equa-tions may include terms for the influence of vegetation on turbu-lent energy cascade and dissipation, as well as TKE production viathe generation of small-scale eddies in the wake of vegetationelements (e.g., branches or leaves) (Aumond et al. 2013; Dupontand Brunet, 2008a; Pimont et al. 2009; Shaw and Patton 2003; Suet al. 1998). However, it has been shown that the effect of wakeproduction is minimal in such flows (Shaw and Schumann 1992),and the primary influence of wake scale structures is to enhancedissipation of SGS TKE (Shaw and Patton 2003).

WFDS incorporates vegetative fuel and employs the multiphaseformulation introduced by Larini et al. (1998) and inspired byGrishin (1997). Vegetation is considered to be comprised of a ran-dom distribution of small identical particles, as shown in Fig. 1,that can be described by their bulk properties within a controlvolume. The influence of the forest canopy elements on momen-tum, through pressure and friction drag, is represented by a bodyforce term. Following the multiphase formulation, the volumetricdrag force, fd,i, is written as the bulk influence of these particles(Larini et al. 1998):

(4) fd,i � ��cscd� ui�u�

where cs is a shape factor, cd is a drag coefficient, � is the surface-to-volume ratio of a particle, and is the solid volume fraction ofvegetation. However, assuming the projected frontal area of aparticle to be half of the total surface area, as with flat leaves,leads to

(5)� 2

� af

where af is the frontal area density (one-sided leaf area per vol-ume) (Pimont et al. 2009). By absorbing the shape factor and the[1/2] factor into the drag coefficient, the equation can be rewrittenin terms more familiar to the atmospheric modeling community:

(6) fd,i � ��cdafui�u�

Suggested drag coefficients in canopies range between 0.15 and0.37 (Gillies et al. 2002; Pimont et al. 2009; Shaw and Schumann1992). These are based on experimental measurement and repre-sent an average value that accounts for the fact that real leaveswill have a distribution of orientations. Profiles of leaf frontal areadensity must be determined for a given forest type.

3. Numerical detailsFor all simulations, the grid cell size was set to 2 × 2 × 1 m3. This

choice was intended to be similar to the resolution used in othersuch studies (Dupont et al. 2011; Pimont et al. 2009; Su et al. 1998)and of appropriate size to resolve the dominant coherent struc-tures of the wind flow. The size of such structures in the uppercanopy of such flows has been found to be on the order of h in thehorizontal direction and h/3 in the vertical direction (where h isthe canopy height) (Finnigan 2000). The two distinct profiles offrontal area density within the canopy, shown in Fig. 2, weretaken from literature (Dupont et al. 2011; Su et al. 1998). A drag

coefficient of cd = 0.26 was selected for both forest types, roughlyconsistent with other LES simulations of these canopies. It shouldbe noted that for the simple case, h = 18 m, and for the complexcase, h = 22 m. Details of the choice of domain size, canopy size,and canopy architecture profile for each simulation can be foundin Table 1. Averages of flow variables were taken over a 30-mininterval, the duration used in obtaining the experimental mea-surement used for comparison (Dupont et al. 2011; Su et al. 1998).A 1 Hz sampling rate was used, and temporal averaging is indi-cated by an overbar. Simulations were conducted using Intel XeonE5620 processors.

The velocity components were initialized using a logarithmicprofile of the following form:

(7) u(z)0 �u2h0

log(z)

log(2h), v0(z) � w0(z) � 0

with u2h0= 6.0 m·s−1. An adiabatic lapse rate of � = –0.0098 °C·m−1

was set, corresponding to an initial uniform profile of potentialtemperature at 295 K. In all simulations, the lower boundary uti-lized the Werner Wengle wall model (default condition in FDS)(McGrattan et al. 2013b). This model is a power law adaptation ofthe classic log-law wall model for obtaining the wall shear stress

Fig. 1. Vegetation approximation in the multiphase formulation.

Fig. 2. Vertical profile of frontal area density for the simple (solid)and complex (dashed) canopy arrangements. These were estimatedfrom observations in the two experimental sites: the simple canopyis from Su et al. (1998), and the complex canopy is from Dupontet al. (2011). For abbreviations, see List of symbols.

f

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(which must be modeled due to an inability to properly resolvethe velocity gradient).

