Scale-Dependent Effects of Bank Vegetation on Channel Processes:Field Data, Computational Fluid Dynamics Modeling, and Restoration Design

Brian P. Bledsoe,1 Shaun K. Carney,1,2 and Russell J. Anderson1,3

1Department oState University, F

2Now at RiveUSA.

3Now at Morri

Stream RestoratApproaches, AnalGeophysical MonCopyright 2011 b10.1029/2010GM

Bank vegetation substantially influences flow resistance, velocity, shear stressdistributions, and geomorphic stability in many natural river settings. We analyzefield data from gravel bed streams with typed bank vegetation characteristics andemploy three-dimensional computational fluid dynamics (CFD) modeling to ex-amine whether the effects of bank vegetation on channel form and processes arescale dependent. Field data from the United States and United Kingdom indicatethat mean bankfull dimensionless shear stresses are significantly higher in channelswith thick woody vegetation but only for channel widths less than ~20 m. Becausespecific mechanisms controlling the apparent scale dependency are difficult toisolate in natural channels, we develop CFD models of streams with coarse bedsand bank vegetation to investigate physical processes in channels with variable bedand bank roughness. The CFD models are applied in two sets of simulations toimprove mechanistic understanding of patterns in the field data and to examine(1) spatial scale dependency between channel width and vegetation effects and(2) the coevolution of flow hydraulics, channel form, and vegetation establishment.The scale-dependent bank vegetation effects on shear stress distributions in theCFD representations are consistent with field data from gravel bed streams andsuggest that the length scale of bank vegetation protrusion relative to channel widthis an important factor that could improve shear stress partitioning models. Ingeneral, the field data and CFD simulations indicate a significant scale-dependenteffect of bank vegetation with important implications for stream restoration designsbased on tractive force, regime, and analytical approaches.

f Civil and Environmental Engineering, Coloradoort Collins, Colorado, USA.rside Technology, Inc., Fort Collins, Colorado,

son-Maierle, Inc., Helena, Montana, USA.

ion in Dynamic Fluvial Systems: Scientificyses, and Toolsograph Series 194y the American Geophysical Union.000959

151

1. INTRODUCTION

Bank vegetation along streams and rivers performs impor-tant ecological and geomorphic functions by influencingflow hydraulics, channel form and stability, and habitat di-versity. Stream restoration plans frequently include reestab-lishment of bank vegetation to increase geotechnical stabilityof banks due to root reinforcement [Abernethy and Ruther-furd, 2000; Simon and Collison, 2002], influence flow pat-terns in streams and decrease near-bank velocities [Thorneand Furbish, 1995]. Decreased flow velocities in the vicinityof vegetated banks can significantly alter distributions ofshear stress and sediment transport across the entire channel

152 SCALE-DEPENDENT EFFECTS OF BANK VEGETATION ON CHANNEL PROCESSES

and particularly in the near-bank region. Many researchershave found riparian vegetation significantly influences chan-nel form, including hydraulic geometry [Charlton et al.,1978; Andrews, 1984; Hey and Thorne, 1986; Soar andThorne, 2001], planform characteristics [Millar, 2000],and scour pool characteristics [Gran and Paola, 2001]. Bankand floodplain vegetation also affect stage-discharge rela-tionships in rivers, and specific methods for estimating flowresistance due to riparian vegetation have been previouslydeveloped [Darby and Thorne, 1996; Darby, 1999].Previous work on the influence of bank vegetation on flow

hydraulics has typically focused on empirically estimatingincreases in channel resistance due to vegetation [Coon,1998], partitioning resistance between vegetated and nonve-getated portions of the channel [Darby and Thorne, 1996;Darby, 1999; Yen, 2002], or computing average flow profilesover or through vegetation [Fischenich, 1996]. Fischenich[1997] and Lopez and Garcia [1997] provide reviews ofmany of the basic qualitative and quantitative methods ofaccounting for channel vegetation.Previous research also suggests that the influence of bank

vegetation is scale dependent [Anderson et al., 2004]. Forexample, Coon [1998] investigated the influence of bankvegetation on Manning’s roughness coefficient and concludedthat the influence was minimal in channels wider than about20 m and could not be discerned in channels wider thanapproximately 30 m. Likewise, modeling byMasterman andThorne [1992] indicates that the effects of riparian vegetationon flow hydraulics is limited when width-to-depth ratiosincrease beyond about 15. A better understanding of thefundamental processes controlling channel form and stabilityin terms of scale-dependent influence of vegetation on flowhydraulics would benefit channel evolution modeling, char-acterization of material fluxes and instream habitats, andstream restoration design.Although field investigations could further clarify these

processes, field measurements of detailed flow fields in thevicinity of vegetation are difficult to collect due to the infre-quency of high-flow events that inundate vegetated banksand the associated measurement difficulties during highflows. Furthermore, finding multiple stream reaches withsimilar characteristics is challenging due to differences invegetation characteristics, nonvegetative form roughness,sediment supply, flow regime, anthropogenic disturbance,and other influences. Physical modeling provides anothertool for analyzing the influence of vegetation, but can becostly and time consuming. Selecting appropriate variabletest ranges and scaling factors for vegetation and channeldimensions can also be challenging. Numerical modeling isan attractive alternative, provided that vegetation can beappropriately represented.

