Geomorphology 204 (2014) 314–324

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Geomorphology

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Flow characteristics in different densities of submerged flexiblevegetation from an open-channel flume study of artificial plants

Yiping Li a,b, Ying Wang a,b, Desmond Ofosu Anim b,c, Chunyan Tang b, Wei Du b, Lixiao Ni b,Zhongbo Yu d,e, Kumud Acharya f,⁎a Key Laboratory of Integrated Regulation and Resource Development on Shallow Lakes, Ministry of Education, Hohai University, Nanjing 210098, Chinab College of Environment, Hohai University, Nanjing 210098, Chinac College of Engineering, Kwame Nkrumah University of Science and Technology, Kumasi, Ghanad Department of Geoscience, University of Nevada, Las Vegas, NV 89119, USAe State Key Laboratory of Hydrology Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, Chinaf Division of Hydrologic Sciences, Desert Research Institute, Las Vegas, NV 89119, USA

⁎ Corresponding author.E-mail address: kumud.acharya@dri.edu (K. Acharya).

0169-555X/$ – see front matter © 2013 Elsevier B.V. All rhttp://dx.doi.org/10.1016/j.geomorph.2013.08.015

a b s t r a c t

a r t i c l e i n f o

Article history:Received 28 December 2012Received in revised form 11 August 2013Accepted 14 August 2013Available online 30 August 2013

Keywords:Flow velocityReynolds stressTurbulence intensityManning coefficientSubmerged artificial plantsOpen-channel flume

The effect of submerged flexible vegetation on flow structure (e.g. flow velocity, Reynolds shear stress, turbulenceintensity and Manning coefficient) was experimentally studied with a 3D Acoustic Doppler Velocimeter (ADV) inan open-channelflume. The results from flowobservations over artificial plants (designed to simulate natural veg-etation) showed that flow structure was affectedmarkedly by the presence of submerged flexible vegetation. Thestudy provides understanding of flow patterns, variation in velocity profile and turbulence structures that are af-fected by plant stem density. The study also reveals how the flow patterns return to stability at the downstreamend of the vegetated area which is critical in determining the length of the vegetated areas for restoration cases.Also, new mathematical expressions (equations) have been formulated to clearly express variations in velocityprofile, Manning coefficient and flow discharge ratio with vegetation density. Vertically, the velocity profilecould be roughly divided into three layers, including the upper non-vegetated layer, the middle canopy layer,and the lower sheath layer. In the upper non-vegetated layer, velocity profiles followed the logarithmic law, anda corresponding empirical equation was developed based on the observed data. The flow is from left to right inthis study, and the velocity profile followed a left round bracket “(”with theminimum point located at the canopyarea (0.7Hv, where Hv denotes vegetation height) within the middle canopy layer. However, the velocity profilefollowed a right round bracket “)” in the lower sheath section layer with themaximumpoint located at the sheathsection (0.2Hv). With increasing vegetation density, the velocity and corresponding flow rate increased in theupper non-vegetated layer and decreased within the middle canopy layer and the lower sheath layer. The ratioof average flow discharge in the non-vegetated and vegetated layers followed the exponential function law withincreasing vegetation density. This analysis revealed the effect of vegetation on flood potential and flow bottomscour. Reynolds stresses peaked above the canopy top (z/Hv = 1.0–1.2, here z denotes vertical coordinate), andthe turbulence intensities reached their maximum peak at two locations including the sheath section (z/Hv =0.1–0.4) and the canopy top (z/Hv = 1.0–1.6) for all vegetation densities. Manning coefficientwas highly correlat-ed to vegetation density and inflow rate with new empirical equations being proposed.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

Vegetation plays an important role in altering flow characteristics(such as flowvelocity, Reynolds stress, turbulence intensity andManningroughness coefficient) compared with non-vegetated conditions in lakesand rivers. Such variations influence the hydrodynamics of the flow field.The presence of in-channel vegetation is sometimes regarded as a prob-lem because it can reduce flow capacity, with implications for flooding.Flume experiments have demonstrated that vegetation alters flow

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structures and enhances sedimentation (Leonard and Croft, 2006).These changes substantially affect nutrient and contaminant transport,and also greatly contribute to sediment resuspension and bank erosion(Järvelä, 2002). Thus, vegetation is a key factor in sediment transport,flow connection and geomorphology in rivers and lakes (Tsujimoto,1999). Furthermore, parameters commonly used in numerical hydrody-namic simulations, such as Manning coefficient, are strongly impactedby vegetation (Noarayanan et al., 2011). Hence, investigating the impactof aquatic vegetation on flow characteristics is of substantial importancein river and lake management and restoration. Moreover, investigationssuch as these provide a foundation for further study on sediment erosionand mass transport (Wu et al., 1999).