3.1. PeriodicFor the first three simulations, periodic boundary conditions

were used in both streamwise and spanwise lateral directions. Ano-flux boundary was enforced at the top of the domain, with aconstant tangential velocity in the streamwise direction. This con-stant wind served to balance the loss of momentum in the canopy,and its value was determined by the logarithmic profile of eq. 7.Simulations 1 and 2 were set to the same domain size and had acontinuous forest canopy layer. Simulation 3 had a longer do-main, with canopy over only the last 300 m (in the downwind xdirection), to simulate a forest edge. The 30-min temporal averag-ing interval was taken over 9000 to 10 800 s of simulation time.For simulations 1 and 2, flow variables were also spatially aver-aged along a plane, which bisected the domain in the spanwisedirection. Spatial averaging is indicated by pointed brackets.

3.2. InflowFor the simulation with specified static inflow conditions, the

velocities on the upwind y–z plane were prescribed as a time-independent function of z, based on eq. 7. The domain was set to1050 × 150 × 200 m3, and the canopy layer extended for 1000 m inthe x direction, with the first 50 m left clear to allow for someestablishment of the flow over open terrain. The longer domainwas chosen to provide a clearer picture of how the flow developedalong distance. Temporal averages were taken over the same in-terval as used for the periodic simulations. For the dynamic inflowconditions, the velocities on the upwind y–z plane were pre-scribed from recoded instantaneous values from a precursor sim-ulation that had periodic boundary conditions. Thus, the inflowconditions were time-dependent and varied as a function of bothy and z. The domain was set to 400 × 150 × 200 m3, and the canopycovered the whole length of the domain. A sampled interval fromthe periodic precursor simulation of 7000 to 10 900 s was used forthe inlet. Therefore the simulation only ran for 3900 computa-tional seconds. Temporal averages were taken over a period from2000 to 3800 s, which allowed time for the flow to establish first.

In both the static and dynamic inflow cases, the velocity andpotential temperature were initialized in the same manner as theperiodic simulations. The downstream, spanwise, and upperboundaries were specified as open, corresponding to a Dirichletboundary condition for the Poisson pressure equation in whichthe total pressure is assumed to be constant along a streamline.The lower boundary used the same wall model as before. Canopyheight and architecture matched the simple canopy case shown inFig. 2.

4. Results and discussionTurbulent flows in forest canopies have been well studied. Such

flows differ from the typical surface layer characteristics, whichare often applied to the inertial sublayer of the atmosphericboundary layer. This has often been described by a mixing-layeranalogy (Raupach et al. 1996), which is characterized by a strongshear at the canopy top. This is manifested in an inflection pointin the mean velocity profile. Canopy shear is responsible for the

generation of large coherent eddy structures, which are the driv-ing force behind the transfer of stress down into (sweeps andejections) or up out of (inward and outward interactions) the can-opy (Finnigan 2000; Raupach and Thom 1981).

4.1. Periodic simulations

4.1.1. Simple canopy (simulation 1)Flow variables produced by the simple canopy simulation are

reported in Fig. 3. Streamwise velocity (u) and resolved turbulentkinetic energy (k � 1/2�u ′2 � v ′2 � w ′2�) are normalized by theirrespective values at canopy height (h), whereas momentum flux(u ′w ′�) and the velocity deviations (�u,v,w) are normalized by frictionvelocity (u∗ � � � u ′wh

′��1/2). Normalization variables are also spa-tially averaged in the streamwise direction, and their values aregiven in Table 2. This table shows that the simulated streamwisevelocity at canopy height (ur) decayed from its initial value pre-scribed by eq. 7 as the momentum sink in the canopy balanceswith the flow higher up.