Computational fluid dynamic (CFD) modeling offers anincreasingly viable means of analyzing the influence of bankvegetation on channel hydraulics and form in a variety ofapplications. With a growing number of CFD softwarepackages and advances in computational efficiency, two-dimensional (2-D) and three-dimensional (3-D) modeling ofriver flow problems have become more feasible and widelyutilized. CFD has been utilized to investigate many complexflow situations typical to natural channels [e.g., Bradbrooket al., 1998; Nicholas and Sambrook-Smith, 1999; Bookeret al., 2001; Morvan et al., 2002; Rameshwaran and Naden,2003; Nicholas and McLelland, 2004], model erosion andsedimentation patterns [e.g., Wu et al., 2000; Shams et al.,2002], and study habitat suitability for fish species [e.g.,Crowder and Diplas, 2000; Booker, 2003]. In CFD model-ing, detailed 3-D velocity fields and shear stress distributionscan be resolved for a given channel geometry. CFD model-ing also offers the advantage of allowing the investigation ofa variety of cases and scenarios with less labor and expensesthan would be required to complete comparable physicalexperiments and can be used to design and optimize physicalmodeling efforts. The commercially available CFD packageFLUENT [Fluent Inc., 2003] has been widely applied tomodel open-channel flows [e.g., Nicholas and Sambrook-Smith, 1999; Nicholas, 2001; Gessler and Meroney, 2002;Ma et al., 2002; Shams et al., 2002; Prinos et al., 2003;Nicholas and McLelland, 2004].In this study, we (1) analyze field data from gravel bed

streams and rivers in the United States and United Kingdomwith various bank vegetation characteristics and (2) employ3-D CFD modeling in FLUENT to examine the influence ofbank vegetation in gravel bed channels and whether theeffects of bank vegetation on key hydraulic parameters usedin restoration design of gravel bed streams are scale depen-dent. We hypothesize that in relatively narrow channels,dense woody vegetation protruding appreciably into thebankfull flow field results in significantly higher values ofbankfull dimensionless shear stress (τ*) and slope (S). In theCFD modeling experiments, a drag force representation ofvegetation [e.g., Fischer-Antze et al., 2001] is coupled withthe porous treatment of bed roughness described by Carneyet al. [2006] to investigate the influence of bank vegetationon flow hydraulics in trapezoidal channels. The resultingmodel is used to elucidate processes responsible for patternsobserved in the field data and to specifically examine (1) scaledependency of vegetation influence in channels with similarcharacteristics but different widths and (2) changes in flowhydraulics following a succession of vegetation establish-ment along a channel. CFD modeling results are comparedwith data from natural channels of various scales withtyped bank vegetation to examine the magnitude and scale

BLEDSOE ET AL. 153

dependency of hydraulic effects. Finally, implications forgeomorphic analysis, CFD modeling, and restoration designof natural gravel channels with successional bank vegetationare discussed.

2. METHODS

2.1. Analysis of Field Data

We compared mean values of bankfull dimensionlessshear stress (τ*) for channels with different bank vegetationconditions using data from field studies of gravel bed streamsand rivers in the western United States by Andrews [1984]and in the United Kingdom by Charlton et al. [1978] andHey and Thorne [1986]. These studies were selected becausebank vegetation was typed for each study site, and the datasets contain the necessary geomorphic and hydraulic data forexamining τ* as it varies with channel width and vegetationtype. Bankfull dimensionless shear stress is referenced to themedian grain size (D50) and defined as

s* ¼RS

ðG−1ÞD50 ; ð1Þ

where R is hydraulic radius, S is slope, and G is the specificgravity of sediment assumed to equal 2.65.Throughout this chapter, bank vegetation conditions are

referred to as “thick” or “thin.” If percent coverage data wereavailable, “thick” vegetation refers to bank vegetation qual-itatively described by the researchers as forested, heavy, orthick vegetated bank conditions with greater than 5% tree/shrub cover. “Thin” vegetation refers to grass-covered banks,nonforested channels, or channels where tree/shrub coverageis less than 5%. It should be noted that thick does not equateto density, as grasses may be much denser than woodyvegetation on a stem per area basis. Thus, the term thick isbest described as a qualitative index of woody vegetationdominance (density, basal area, and coverage) that is directlyrelated to the stiffness and length scale of bank roughnesselements [Anderson et al., 2004].Mean comparisons of τ*, relative submergence (R/D90,

R/D84, and h/D84 for the Andrews [1984], Charlton et al.[1978], and Hey and Thorne [1986] data sets, respectively),substrate gradation D84/D50 (D90/D50 for Andrews [1984]),and S between channels of differing sizes and bank vegeta-tion types were performed using Student’s t tests [Snedecorand Cochran, 1989]. Following Coon [1998], channels withtop widths

Figure 1. Channel configurations for the scale-dependent simula-tions. Width is the only channel characteristic changing amongsimulations (So = 0.001; D84 = 50 mm; CDAv = 11.5 m

�1 for thevegetation on both banks). The hashed region on both banks repre-sents the shape of the vegetation zone extending into the channel.The depth and slope were held constant, and discharge was varied.