315Y. Li et al. / Geomorphology 204 (2014) 314–324

The impact of vegetation on commonlymeasuredflowparameters isrelated to plant structure, such as the distribution of sheath, branchesand leaves (Hui and Hu, 2010). In addition, the impact of plants onflow parameters varies with the flexibility and structure of plants. Forexample, Wilson et al. (2003) mentioned that the turbulence intensityand drag force induced by rods with front foliages attached are largerand fluctuated more than that by rods without front foliages. Previousstudies have divided the velocity profile into two or three layers: theupper non-vegetated layer, and themiddle and bottom layers with veg-etation (Klopstra et al., 1997; Righetti and Armanini, 2002; Neary, 2003;Cheng, 2007; Huai et al., 2009a; Pietri et al., 2009; Chen et al., 2011).Klopstra et al. (1997) simply divided the layers into vegetation layerand surface layer. Cheng (2007) divided the layers into viscous sub-layer, overlap region andwake zone by velocity profile shape. The thick-ness and location of the three layers changed under different vegetationdensities, depths and configurations. Järvelä (2005) carried out an ex-perimental study with natural submerged flexible wheat plants andfound that the flow structure above the submerged flexible part (theupper layer) follows the log law and that the maximum velocity occursat the maximum deflected plant height. Liu et al. (2010) found that ve-locity within the canopy is nearly constant and that velocity increasessubstantially above the canopy top towards the free water surface.

Huai et al. (2009a) found that Reynolds shear stress reached thepeak value around the canopy top, and decays to a relative uniformvalue for flow depths from the peak value to the free water surface orthe bottom bed, respectively (Nepf and Vivoni, 2000; Huai et al.,2009a; Hossein et al., 2011). The maximum velocity is located at the lo-cation of zero Reynolds shear stress (Hossein et al., 2011). Cui andNeary(2008) noted that the impact of vegetation on turbulence intensity is re-lated to the submerged depth. Leonard and Croft (2006) found that thepresence of plants damps large-scale eddies, which impacts turbulencestructure within the vegetated canopy. Hossein et al. (2011) showedthat the maximum turbulence intensity is located at the inflectionpoint of the plant stem when swaying. The vertical exchange of massand momentum between the non-vegetated layer and the vegetationcanopy influencing both themean velocity and turbulence makes it dif-ficult to analyze and explain themeasured data provided by the verticalprofiles (Huai et al., 2009a). Noarayanan et al. (2011) found that vegeta-tion density, diameter, flexibility and height are all affect the Manningcoefficient. However, the flexibility of vegetation is difficult to measure(Fathi-Moghadam and Kouwen, 1997). Hence, the vegetation flexibilitywas not considered in this study; instead flow behavior was studiedover various densities of artificial plants. Although previous studieshave identified that vegetation has an important impact on flow charac-teristics, there exists little detailed analysis of the relationship between

Fig. 1. Side view of the experimental re-circula

flow structure and variation in vegetation density. This studywasmoti-vated in part by the need for a detailed understanding of how the flowpatterns in rivers and channels are impacted differently by changes invegetation density.

The objectives of this study were to investigate the impact of sub-merged artificial plants on the flow structure with different densitiesat different stream-wise positions within a channel flume. In addition,the equations for describing the flow structure in different vegetationdensities associated with the submerged height, and water depthwere determined. The profiles of flow velocity, Reynolds shear stressand turbulence intensity were also investigated and compared, andthe relationships between Manning coefficient and vegetation densityat different flow rates were studied.

2. Materials and methods

2.1. Experimental apparatus and conditions

The experimental system (Fig. 1) was composed of two pumps toforce water through the system andmaintain recirculation, an inlet sec-tion with turning valves at the upstream end to control the flow dis-charge and generates fully developed turbulent flow, a major testsection with a re-circulating open-channel rectangle flume to controlinteractions between overflow and vegetation, and an outlet sectionwith a triangular adjustable weir at the downstream end to controlthe water level. The flume was 30.0 m long, 0.5 m wide and 1.0 mhighwith glass-sidewalls and a concrete bottom so that the interactionsbetween the vegetation and flow could be observed clearly. The waterlevels were kept at approximately 0.5 m with two fixed flow rates ofQ = 0.06 and 0.025 m3/s. The corresponding mean stream-wise veloc-ities of fully developed non-vegetated flow were uo = 24 and 10 cm/s,which arewithin the generalminimum andmaximumvelocity range ofmost channels during the growing season of vegetation in eastern China(Yan et al., 2011).