The simulated streamwise velocity (Fig. 3a) shows the expectedlogarithmic inertial sublayer profile above the canopy, with aninflection point at the interface (Finnigan 2000). Within the can-opy, the velocity decays due to the drag sink term in the momen-tum equation, following the approximately exponential form(Finnigan 2000; Inoue 1963). In general, the profile is well matchedto the experimental data. Simulated TKE (Fig. 3b) is relativelyuniform directly above the canopy, with a very slight underpre-diction at twice the canopy height. The rapid decay of TKE withinthe canopy layer is accurately represented. The same is true of themomentum flux profile (Fig. 3c). Momentum flux can be thoughtof as the transfer of momentum caused by shear stress. Positivevalues shown in Fig. 3c correspond to negative momentum flux.This downward transfer of momentum is the result of sweeps(u= > 0; w= < 0) or ejections (u= < 0; w= > 0) (Shaw et al. 1983). Largesweep events have been found to play the main role in momen-tum flux in plant canopies, although these tend to be quite inter-mittent (Finnigan 2000). The velocity component variances(Figs. 3d–3f) do appear to be somewhat underpredicted by themodel. However, these represent the components of the TKE, andgiven the good match of the TKE profile, it is likely that a slightoverprediction in the normalization variable is causing the gen-eral shift to the left. Indeed, profiles still match the expectedshape and relative distribution of magnitude between compo-nents along the whole height. Lastly, the third-order moments(Fig. 3g), or skewness, for the streamwise and vertical velocity givethe same signs as the experiments. Skewness is a measure of theasymmetry of a probability distribution. The positive horizontalvelocity skewness and negative vertical velocity skewness indi-cates the importance of sweeps (skewed towards u= > 0 and w= < 0),as mentioned previously.

Basic sensitivity studies were conducted on drag coefficient,initial velocity magnitude (u2h0

), and the mesh size. It was foundthat increasing drag coefficients resulted in a decrease in normal-ized mean streamwise velocity within the canopy and an increaseabove the canopy. The above-canopy increase can be attributed tothe fact that the driving velocity specified at the upper boundaryremained the same as the drag was increased, resulting in a

Table 1. Summary of the different numerical conditions used for each simulation (Sim.) conducted in this study.

Sim.no. Streamwise boundary conditions (BCs)

SpanwiseBCs Upper BC Domain (m3) Canopy (m3) Canopy profile

CPUprocesses

1 Periodic Periodic Static tangential velocity 200×150×200 200×150×18 Simple 82 Periodic Periodic Static tangential velocity 200×150×200 200×150×22 Complex 83 Periodic Periodic Static tangential velocity 750×150×200 300×150×22 Complex (edge case) 304 Static velocity upwind, open downwind Open Open 1050×150×200 1000×150×18 Simple 425 Dynamic velocity upwind, open downwind Open Open 400×150×200 400×150×18 Simple 16

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higher gradient at the canopy interface. Decreases in the values ofturbulent statistics (TKE and momentum flux) were also observedwithin the canopy. These results agree with the work of Dupontand Brunet (2008c) in which the sensitivity to canopy foliar den-sity (analogous to drag coefficient) was studied. The study of initialvelocity magnitude sensitivity revealed no clear monotonic corre-lation. It appeared that differences in profiles of mean flow andturbulent statistics observed between the five cases studied wereactually the result of large-scale turbulent structures above thecanopy. Such structures were not adequately captured by the av-eraging interval and yielded differences in above-canopy valuesbetween simulations. The mesh sensitivity was tested by doublingthe number of grid cells in all three directions. Along the intervalfrom z/h = 0.5 to z/h = 2 the average change in normalized velocitywas roughly 2%, with a maximum of 5%. For normalized TKE, theaverage change along this interval was roughly 7%, with a maxi-mum of 17%. It was found that the sensitivity increased close to the

lower boundary, seemingly due to issues with the wall model,particularly at such relatively coarse grid resolutions. At z = 1 m,normalized velocity and TKE changed by 27% and 32%, respec-tively.

4.1.2. Complex canopy stand (simulation 2)The results of the stand case for the complex canopy simulation

are presented in Fig. 4. Streamwise velocity, vertical velocity, andTKE are all normalized by a reference velocity, and momentumflux is normalized by a reference friction velocity, both of whichare computed at the location of the uppermost experimental mea-surement (z/h = 1.9) and are spatially averaged in the streamwisedirection. Their values are given in Table 2.