154 SCALE-DEPENDENT EFFECTS OF BANK VEGETATION ON CHANNEL PROCESSES

sizes (Figure 1). For each configuration, one realization wasperformed with bank vegetation, and another was madewithout bank vegetation.Following disturbances such as large floods, fires, grazing,

or clearing, vegetation will often regenerate in stream ripar-ian areas. Reestablishing vegetation on stream banks is also acommon strategy of stream restoration. Whether natural re-generation or accelerated reestablishment due to rehabilita-tion efforts, bank vegetation typically is sparse immediatelyfollowing disturbance or implementation of a restorationplan. Thus, the influence of bank vegetation on flow hydrau-lics evolves as density, stiffness, and protrusion change overtime.In the second set of model simulations, we simulated

vegetative succession in a channel of fixed characteristics(width, side slope, bed roughness, and channel slope) withfour vegetation treatments. In the first case, no vegetationwas simulated, and channel roughness was limited to theporous treatment of the bed. In each subsequent scenario,simulated vegetation is included on the banks of the channelwith incrementally greater amounts of protrusion. The pro-trusion of the simulated vegetation into the channel is in-creased in each scenario by lowering the minimum elevationof vegetation on the bank. The inertial loss coefficient of thevegetation zones is increased to simulate increasing flowresistance as vegetation matures and becomes denser andstiffer. Channel slope was set through the pressure gradientin the periodic boundary condition. Flow depth was thenvaried by iteratively regridding the domain and rerunningthe solver until an equal discharge (±1%) was achieved forall scenarios.

2.3. Background on CFD Modeling Approach

Numerous researchers have recognized the potential CFDmodeling provides for geomorphic analyses involving vege-tation. In CFD, roughness is typically parameterized using a

roughness length in some form of logarithmic velocity equa-tion [e.g., Hey, 1979]. The representation of boundary rough-ness using a roughness length inadequately represents thephysical processes creating flow profiles over and throughvegetation. Alternative modeling methods have been pro-posed based on drag force representations of vegetation.Shimizu and Tsujimoto [1994] proposed the addition of asink term in the governing momentum equations based onthe drag due to vegetation. The drag force was parameterizedas a function of vegetation density and drag coefficients. Inthe Shimizu and Tsujimoto [1994] model, two additionalterms are included in the turbulent kinetic energy and turbu-lence dissipation rate equations of the k-e turbulence modelto account for the additional effects of vegetation on turbu-lence. These terms were also a function of the vegetationdensity and drag coefficients, but were treated as calibrationparameters. Detailed flow observations through vertical rodsin a laboratory flume were used to calibrate and verify theirmodel.Lopez and Garcia [1997] developed a similar vegetation

representation based on atmospheric science studies [Rau-pach and Shaw, 1982]. Their model also used vegetationdensity and associated drag coefficients to represent vegeta-tion, although they gave a theoretical basis for two additionalterms included in the turbulent kinetic energy and turbulencedissipation rate equations. Their model was also compared todetailed velocity measurements in a flume setting, with veg-etation represented as either stiff or flexible submergeddowels.Fischer-Antze et al. [2001] noted differences among model

coefficients used in the Shimizu and Tsujimoto [1994] andLopez and Garcia [1997] studies, and postulated that theturbulent diffusive terms introduced by both modelers wereof minor importance relative to the drag term in the momen-tum equations. In the Fischer-Antze et al. [2001] model, thesame vegetation representation is utilized to include a dragforce in the momentum equations without modifications tothe turbulence equations of the k-e model. Using the samedata sets as Shimizu and Tsujimoto [1994] and Lopez andGarcia [1997], Fischer-Antze et al. [2001] added a thirdflume data set [Pasche, 1984] and demonstrated that velocityprofiles of similar accuracy could be captured without turbu-lence model modifications. We also use these data sets toverify model simulations as described below.Each of the above studies presented different vegetation

modeling methods and compared the results with laboratoryflume data, but did not extend those studies to natural chan-nels or use the models to investigate the geomorphic influ-ence of vegetation in open-channel flow. Kean and Smith[2004] present a simplified model based on an algebraicturbulence closure with vegetation represented using similar

Figure 2. Computational grid (cross-section view, half channel) forthe second set of simulations.