A three dimensional sideways Macro-Acoustic Doppler Velocimetry(ADV) (SonTek, San Diego, CA, USA) was used to measure the instanta-neous velocity and turbulence along the vertical direction at varioussections at a frequency of 20 Hzwith a 30 s sampling time. From controlruns conducted prior to the experiment, it was revealed that this dura-tion for sampling was satisfactory for determining accurate turbulencestatistics. Thus, a total of 600 data measurements were collected ateach location. With a post-treatment software, WinADV (Wahl, 2000),the average velocity and turbulence values were processed andobtained. Measurements at 50 mm below the surface could notbe taken due to ADV limitations. For more information about the

ting open-channel rectangle flume setup.

316 Y. Li et al. / Geomorphology 204 (2014) 314–324

application of ADV on flowmeasurements in a flume, refer to Chen et al.(2011).

2.2. Vegetation materials and configurations

Flexible artificial plants were used in this experiment to mimic thereal vegetation (Fig. 2a). These plants usedwere to simulate the real spe-cies, Hydrilla verticalla. Many recent studies express the significance ofplant morphology and biomechanical properties in flow resistance asplant–flow interactions occur (Sand-Jensen, 2003; Nikora, 2010). Theseinteractions are seen at different scales and the best measurementmethods currently employed are unable to resolve accurately the degreeof resistance at these spatial scales during the physical interactions(Statzner et al., 2006). However, one of the important parameters forthe control of vegetation flow resistance is the vegetation density(Righetti and Armanini, 2002; Wang and Wang, 2007; Noarayananet al., 2011), which was considered in this study. So the plastic plantsare produced from materials of appropriate density with the requiredflexural rigidity. The plants bear a biomechanical and flow resistanceability resembling the species they simulate. Hence, its usage in these ex-ploratory simulationswas suitable. This is similar to themethods used byother authors (e.g., Nepf, 1999; Nepf and Vivoni, 2000; Wilson et al.,2003; Järvelä, 2005)who investigated scalemodels of flexible vegetationand have discovered it to be appropriate to use as generalized and sim-plified plant forms similar to the real vegetation. Table 1 shows a sum-mary of the physical properties of the submerged plant material used.Fiala (1976), Langeland (1996) and Sousa (2011) described the vegeta-tive morphology of H. verticalla. The diameters of each sheath sectionand each leaf section were 0.2 cm and 3.5 cm, respectively. Each stump

(a)

Fig. 2. (a) Image of the experimental flexible submerged vegetation which is simulated by plasdifferent vegetation heights,Wd represents frontal width of a plant clump and Hv represents vevertical distribution of the stream-wise velocity profile with the presence of submerged flexibl

was 16 cm high and each sheath section was 6 cm long. The frontalwidth of a plant clump increased with the height of the plant, with themaximum and minimum values at the canopy area (z = 6–16 cm)and the sheath section (z = 0–6 cm), respectively (Fig. 2b). Surrogateplants were fixed to a board (7 m × 0.5 m × 0.01 m) with pre-drilledholes (Fig. 3a), placed 15 m from the upstream inlet where the flowwas stable and the velocity profile was fully developed. Five densitiesof plants in an irregular grid arrangement were used: 90, 70, 50, 30and 10 stems/m2 (Fig. 3b).

2.3. Locations of flow measurements

Flow characteristicsweremeasured at seven locations, numbered po-sitions 1 to 7 in Fig. 4. Positions 1 and 7, located outside of the vegetationarea,were intended for studying the effect of rising and lowering ofwaterlevel on flow characteristics. Positions 2 and 6 were intended for investi-gating the influence of vegetation-edge, upstream and downstream ofthe vegetation area, on flow characteristics. Positions 3 and 5 were fortesting the variation of flow characteristics between vegetation-edgeand vegetation-center. Position 4 was at the center of the vegetationarea. At each position,flowcharacteristics (velocity, Reynolds shear stressand turbulence intensity) were measured at 10 points starting from bot-tom of the bed to 40 cm near the water surface. However, due to ADVlimitations and flume channel structure, the ADV sensor suspended at5 cm above the flume bed still measures the flow characteristics at thenear bed. The measurement was done at 2.5 cm increments from 5 to20 cm near the bed and then at 5 cm increments from 20 to 40 cm to-wards the free water surface.