Above the canopy, simulated mean streamwise velocity (Fig. 5a)has an accurate profile when compared with the experiments. Theinflection point caused by strong shear at the upper surface of thecanopy is present, and the high velocity gradient in the upper partof the canopy is matched. In the sparse trunk space, experimentalobservations revealed a slight secondary maximum. The simula-tion was unable to reproduce this, showing a very low velocity,gradually decreasing to zero. The simulated mean vertical velocity(Fig. 4b) appears to have a noticeable bias toward the downwarddirection, whereas the experimental measurements fall closer tozero. It was determined that this was a result of very low fre-quency turbulent structures in the simulation, and this profilewill fall closer to zero depending on the averaging interval

Fig. 3. Normalized mean variables for the simple canopy case (simulation 1). Simulated profiles (solid lines) are compared with reportedmeasurements (symbols) (Su et al. 1998) for (a) streamwise velocity, (b) resolved TKE, (c) momentum flux, (d–f) velocity variances, and(g) streamwise velocity skewness (solid line, squares) and vertical velocity skewness (dashed line, triangles). Error bars represent experimentalvariation over a series of 30-min measurement intervals. For abbreviations, see List of symbols.

Table 2. Simulated numerical values of normal-ization variables.

Simulation no. ur (m·s−1) kr (m2·s−2) u∗ (m·s−1)

1 0.47 0.05 0.142 1.37 — 0.173 1.48 — 0.22

Note: For abbreviations, see List of symbols.

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selected. This feature appears to be present in the experiments aswell, as evidenced by the error bars reported for a large number of30-min intervals (Dupont et al. 2011). As the simulated averageswere only taken along a plane bisecting the spanwise direction, itshould be noted that this does not represent a mean downwardflow over the entire domain, which would be unrealistic. Abovethe canopy, the simulated TKE (Fig. 4c) is essentially height invari-ant. Although there is an underprediction of TKE at the upper-most experimental point, it does fall within the range of thereported error bar. TKE drops off rapidly within the upper half ofthe crown layer, falling by about 87% of the magnitude above thecanopy. This decline is also seen experimentally, with a 72% dropin this distance. Below the canopy, the simulation shows a verylow TKE that diminishes gradually towards the surface, and it iswell matched to the experiments. The simulation also closely re-creates the momentum flux profile (Fig. 4d), particularly the rapiddecline to an essentially zero value by the bottom of the crownlayer. As in the experiments, the downward transport of momen-tum is nearly all absorbed by vegetation elements.

4.1.3. Complex canopy edge (simulation 3)Simulated mean flow variables are presented in Fig. 5, and

mean turbulent statistics are presented in Fig. 6. Each is a tempo-ral average at one of two distinct locations downstream of the

upwind edge of the canopy (x/h = 4 and x/h = 9). Normalizationvariables are computed at the location of the uppermost experi-mental measurement (x/h = 9, z/h = 1.9), with no spatial averaging.Their values are given in Table 2.

Here again, the mean streamwise velocity above the canopy hasgood agreement with the logarithmic profile observed experi-mentally. The inflection point and reduction of flow within thecanopy, with a local minimum near its centerline, are well repre-sented. Below the canopy, a strong inflection point is not observedin the simulated profile. The simulations appear to underpredictthe flow just below the canopy layer and overpredict the flowclose to the surface. This is particularly apparent at x/h = 4 (Fig. 5a).The simulated secondary maximum in the understory seems to beof a reasonable magnitude. It is 0.63 at x/h = 4 compared with 0.56in the experiments. For x/h = 9, it is 0.45 compared with 0.43.However, the simulated position of the maximum is shifted down-ward and occurs at z/h = 0.045 at both locations (compared withz/h = 0.41 and z/h = 0.32 for the experiment, respectively). Experi-mental data points do have a low vertical resolution, so thesecomparisons can only be used to indicate general trends. Thesimulated mean vertical velocity is close to uniformly zero alongheight (Figs. 5c–5d). Simulated TKE (Figs. 6a–6b) is close to constantabove the canopy, with a slight increase at the canopy interface

Fig. 4. Normalized mean variables for the stand case in the complex canopy (simulation 2). Simulated profiles (solid lines) are compared withreported measurements (symbols) (Dupont et al. 2011) for (a) streamwise velocity, (b) vertical velocity, (c) resolved TKE, and (d) momentum flux.Error bars represent the standard deviation over a series of 30-min measurements For abbreviations, see List of symbols.