BLEDSOE ET AL. 155

drag force concepts. After developing their model and pre-senting a verification based on the Pasche [1984] flume dataset, Kean and Smith [2004] use the model to investigate theimpacts of vegetation on shear stress distributions in straight,clay-bed, prismatic channels. Although the model may besimpler to implement, its applicability is limited to relativelysimple channel geometries. In a different application, Nicho-las and McLelland [2004] used CFD to model overbank flowthrough vegetation by implementing the Fischer-Antze et al.[2001] representation of vegetation, a roughness length rep-resentation of boundary roughness, and a renormalized grouptheory (RNG) k-e turbulence closure model. Nicholas andMcLelland [2004] recognized the potential to utilize a simpledrag force representation of vegetation to reproduce velocityand turbulence profiles in the vicinity of vegetation, yet theynoted the inherent challenges associated with determiningappropriate model parameters to represent vegetation.In the present study, the vegetation representation of

Fischer-Antze et al. [2001] is implemented. Vegetative resis-tance is parameterized in terms of a drag coefficient and ameasure of vegetation density:

FD;iVfluid

¼ 12ρCDAvumagui; ð2Þ

where FD,i is the drag force in the ith (x, y, or z) direction,Vfluid is the fluid volume over which the drag force is applied(equal to unity), ρ is density of the fluid-sediment mixture(assumed equal to 1000 kg m�3), umag is the resultant refer-ence velocity magnitude, and ui is the reference velocity inthe ith direction (the velocity which would be present if thestem being acted upon were removed from the flow [Keanand Smith, 2004]). If the resistance due to vegetation is dueprimarily to rigid stems that can be modeled as rigid cylin-ders, the value of Av may be determined from:

Av ¼ nDs ¼ Dsλ2

; ð3Þ

where n is number of stems per unit area, Ds is average stemdiameter, and λ is average stem spacing (L). Shimizu andTsujimoto [1994], Lopez and Garcia [1997], Fischer-Antzeet al. [2001], and Kean and Smith [2004] all representvegetative resistance in the form presented in equations (2)and (3). Alternatively, Fischenich [1996] and Fischenich andDudley [2000] compiled numerous data sets (primarily Rah-meyer et al. [1995]) and presented methods for computingCDAv for different riparian vegetation species. Their data setsare based on flume studies involving actual vegetation spe-cies assemblages. These sources provide an alternativemeans of estimating drag coefficients and representative

areas for typical riparian vegetation without representingvegetation as a field of rigid cylinders. The range of repre-sentative CDAv values used in the present study was extractedfrom Fischenich [1996].The vegetative resistance computed according to equation

(2) is included as a source term in the governing momentumequations. Assuming the turbulent diffusive terms due tovegetation are dominated by the vegetative drag term perFischer-Antze et al. [2001], the drag force may be appliedthrough the use of a porous media zone in FLUENTwithoutmodification to the turbulence models. Carney [2004] dem-onstrated that the vegetation representation used in this studycould be coupled with the RNG k-e turbulence model toreasonably reproduce the laboratory velocity profiles ofTsujimoto et al. [1991], Dunn et al. [1996], and Pasche[1984]. Carney [2004] also conducted grid-dependency teststo quantify the uncertainty in simulated results followingHardyet al. [2003] for the flume study verification model runs. Themean absolute percentage error in simulated downstream ve-locities among different resolution grids was less than 5% forall tested cases. The grids used for the case studies were of asimilar resolution to those generated for the grid-dependencytests and contained 25 to 30 vertical cells with similar resolu-tion horizontally. Cells were more closely concentrated inregions where higher velocity gradients were expected. Atypical grid used in this simulation is shown in Figure 2.

2.3.1. Bed roughness representation. CFD modeling ofcoarse-grained channels can be challenging due to difficul-ties with roughness parameterization [Nicholas, 2001] as themaximum roughness length is limited to half the thickness ofthe near-bed cells [Fluent Inc., 2003]. Carney et al. [2006]adapted the model of Wiberg and Smith [1991] to representcoarse-bedded channels in CFD. In this approach, the dragforce per unit volume acting over the height of the D84 grainsize is:

FD;totalðzÞVtotal

¼ cbρ2CD

π4DmyDmzuðzÞ2

π6DmxDmyDmz

¼ 34ρcbCDD84x

uðzÞ2; ð4Þ

where cb represents the inverse of the average porosity ofthe bed, Dmx, Dmy, and Dmz are the grain dimensions in

156 SCALE-DEPENDENT EFFECTS OF BANK VEGETATION ON CHANNEL PROCESSES

the downstream, cross-sectional, and vertical directions, re-spectively, and the drag force at a level z between the top andbottom of a grain, FD(z), is computed by replacing theaverage velocity with the velocity at the height z, u(z). Azone is created adjacent to the bed the height of the D84 grainsize, and a momentum sink term defined according to equa-tion (2) is assigned to this zone. In the FLUENT application,the above may be accomplished using a porous media zone[Carney et al., 2006]. Field observations indicate that cbtypically takes a value of about 0.6, which is used in thismodel [Wiberg and Smith, 1991]. The value of CD is set to0.45 based on drag relationships for spheres [Coleman,1967].Shear stress at a channel boundary is typically computed in

CFD using a wall function. However, when bed roughness isrepresented using the above approach, the channel wall islocated below the grains composing the bed. Therefore,shear stresses were computed at the top of the D84 particlesize for comparisons among model runs based on the Rey-nolds stress and molecular shear stress at a point:

τij ¼ ðμþ μeÞ∂ui∂xj

þ ∂uj∂xi

� �; ð5Þ

where μ is the molecular viscosity, μe is the eddy viscosity(computed by the turbulence model), and ui and uj are thevelocities in the xi and xj directions, respectively. The resultantof the applied forces was taken to determine the total shearstress at a point. The average bed shear (τbed,avg) could then becomputed over the bed of the cross-section according to:

τbed;avg ¼ ∑ðτijdÞwW ; ð6Þ

where d is the width of a cell in the cross-stream direction overwhich the shear stress τij is computed, the summation iscomputed over all cells across the cross-section, andW is thebottom width of the channel. These estimates of average bedshear stress are contrasted with cross-section averaged shearstresses (τo) defined as τo = ρgRS.