(b)

(c)

tic material surrogate. (b) Profile of the frontal width of submerged vegetation changes atgetation height. (c) A schematic diagram of the division of the three layers to describe thee vegetation.

Table 1Summary of the physical properties of the submerged plant material.

Property Value

Plant total height 16 cmApproximate heightLeaf section 9.6 cmStem section 6.4 cm

Average diameterLeaf section 3.5 cmStem section 0.2 cm

Average widthLeaf section 6 cm

Average surface areaLeaf section 0.005 m2

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2.4. The Manning coefficient

The Manning coefficient is related to vegetation density and flowvelocity. The general equation for Manning coefficient is as follows:

n ¼ 1uR

23S

12 ð1Þ

where n is the Manning coefficient, u is the velocity of flow, R is thehydraulic radius, and S is the energy slope. However, this formula isfor non-vegetated conditions. Through a series of modifications,Noarayanan et al. (2011) modified this equation for vegetated condi-tions, using rigid tubes to mimic plants. The modified equation wasused in this work and is as follows:

n vegð Þ ¼1

u vegþwallð Þ

!� R

23 � S1

2vegþwall

� �( )− 1

u wallð Þ

!� R

23 � S1

2wall

� �( )

ð2Þ

S wallð Þ ¼H f wallð ÞBG

ð3Þ

(a) (b) (c)

Fig. 3. (a) The plastic board used to hold vegetation with pre-drilled holes. (b) The five vegetatcross with a circle represents where a plant is present, while the cross without a circle means(e) 10 stem/m2.

H f wallð Þ ¼u2u wallð Þ−u2

d wallð Þ2g

!þ hu wallð Þ−hd wallð Þ� �( )

ð4Þ

where n(veg) is the Manning coefficient only due to vegetation,uu(veg + wall) is the upstream velocitymeasuredwith vegetation, uu(wall)

is the upstreamvelocitymeasuredwithout vegetation, hu(veg + wall) is thedepth of flow upstream of the vegetation, hu(wall) is the depth of flow atthe upstream location without vegetation, ud(veg + wall) is the down-stream velocity measured with vegetation, ud(wall) is the downstreamvelocity measured without vegetation, hd(veg + wall) is the depth of flowat the downstream location with vegetation, hd(wall) is the depth of flowat the downstream location without vegetation, S(veg + wall) is the energyslopewith vegetation, S(wall) is the energy slopewithout vegetation, BG isthe length of the vegetation area and R is the hydraulic radius.

3. Results

Distributed vertical profiles of stream-wise velocity, Reynolds stress,and turbulence intensity measured at various positions for each vegeta-tion density are presented and analyzed (Figs. 5–9). Each flow parame-ter exhibits unique changes with the addition of vegetation. Thevariations are most prominent at large vegetation densities and highflow rates. The analysis of these flow parameters, profiles, and varia-tions with vegetation is discussed next.

3.1. Mean velocity profiles

The vertical distribution of stream-wise velocity could be divided intothree layers: the upper non-vegetated layer (1.0–2.5Hv), the middle can-opy layer (0.4–1.0Hv), and the lower sheath section layer (0–0.4Hv)(Fig. 5). The upper non-vegetated layer was from the canopy top(1.0Hv) to the water surface (2.5Hv), the middle canopy layer was fromthe intersection of sheath and leaf (0.4Hv) to the canopy top (1.0Hv),and the lower sheath section layer was the remaining section to the bed(0–0.4Hv). The shape of the velocity profile in each of the three layers

(a)

(b)

(d) (e)

ion configurations represented five different densities of vegetation used in the flume. Thethere is no plant. (a) 90 stem/m2; (b) 70 stem/m2; (c) 50 stem/m2; (d) 30 stem/m2; and

Fig. 4. Location of the seven measuring positions in the ADV. P1 to P7 represent position 1 to position 7, respectively.