Fig. 5. Normalized mean velocity variables for the edge case in the complex canopy (simulation 3). Simulated profiles (solid lines) arecompared with reported measurements (symbols) (Dupont et al. 2011) for (a–b) streamwise velocity and (c–d) vertical velocity at x/h = 4 (a, c)and x/h = 9 (b, d). Error bars represent the standard deviation over a series of 30-min intervals. For abbreviations, see List of symbols.

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at x/h = 4. This can be attributed to the transition from openflow to the development of the roughness sublayer above thecanopy at the upwind edge. The rapid decrease of TKE along theheight of the canopy crown agrees well with the experiments.These profiles do not show the slight dissipation of TKE in thetrunk space observed experimentally in the downstream direc-tion. Simulated momentum flux (Figs. 6c–6d) also has good agree-ment with the experiments, especially at x/h = 9, though the smallnegative flux measured close to the surface, particularly at x/h = 4,is not replicated.

Unlike the previous simulations for which flow variables werespatially averaged, edge flow simulations are inherently a two-dimensional problem. The plots shown in Fig. 7 help understand-ing the role that the forest edge has in generating the profilesobserved in Figs. 5 and 6. The vector plot of horizontal and verticalvelocity (Fig. 7a) is particularly revealing of the interaction of theflow with the leading edge of the canopy. Momentum conserva-tion results in an upward flow above this edge, as well as a down-ward flow into the trunk space. Due to the considerably low dragforces in this lower layer, a wind jet forms, which can be seen inthe plot of streamwise velocity. This jet persists throughout thelength of simulated canopy, though it does diminish in intensityfurther along the canopy.

Figure 7b shows that there does appear to be some dissipation ofTKE very deep within the trunk space in the streamwise direction,which was not revealed between Figs. 6a and 6b. The generation ofTKE by shear above the canopy, in the roughness sublayer, is alsovisible. This layer has a clear growth from the leading edge ofthe canopy, as upwind values at canopy height transition fromaround 0.04 to 0.07 and then stabilize near 0.06 downstream.Additionally, local maxima of TKE are observed within the trunkspace. This is caused by a combination of streamwise turbulentadvection into this space, transport through the canopy fromabove by eddies formed in the roughness sublayer, and a secondshear layer formed at the underside of the dense crowns. Thegrowth of this layer can also be seen in the plot of momentum flux(Fig. 7c) in which relatively large downward fluxes develop alongthe canopy top. The development of upward (positive) momen-tum flux within the trunk space is visible, with local maxima atbottom edge of the crowns. These positive values are shown topersist along the length of the domain, with a gradual decline inmagnitude. These downward and upward fluxes are a result of thelocal momentum gradients caused by canopy shear.

4.1.4. Trunk space flowOne aspect that the model had some difficulties simulating was

the subcrown flow in the case of a canopy with a very sparse trunkspace. In the scenario that assumed a continuous stand (simula-tion 2), Fig. 4a shows that the simulated mean streamwise velocitywas underpredicted in this area. Although the velocity is nonzero,the profile lacks the secondary maximum observed experimen-tally. This feature has been observed many times previously, asdescribed by Shaw (1977). It has been attributed, by some, to thelow significance of the Coriolis effect on low velocity flows withinthe canopy combined with the influence of the mesoscale pres-sure gradient. It is associated with a swing in mean velocity direc-tion due to the Coriolis and pressure forces no longer beingbalanced (Kondo and Akashi, 1976; Smith et al. 1972). This effect isnot represented by the WFDS model, as there is no additionalmomentum source in this region. However, as stated by Dupontet al. (2011), no associated swing in velocity direction was mea-sured in the trunk space. It is suggested that the increased flowunder the crowns is the result of horizontal advection and thatedge effects are still present at this distance in the forest. Thus, theassumption of a continuous forest stand is not entirely appropri-ate for this case. Dupont et al. (2011) found that by simulating alonger section of the edge flow case, the experimental profile inthe stand case is obtained at approximately x/h = 18.