2.3.2. Additional modeling details. We used the RNG k-eturbulence model with standard equilibrium wall functions[Yakhot and Orszag, 1986]. The RNG k-e turbulence modelhas been shown to perform better than the standard k-emodelin natural streams involving complex flow geometry [e.g.,Bradbrook et al., 1998] and was utilized by Nicholas andMcLelland [2004] to model flow through natural vegetationusing the same vegetation treatment.FLUENT discretizes the governing conservation of mass

and momentum equations using a finite volume approach

[Fluent Inc., 2003]. The momentum equations and turbu-lence equations were discretized using second-order upwinddifferencing. SIMPLEC pressure-velocity coupling wasutilized, which permitted higher under-relaxation factors(0.8–1.0). The water surface was modeled using a fixed lidapproach where the free surface was simulated as a symme-try plane with normal velocity components and normal gra-dients of all variables equal to zero.The banks of natural channels exhibit substantial variabil-

ity as channel meandering characteristics, bed topographysuch as pool-riffle sequences, or other channel variabilityinfluences shear stress, turbulence, and velocity characteris-tics [Buffington and Montgomery, 1999; Wohl, 2000; Nicho-las and McLelland, 2004]. In this study, the objective was tospecifically isolate the impact of vegetation on flow hydrau-lics, and only straight prismatic channels were modeled.Vegetation characteristics (density, species, maturity, and

extent of protrusion into the channel) can vary significantlyin a given channel reach and contributes to flow complexity.However, Carney [2004] demonstrated that by representingthe vegetation in the model with a constant width and density(drag characteristics), the essential flow characteristics couldbe captured, providing a substantial simplification formodeling.Modeling prismatic channels with constant vegetation

characteristics permitted analysis with a periodic inlet/outletboundary condition to achieve a fully developed flow profilethrough the flow domain. With the periodic boundary condi-tion, discharge Q through the domain was adjusted until theslope computed based on the downstream pressure gradientSo,P, matches the desired channel slope [Nicholas, 2001],where

So;P ¼ 1ρgdP

dxð7Þ

and g, P, and x are gravitational acceleration, pressure, anddownstream distance, respectively. The periodic boundarycondition also permits modeling a short reach, reducingcomputational costs.

3. RESULTS

3.1. Analysis of Field Data Results

Analysis of the three field data sets indicates vegetativeeffects on shear stress magnitudes and scale dependency indimensionless shear stress values. Mean values of bankfulldimensionless shear stresses in channels

Table 1. Mean Values of Bankfull Dimensionless Shear Stress (τ*) Stratified by Bank Vegetation and Channel Sizea

Channels With Width 20 m

Thin Thick p Value Thin Thick p Valueb

Andrews [1984] 0.034 0.058 0.0003 0.038 0.030 0.310Charlton et al. [1978] 0.032 0.073 0.0040 0.038 0.047 0.397Hey and Thorne [1986]c 0.045 0.094 0.0002 0.048 0.050 0.849

aDifferences in τ* by vegetation type are significant only for channels 20 m (Figure 3).Relative submergence in channels with widths

Table 2. Comparison of τbed,avg/τo and the Portion of Shear StressConsumed by the Vegetation for Channels of Different Widthsa

Top Width(m)

Bed Shear StressFraction

Vegetation Shear StressFraction

τbed,avg/τo 1 � τbed,avg/τo6 0.37 0.6312 0.74 0.2620 0.86 0.1430 0.91 0.09

aIn this case, for consistency of comparison between computedshear stresses, τo is computed as the average shear stress over theentire boundary in an unvegetated channel according to equations(5) and (6).

158 SCALE-DEPENDENT EFFECTS OF BANK VEGETATION ON CHANNEL PROCESSES

average 60% and 105% steeper for a given combination of Qand D84 in the Hey and Thorne [1986] and Charlton et al.[1978] data sets, respectively.

3.2. Modeling Study Results

3.2.1. Scale-dependent influence of vegetation. For thefirst modeling scenario, Figure 4 depicts the resulting shearstress distributions along the bed of the channel for selectedchannel widths. For each channel width, τo is equal for thevegetated and unvegetated cases because hydraulic radiusand channel slope were held constant for each realization.For a given width, the actual shear stress on the bed of thevegetated channel (τbed,avg) is less than the shear stress on thebed of the unvegetated channel and reflects the additionalenergy attenuated by the vegetation. Thus, although τo is thesame for vegetated and unvegetated channels, shear stressdistributions on channel beds differ markedly and depend onchannel width.