318 Y. Li et al. / Geomorphology 204 (2014) 314–324

was dependent on the stream-wise position of the profile relative to thevegetation stand. In the upper non-vegetated layer, the velocity profilewas uniform at positions 1, 2 and 7 and logarithmic at positions 3, 5 and6. At position 4, the velocity profile in the upper layer was disordered atall vegetation densities. In most cases, within the upper non-vegetatedlayer, the maximum and minimum velocity occurred at the top and thebottom, respectively. In the middle canopy layer, the magnitude ofstream-wise velocityfluctuated frompositions 1 to 4 butwas stable at po-sitions 5 and 6. The stabilized velocity profile looked like a left roundbracket “(”with the minimum point located at the canopy area wherethe frontalwidthwas at amaximum(0.7Hv) (Fig. 2c). In the lower sheathlayer, the velocity profiles also fluctuated from positions 1 to 4 and werestable at positions 5 and 6. The velocity reached its maximum value (in-flection point) at the sheath section (0.2Hv) and then decreased graduallytowards the bottom of the flume. However, due to the previously notedexperimental limitation for the ADV, we couldn't measure the minimumvelocity close to the flume bottom. The patterns for the three-layer veloc-ity profiles remained consistent for all vegetation densities, except thelowest density (10 stems/m2) where the velocity profile was approxi-mately a straight vertical line at all positions.

For the vertical distribution of velocity magnitude in the three layers,the mean stream-wise velocity in the upper non-vegetated layer waslarger than that of the other two layers within the vegetation area. Forthe vegetation measuring positions (positions 2 to 6), the mean velocityin the middle canopy layer was smallest but exhibited the largest varia-tion. Furthermore, with increasing vegetation density, the mean velocityincreased in the upper non-vegetated layer, and decreased within themiddle canopy layer and the lower sheath layer. In addition, the above-mentioned variation with vegetation density became more evidentwhen the flow became stable (position 6). For example, when the vege-tation density was 90 stems/m2, the mean velocity was largest in theupper non-vegetated layer and smallest within the vegetation area com-pared to velocities under 10, 30, 50 and 70 stems/m2 vegetation densi-ties. However, the mean velocities in the vegetated layers under all

Fig. 5. Vertical distribution profiles of stream-wise velocity under different densities at differentrepresents themeasured stream-wise velocity, and uo represents themean stream-wise velocitilower dotted line represents z = 0.4Hv.

vegetation densitieswere smaller than the velocity (uo) under the condi-tion of no vegetation, suggesting that vegetation did play an importantrole in altering the flow structure in the flume.

The fully developed velocity in the upper non-vegetated layerfollowed a log law in the flume. The velocity profiles above vegetationcanopy of this experiment can be described by a formula given byChen et al. (2011), which expresses the stream-wise variation of theupper non-vegetated layer velocity profile distribution as:

uuo

¼ aþ b � C zhp

!ð5Þ

where u is the mean point velocity, uo is the average stream-wise veloc-ity of a fully developed flow, z is the vertical coordinate, hp is thedeflectedplant height,C z

hp

� �is a function of z/hp, which can be represent-

ed by different log equations (ln x/x, ln x/x2, ln x, x0.5 ln x, x ln x, x2 lnx, where x = z/hp), and a and b are constants. Table 2 lists a, b and

C zhp

� �in the equations of velocity profiles in the upper layer at eachmea-

suring positionwithin the vegetation area under each vegetation density.Different log equations represent different slopes of the velocity profile.The slope gradients, which varied with z/hp, were ln x/x2 N ln x/x N ln xand x2 ln x N x ln x N x0.5 ln x N ln x. The upper layer velocity gradientwas greater with larger vegetation density, while slope gradient of thelog equation was lower with larger vegetation density. Hence the logequation slope gradient decreased as vegetation density increased. Itwas confirmed that the log equation x2 ln x only occurred at smaller veg-etation densities of 30 and 10 stems/m2, which was in agreement withthe earlier mentioned observation that the velocity profile was almost astraight line with low vegetation densities, especially for 10 stems/m2.The log equation slope gradient decreased slightly from the upstreamto the downstream vegetation end for each vegetation density, whichalso confirmed that the velocity profile turned into a log law when theflow was stable. The flows with smaller vegetation densities had the

positions. Here z represents the vertical coordinate,Hv represents the vegetation height, ues of fully developed non-vegetated flow. The upper dotted line represents z = Hv, and the

Fig. 6.Vertical distributions of the three Reynolds shear stresses (−u′v′,−v′w′, and−u′w′)at position 6 under the five vegetation densities. The dotted line represents z = Hv.