In the canopy edge case (simulation 3; see Fig. 5), the simulatedsecondary velocity maximum in the trunk space is closer to thesurface than was observed in the experiments. The high velocitygradient here corresponds to a large wall-shear stress. It is possi-ble that the wall model has trouble resolving the effects of thesurface boundary layer at this relatively coarse grid resolution,though this needs to be investigated further. However, it is alsoimportant to consider that the surface will have a vegetative litterlayer and possibly small plants or shrubs. This will contribute to aroughness layer, which was not simulated because it was notmeasured in the experiments. In either case, a boundary condi-tion that enforces a reduced velocity gradient in this near-wallregion should, through momentum conservation, force the sec-ondary maximum higher into the trunk space. Additionally, amore accurate boundary condition might add to the downstreamturbulent dissipation in the trunk space, which is somewhatpoorly represented by the model. It was noted that Fig. 7b doesshow an eventual dissipation, but this is close to the boundary andshould be investigated further. Ultimately, the representation ofthe boundary and potential surface vegetation is critical. Such

Fig. 6. Normalized mean turbulent statistics for the edge case in the complex canopy (simulation 3). Simulated profiles (solid lines) arecompared with reported measurements (symbols) (Dupont et al. 2011) for (a–b) resolved TKE and (c–d) momentum flux at x/h = 4 (a, c) andx/h = 9 (b, d). Error bars represent experimental variation over a series of 30-min intervals. For abbreviations, see List of symbols.

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vegetation will feed surface fires and their influence on localwinds affects estimates of flame spread. This could even impactpredictions of surface fire to crown fire transition.

4.2. Inflow-type simulations

4.2.1. Static inflow (simulation 4)In the case of the static inflow conditions, Figs. 8a and 8b show

the downstream development of both mean normalized stream-wise velocity and resolved TKE from the canopy edge (x/h = 0) atone-half and twice the canopy height. Reference values used fornormalization were taken at z/h = 1 to allow comparison withquasi-steady values from simulation 1 (see Fig. 3). Normalizationvalues are computed for each point simulated in the streamwisedirection (no spatial averaging). A sharp increase is seen in bothnormalized mean velocity and TKE close to the inlet. This iscaused by ur and kr becoming very low in this region and thenormalization resulting in a near division by zero. The velocity atone-half canopy height approaches its quasi-steady value aroundx/h = 15, whereas this distance is closer to x/h = 19 at twice canopyheight. TKE within the canopy stabilizes around the same loca-tion, whereas above the canopy, this occurs at an even greaterdistance from the edge (approximately x/h = 28). This discrepancycan be attributed to the canopy drag, which will damp fluctua-tions within the canopy and lessen the influence of the developingroughness sublayer at the canopy top. As a quantification of thedownstream flow variability, the standard deviation of normal-ized TKE was computed over the range from x/h = 25 to x/h = 45. Itis about 0.02 at one-half canopy height and 0.27 at twice canopyheight. However, the magnitude of the TKE is still decaying along

this region. At twice canopy height, the TKE mean value over x/h =42 to x/h = 45 is roughly 69% of the mean value over x/h = 25 to x/h =28. Therefore, although the normalized shapes of the flow profilesare quasi-steady here, the absolute turbulent conditions are not.

Figure 8c shows the (un-normalized) vectors of streamwise andvertical velocity. The pressure gradient at the canopy edge, gener-ated by the reduction in flow due to drag forces, causes an upwarddeflection in the flow direction. This, coupled with the effects ofdrag deeper into the canopy, causes an area of very low flow,which reaches a minimum along canopy height at about x/h = 15.This region resembles flow separation. Despite the differences incanopy density profile from the edge case (simulation 3; see Fig. 7),comparison between the two still suggests that this region of theflow is unrealistic. This assertion is strengthened by comparingwith other edge flow simulations such as those of Dupont andBrunet (2008b) or Pimont et al. (2009) in which such a flow sepa-ration was not observed. This unrealistic separation may be linkedto the laminar nature of the flow upstream as a result of the staticinflow profile, which would not be expected in the real atmo-spheric boundary layer. Additionally, the boundary condition atthe outflow plane appears to have some influence on the flowupstream, as streamwise velocity just above the canopy top de-creases noticeably past x/h = 45.