Table 3. Channel Characteristics for Scenarios Simulating Establishm

1 (No Vegetatio

Distance from bed vegetation begins (m) –CDAv (m

�1) –Depth, z above the D84 grain height (m) 1ū (m s�1) 1.28umax (m s

�1) 1.80τo(Pa) 24.4τbed,avg (Pa) 25.6τbed,max (Pa) 28.5

aBottom width is 4 m; side slopes equal 1:1; So = 0.003; D84 = 50grains. Here ū and umax are the average and maximum downstream velaverage and maximum bed shear stress, respectively, computed usinboundary.

The largest channel shown in Figure 4 is 20 m wide. Thedrop in shear stress at the bank toe for the unvegetatedchannels is due to the trapezoidal channel shape. Comparingthe shear stress along the channel bed in vegetated andunvegetated channel scenarios, vegetation affects bed shearstress approximately 6 m into the channel from each bank orapproximately 60% of the total width. In the channel centerbeyond the zone of vegetation influence, shear stresses arevirtually identical, regardless of vegetation conditions. Forchannels wider than 20 m, the same pattern is observed.Simulated vegetation affects the shear stress across the entireperimeter of a 12 m channel (Figure 4), with a much smallerzone in the channel center that remains unaffected by thesimulated vegetation. Finally, in channels narrower thanabout 12 m, a considerable drop in shear stress on the bedof the channel is present under the vegetated case. The ratioof average boundary shear stress to cross-section averagedshear stress for the vegetated channels of different widths arepresented in Table 2. In this table, the average shear stressover the bed of the channel is computed using equations (5)and (6). To provide a consistent comparison between theshear stress computed using this method and the cross-section averaged shear stress, the shear stress over the entireboundary in an unvegetated channel is computed usingequations (5) and (6). If no other factors contribute to theshear stress, this can be assumed equivalent to τo. Thevegetation fraction of the total shear stress is over four timesgreater with the decrement of channel width from 20 to 6 m.

3.2.2. Vegetation reestablishment following disturbanceor restoration. For the second set of model simulationsfocusing on bank vegetation succession, channel character-istics and resulting flow depths with average velocities foreach scenario are presented in Table 3. In these scenarios,

ent of Bank Vegetationa

Scenario

n) 2 3 4 (Full Vegetation)

0.75 0.5 0.250.4 0.8 1.21.01 1.06 1.171.27 1.20 1.071.81 1.87 1.9524.5 25.6 27.825.6 25.3 23.728.7 29.9 31.4

mm; Q = 5.75 m3 s�1. Depth is measured from the top of the D84ocities for the cross-section, respectively; τbed,avg and τbed,max are theg equations (5) and (6) at the D84 grain height across the channel

Figure 5.Velocity contours (m s�1) for four increments of simulated vegetation establishment. The white line indicates theedge of the simulated vegetation.

BLEDSOE ET AL. 159

increases in width and depth were necessary to convey aconstant discharge. Figures 5 and 6 depict velocity contoursand contours of the fluid shear stress computed according toequation (8), respectively, for each of the four scenarios.These simulations indicate that as vegetation establishes onchannel banks, near-bank velocities are reduced. Lower ve-locities in near-bank regions result in an increase in the depthrequired to convey a constant flow. Accordingly, from theunvegetated scenario (scenario 1) to the scenario with fullyestablished vegetation (scenario 4), there is a 17% increase inthe flow depth and a 16% reduction in average velocity. Bank

Figure 6. Contours of fluid shear stress (Pa) for four incremindicates the edge of the simulated vegetation. Simulated vegemaximum shear stress of 123 Pa occurs in the bottom plot neamain channel flow.

vegetation concentrates flow away from the bank toe and intothe channel center. Although there is a large reduction innear-bank velocities due to the vegetation, maximum veloc-ity in the channel center increases 8% from scenarios 1 to 4.Examination of shear stresses reveals similar patterns

(Table 3 and Figure 7). Cross-section averaged shear stress,which was not held constant in these scenarios, increases14% from scenario 1 to scenario 4 due to increases in flowdepth. Average bed shear stress (τbed,avg) computed accord-ing to equations (5) and (6), however, follows an oppositetrend and decreases 7% from scenario 1 to scenario 4. The

ents of simulated vegetation establishment. The white linetation density and protrusion increase from top to bottom. Ar the water surface at the interface between porous zone and

Figure 7. Boundary shear stress profiles for four increments of simulated vegetation establishment.

160 SCALE-DEPENDENT EFFECTS OF BANK VEGETATION ON CHANNEL PROCESSES

reduction in boundary shear stress is most significant onthe channel banks, as with the velocities. The loweredshear stresses are not limited to flows within the vegeta-tion, but extend beyond the bank toe. This reduction can beattributed in part to the large amount of energy lost in andadjacent to the simulated vegetation zone, which is re-flected in the high shear stresses at the vegetation edgenear the water surface. In scenario 4, the shear stress at thepoint of greatest vegetation protrusion is 123 Pa, signifi-cantly higher than at any other point in the channel. Themagnitude of this high shear stress at the edge of thevegetation may be an artifact of modeling assumptions andlimitations to turbulence closure, as this zone typicallyexhibits highly anisotropic behavior [Nezu and Onitsuka,2001]. However, this zone of shear is consistent withvisual observations of vortex shedding in the field, andsuggests that this location could be an important sourceof energy dissipation in vegetated channels. Although thevegetation consumes a large amount of energy and reducesshear stresses in the vicinity of banks, shear stress in thechannel center actually increases 9% from scenarios 1 to 4.A trapezoidal channel was modeled in each of the scenar-