4.2.2. Dynamic inflow (simulation 5)Figure 9 shows results from the precursor-driven dynamic in-

flow simulation. The downstream development of both mean nor-malized velocity (Fig. 9a) and TKE (Fig. 9b) at both one-half andtwice the canopy height and a vector plot of the un-normalized

Fig. 7. (a) Vector plot of mean streamwise and vertical velocity; and contour plots of (b) mean normalized resolved TKE and (c) meannormalized momentum flux for the edge case in the complex canopy (simulation 3). All plots are along the spanwise centerline of thedomain. For abbreviations, see List of symbols.

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flow (Fig. 9c) are shown. This case was set to a domain length of400 m in the streamwise direction to minimize the upstreameffect of the outflow plane that was observed in simulation 4.With a 200 m domain, this had an impact on a greater percentage

of the distance and could not be ignored. Figures 9a and 9b showthat the normalized flow was much more stable than simulation 4(Fig. 8) when considered across the entire length of the domain asthe significant effects of the flow separation were not present. The

Fig. 8. Downstream flow development for the case of a static inflow profile (simulation 4). Streamwise profiles of (a) mean normalizedstreamwise velocity and (b) mean normalized resolved TKE are compared with quasi-steady values from the periodic simulation (dashed lines)for both one-half (thin lines) and twice canopy height (thick lines). (c) A vector plot of mean streamwise and vertical velocity on the spanwisecenterline is also shown. For abbreviations, see List of symbols.

Fig. 9. Downstream flow development for the case of a dynamic inflow profile (simulation 5). Streamwise profiles of (a) mean normalizedstreamwise velocity and (b) mean normalized resolved TKE are compared with quasi-steady values from the periodic simulation (dashed lines)for both one-half (thin lines) and twice canopy height (thick lines). (c) A vector plot of mean streamwise and vertical velocity on the spanwisecenterline is also shown. For abbreviations, see List of symbols.

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standard deviation of normalized TKE was computed over therange from x/h = 0 to x/h = 20. It is about 0.02 at one-half canopyheight and 0.20 at twice canopy height. Thus, this scenario hascomparable variability to the previous case. Also at twice canopyheight, the absolute TKE mean value on the interval x/h = 17 tox/h = 20 is roughly 97% of the mean value on the interval x/h = 0 tox/h = 3. Considering the influence of small, spatially dependentfluctuations, this indicates no significant decay in TKE.

Although the mean velocity and TKE in Figs. 9a and 9b do ap-pear to be shifted from the expected quasi-steady (dotted line)values, they do not show the same large fluctuations close to thecanopy edge as observed in Fig. 8. The shift in magnitude is linkeddirectly to the inflow conditions as the sampled wind data fromthe precursor simulation came from one specific plane in thestreamwise direction and one particular 30-min sampling period.The sensitivity to averaging intervals, both spatially and tempo-rally, has already been mentioned, and it can be expected that ifdifferent samplings were selected, the profiles in Figs. 9a and 9bwould be shifted differently. Finally, the influence of the outflowcondition can still be seen in all three plots of Fig. 9, though it isclear that the upstream impact was of relatively limited extent.

The choice of lateral boundary conditions will be quite im-portant to a fire simulation (see section 1). Periodic boundaryconditions will unrealistically recycle fire-induced flow featuresupstream, and explicit velocity profiles at all boundaries will notallow for the influence of an adjacent fire, particularly in terms ofentrainment. The distance from the boundary at which a fire willhave a negligible influence is not well defined and will depend onparameters such as the magnitude of the ambient velocity and theintensity of the fire. Therefore, it is preferable to use boundaryconditions that are dependent on the local flow at a given timestep. This was accomplished by the use of open downstream andspanwise boundaries. The inflow profiles tested here had no suchdependency, and caution must be used when setting the distancebetween a simulated fire and such a boundary.

A static inflow profile may be attractive as it requires no previ-ous knowledge of the flow characteristics or precursor simula-tions. However, realistic flow conditions only established relativelydeep within the canopy, and turbulence continued to decay alongthe region simulated. For increasingly complex canopies, whereconditions can no longer be expected to fully establish in thestreamwise direction, it will be difficult to distinguish which fea-tures of the flow are due to canopy complexity and which areartifacts of this type of static inflow condition.

5. ConclusionsThis study shows that the model is capable of representing the

characteristics of both mean variables and turbulent statistics offlow within and above forest canopies. This is true for both canopyarchitectures tested, though there are some difficulties in simu-lating a sparse trunk space. However, these issues may well bealleviated by the inclusion of surface vegetation and its contribu-tion to surface drag. Additionally, the spatially dependent edgeflow scenario was well represented. These results are encouragingdue to the use of a simplified approach to the Deardorff turbu-lence model, which lacks a SGS TKE conservation equation, and byextension an explicit formulation of the effect of vegetation onthe turbulent energy cascade, dissipation, and wake production.The studies of Pimont et al. (2009) and Shaw and Patton (2003)suggested that there was no strong dependence on the choice ofSGS turbulence scheme. It was determined that the subdivision ofTKE transport into separate scales was found to be unnecessaryand that the increased dissipation caused by canopy drag could beadequately represented by a single SGS TKE equation. However,these conclusions were still specific to cases with a conservationformulation. The results presented here indicate that the simpli-

fied algebraic method for determining SGS TKE is sufficient forthese simple, large-scale canopy flows.

Additionally, this study demonstrates that omission of thegeostrophic pressure gradient and Coriolis force terms was notsignificant in generating the vertical profiles of flow variables.However, this conclusion must be taken with a few caveats. Thefirst is that, in lieu of a pressure term, the driving force for theflow was a constant tangential velocity specified at the top ofthe domain. It was found that the quasi-steady velocity magnitudeclose to the canopy was much lower than the corresponding ini-tial velocity at this point, and therefore a high velocity gradientdeveloped close to the upper boundary. To simulate a high veloc-ity flow in the canopy layer, an unrealistically large driving veloc-ity would need to be specified. The value selected here was basedon eq. 7, which is height dependent, but some further adjustmentof this value may also be required for domains of differentheights. This can be circumvented by the inclusion of a large-scalepressure term. Given the encouraging results of the WFDS model,along with the demonstrated success of this approach by others(Dupont and Brunet 2008c; Shaw and Schumann 1992), it is rea-sonable to expect a good outcome. The second caveat is that, withthe exclusion of both terms, the phenomenon of swing in velocitydirection observed in sparse trunk spaces will not be reproduced.The same will be true if only a geostrophic pressure term is added(Shaw and Schumann 1992) as it will necessarily be aligned withthe mean flow direction. It is not clear that this swing will have asignificant impact on the fire behavior of interest. However, itsabsence is important for model users to note.

Finally, although the model was able to simulate such flows, thechoice of boundary conditions for a fire simulation was impor-tant. It is recommended that the use of a static inflow condition beavoided, unless the portion of the domain in which fire is simu-lated is limited to a region where reasonable quasi-steady flow hasdeveloped. Within the scope of this paper, the use of a precursorsimulation to drive inflow conditions was found to be a superiormethod. In both cases, however, remaining boundary conditionsmust also be defined with care. The discrepancies in velocity closeto the surface, along with the apparent upstream effects of openboundary conditions, could potentially modify fire dynamics andrequire further investigation.

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List of symbols

vegetation solid volume fraction� characteristic grid length, m� lapse rate, °C·m−1

� viscosity, Pa·s�t turbulent eddy viscosity, Pa·s� density, kg·m3

� vegetation surface-to-volume ratio, m−1

�u,v,w velocity variance, m·s−1

�ij deviatoric stress tensor, Paaf canopy frontal area density, m−1

cd vegetation drag coefficientcs vegetation shape factor

fd,i volumetric drag force vector, N·m−3

gi gravity acceleration vector, m∙s–2

h canopy height, mk resolved turbulent kinetic energy, m2·s−2

kr reference turbulent kinetic energy, m2·s−2

ksgs subgrid-scale turbulent kinetic energy, m2·s−2

SKu,w velocity skewness, m3s−2

t time, su=w= momentum flux, m3s−2

u∗ friction velocity, m·s−1

ui velocity vector, m∙s–1

ur reference velocity, m·s−1

xi cartesian coordinate in direction i, m

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