ios presented above. Channels with vertical banks were alsomodeled in sensitivity tests, yet the resulting velocity profilesvaried little from those using a trapezoidal channel with 1:1slopes when there was thick simulated vegetation on thebanks. Similar results were found in simulations involvingmilder side slopes. Alternatively, with no or minor bankvegetation, there was a more pronounced effect of bank angleon the resulting velocity profiles. With respect to hydraulics,these results suggest that as channels develop thicker bankvegetation, bank morphologic characteristics become lessimportant and are overshadowed by the characteristics of thevegetation on the bank.

4. DISCUSSION

Field data from the United Kingdom and the U.S. RockyMountain region indicate a significant scale-dependent effectof bank vegetation that has not been previously accountedfor in downstream hydraulic geometry analyses, regimeslope models, and shear stress partitioning schemes for gravelbed rivers. The small channels with thick bank vegetationexamined in this study have bankfull τ* and τ values that areroughly twofold those of their thinly vegetated counterparts.The field data and results of the CFD modeling simulationssuggest that, as opposed to the traditional focus on relativesubmergence of vegetation in the vertical dimension, thelateral dimension of channel size relative to the length scaleof vegetative roughness is a key missing parameter in under-standing shear stress behavior in small streams.Although there have been numerous physical modeling

studies [e.g., Flintham and Carling, 1988] examining theeffects of channel width-to-depth ratio on shear stress behav-ior, to our knowledge, no flume study has systematicallyexamined (1) shear stress partitioning using models withbanks rougher than the beds and (2) scale-dependent inter-actions between channel size and vegetation characteristicsand their effects on the hydraulic parameters controllingsediment transport and other fluxes in small streams. TheCFD simulation results demonstrate the utility and flexibilityof using porous media to model various combinations of bedand bank roughness. The CFD modeling approach employedin this study, as well as that of Kean and Smith [2004] basedon the work of Houjou et al. [1990], provide promisingcomputational methods for modeling differentially roughbeds and banks that warrant further investigation.Advances in our knowledge of the scale-dependent influ-

ence of bank vegetation have important implications for

BLEDSOE ET AL. 161

restoration design of streams based on “tractive force”(dimensionless shear stress criterion), regime, and analyticalapproaches [e.g., Copeland and McComas, 2001]. Forexample, Millar [2005] presented theoretical regime equa-tions for mobile gravel bed rivers with stable banks thatinclude terms representing relative bank strength as affectedby vegetation. However, in selecting a method for shearstress partitioning, Millar was forced to rely on relation-ships developed in flumes with bed roughness equaling orexceeding bank roughness in all cases [Knight, 1981; Knightet al., 1984; Flintham and Carling, 1988]. The lack of ashear stress partitioning method that accounts for the scale-dependent effects of bank vegetation introduces uncertaintyinto estimates of the sediment transport capacity and sedimentcontinuity in small, differentially rough channels designedusing these methods.In analytical approaches to stream restoration, designers

often generate a “family” of stable channel designs (Figure 8)that all theoretically convey inflowing water and sedimentloads without morphologic change. Uncertainty regardingthe coevolution of bank vegetation, hydraulics, and channelform currently confounds design in that shear stress distribu-tions, roughness, and continuity of water and sediment arechanging with time (Figure 8). A better understanding ofshear stress/vegetation interactions would increase the like-lihood of placing channels on a self-organizing trajectorythat maintains stability as vegetation reestablishes. Thiscould potentially reduce the reliance on hard structures that“lock in” channels at the desired future width and thereby

Figure 8. Schematic of theoretical stable channel design solutionsfor specified inflows of water and sediment with arrows depictinguncertainty in the trajectory and stability of a restoration design asshear stress and conveyance change with vegetation reestablish-ment along small streams. The range of possible channel widths isalso strongly dependent on streamside vegetation as depicted by therange of a, where channel width equals a(bankfull discharge)0.5.

increase the cost effectiveness of stream restoration in manyinstances.Hey [1997] argued that channel slope is not influenced by

bank vegetation, and the absence of such an influence can beinterpreted as a “problem” for extremal hypotheses such asminimum stream power and maximum sediment transportefficiency. The results of this study indicate that slope issignificantly influenced by bank vegetation in channels

162 SCALE-DEPENDENT EFFECTS OF BANK VEGETATION ON CHANNEL PROCESSES

causing expansions, contractions, eddies, and other losses asthe flow moves around and through the vegetation. Thissuggests that future studies should consider the importanceof heterogeneous vegetation. While the CFD vegetation re-presentations account for the influence of the vegetation onthe momentum equations, they do not account for flowblockage effects caused by vegetation. Particularly in thevicinity of woody vegetation, flow blockage effects wouldseem to have a dominant effect on the resulting flow fields.Future research could focus on determining appropriatemeans of accounting for these effects in CFD modeling.The scale-dependent influence of vegetation on channel

hydraulics observed in the CFD simulations appears to sup-port the field observations of Coon [1998], who identified anupper limit for the influence of bank vegetation around 20 to30 m. Similarly, the modeling conducted by Masterman andThorne [1992] suggests at width-to-depth ratios greater thanabout 15, the effects of riparian vegetation are negligible. Inour CFD simulations, the shear stress attributed to the veg-etation was 14% and 9% of the total shear stress for 20 and30 m wide channels, respectively. The Coon [1998] channelscontained rougher bed material than those used for the casestudy, so the vegetation probably had less relative influencein these channels than what is suggested by our simulations.The CFD simulations also point to physical processes that

underlie observed differences in channel form in the fieldstudies from the United Kingdom and the western UnitedStates, which found that channels with thick, woody bankvegetation were generally narrower and deeper than channelswith banks comprised of grasses and thin vegetation. Inthe simulation of vegetation succession, bank vegetationconcentrates flows in the channel center, causing an increasein flow depths for equivalent discharges. Bank vegetationreduces shear stresses in the near-bank zone and increasesshear stresses in the channel center. These effects could bemore pronounced if erosional and depositional processeswere considered. Given time and sufficient supply, aggrada-tion could occur in the low shear stress region along thebank, causing the channel to narrow. In addition, highershear stresses in the channel center could erode the bed,resulting in deeper channels. These effects would be com-bined with the increases in bank strength due to the rootstructure of the vegetation [Simon and Collison, 2002],which would provide additional resistance to erosion innarrower channels, especially in smaller channels whererooting depth is on the order of bank height. Thus, vegetationcan affect hydraulics in a manner that creates a tendencytoward cross-sections that are narrower and deeper thanunvegetated channels (but see Montgomery [1997] and An-derson et al. [2004] for disparate effects due to wood debrisand other factors).

Sediment transport capacity in complex channels likethose examined in this study is frequently computed usingcross-section average shear stress, τo [Julien, 1995]. In thesimulated vegetation succession, however, it was shown thatalthough τo increased with successively thicker simulatedvegetation due to flow depth increases, the average bed shearstress decreased. Thus, using τo to compute sediment trans-port in these channels may yield inaccurate results withoutpartitioning the shear stress between the bed and vegetation;however, the specific response is complex. The differingshear stress distributions would have nonlinear effects onsediment transport rates depending on the bed characteris-tics, and the nonuniform distribution of shear stresses couldbe further magnified in nonprismatic channels [Lisle et al.,2000; Ferguson, 2003]. Variations on the CFD modelingapproach presented here could be used to provide additionalinsights into morphologic influences on sediment transportphenomena and assist in the further development and verifi-cation of shear stress partitioning schemes.In summary, these analyses underscore a fundamental gap

in our understanding of fluvial processes and hydraulics inwadeable streams with variable bank vegetation. Most pre-vious CFD studies have modeled channels with relativelysmooth boundaries for which roughness can be representedusing a roughness height and have ignored the impact ofbank vegetation. This study demonstrated the need to ac-count for both forms of roughness in CFD modeling ofstreams less than approximately 30 m wide. Previous re-search has demonstrated the important influence of vegeta-tion on planform characteristics and meander bendhydraulics [Thorne and Furbish, 1995; Millar, 2000; Granand Paola, 2001]. CFD modeling focusing on more complexgeometries could provide additional insights on the impor-tant effects of bank vegetation on planform characteristics ofstreams. Improved and transferable quantitative tools forpredicting shear stress behavior in small streams of differentscales and bank conditions could improve the physical basisand effectiveness of stream restoration and simultaneouslyadvance understanding of the inverse problem of streamvulnerability to vegetation disturbance and removal.

5. CONCLUSIONS

The effect of bank vegetation roughness on the hydrau-lics of natural channels is scale dependent with processshifts evident at widths less than approximately 20 m. Thisfinding has important implications for improvement ofshear stress partitioning models used in stable channeldesign. Because specific mechanisms controlling the appar-ent scale dependency are difficult to isolate in naturalchannels, the method of representing vegetation in CFD

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applications combined with a porous treatment of roughbeds based on the work of Wiberg and Smith [1991] andCarney et al. [2006] presented in this study can be used tosimulate the mechanisms controlling channel form andreveal patterns and scale dependency in hydraulic para-meters consistent with field data from channels of differentscales and bank vegetation types. Although additional re-search could improve the parameterization of vegetation inthe CFD models, the use of these methods provides ameans to better understand the influence of vegetation, onmaterial fluxes, channel evolution, and geomorphic pro-cesses in wadeable streams and thereby improve the scien-tific basis of restoration designs.

Acknowledgments. We are grateful to Ellen Wohl for providinghelpful comments on a previous version of this manuscript andto Daniel Gessler who provided both astute suggestions on theCFD modeling and insightful comments on an earlier draft. Wealso thank two anonymous reviewers for constructive commentsthat improved the manuscript. This work was supported, in part,by National Science Foundation CAREER Award EAR-0548258.

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