319Y. Li et al. / Geomorphology 204 (2014) 314–324

largest errors with the formula (Table 2). For larger vegetation densities,the velocity profiles above the vegetation canopy fit the formula well ateach measuring position and also at the downstream vegetation area(positions 4, 5 and 6) for each vegetation density. The formula barely fitvelocity profiles at 10 stems/m2, resulting from weak vegetation drageffects at the “soft riverbed” interface for lower vegetation densities.

3.2. Reynolds shear stress

To determine the effect of different vegetation densities on theReynolds stress profile, the distribution of Reynolds stresses in thestream-wise, span-wise and vertical directions (−u′v′ , −v′w′ , and−u′w′ ) against the vertical coordinate, z/Hv, for all seven positionsand all vegetation densities was investigated (Fig. 6). Reynolds stressesfluctuatedwith distance frompositions 1 to 5 andwere relatively stableat downstream positions 6 and 7. Hence, the characteristics of Reynoldsstress at position 6 were selected for further analysis (Fig. 6). The pro-files of Reynolds stresses showed large variations around the canopytop (0.7 b z/Hv b 1.6), and became relatively uniform above 1.6Hv andbelow 0.7Hv. The inflection points where the peak values occurredwere approximately at the canopy top (z/Hv = 1.0) for −u′v′ , −v′w′

and −u′w′ . The shapes of the profiles (−u′v′ and −v′w′) were similarunder different vegetation densities, but with different magnitudes,especially for the peak values at the inflection points. The variation ofpeak values for low vegetation densities (10, 30 stems/m2) rangedfrom 0.11 to 0.99, 0.51 to 1.61, and 4.10 to 8.35 cm2/s2 for the absolutevalues of −u′v′ , −v′w′ and −u′w′ , respectively. These were relatively

Fig. 7. Vertical distribution profiles of Reynolds shear stress (−u′w′) a

small compared to the values under non-vegetated conditions. Howev-er, when vegetation density reached 90 stems/m2, the variation ofpeak values was substantially large, with values of 6.10, 4.26, and12.76 cm2/s2 for −u′v′, −v′w′ and −u′w′, respectively. These resultssuggest that the larger the vegetation density was, the more variedthe peak values for Reynolds stresses would be.

The momentum exchange region is associated with Reynoldsshear stress and highlights where the momentum exchange occurs be-tween flow and vegetation (Okamoto and Nezu, 2009; Chen et al.,2011). Momentum exchange can be determined by large coherentKelvin–Helmholtz (K–H) vortices generated by the inflection point ofthe plant stems when swaying. We determined the momentum ex-change regionwith the lower boundary assumed equivalent to the pen-etration depth (distance from the peak Reynolds stress to the canopyarea, where the Reynolds stress decreased to 10% of its peak value(Nepf and Vivoni, 2000)) and the upper boundary determined by zeroReynolds stress. To determine the range of the momentum exchangeregion, the largest vegetation density of 90 stems/m2 was chosen(Fig. 7). Since the Reynolds stress−u′w′ induced stream-wise and ver-tical momentum exchange in the vertical direction, Fig. 7 showed thatthe range of the momentum exchange region was close to zero at posi-tion 1with no vegetation.With the flowpassing through the vegetationarea, the regions for momentum exchange gradually became larger. Forexample, the upper boundary point of themomentum exchange regionmigrated slightly upward from z/Hv = 1.0 to 1.7 from positions 2 to4 within the vegetation area, and slightly decreased downward fromz/Hv = 2.0 to 1.0 from positions 6 to 7 where the flow exited the vege-tation area. However, the location of the bottom boundary point of themomentum exchange region varied little with the flow moving acrossthe length of the flume.

3.3. Turbulence intensity

To obtain the contribution of submerged vegetation to turbulenceintensity, under all five scenarios the turbulence intensity in three di-mensions (urms, vrms, wrms) at the seven positions was obtained(Fig. 8). The maximum turbulence intensity for urms, vrms, and wrms

was located above the canopy top (z/Hv = 0.7–1.3) for all vegetationdensities at each measuring position. The turbulence intensities forurms, vrms, andwrmswere unstable at the stem sectionwithin the vegeta-tion area, and decreased to a nearly constant value from above the can-opy top to thewater surface (except at position 5). Turbulence intensityincreased upstreamanddownstreamof the vegetation area (positions 1and 7) in the flume, characterized by a spike in turbulence near the bed(sheath layer, z/Hv = 0.1 and 0.4).

From positions 2 to 6, the maximum values of urms, vrms, and wrms

above the canopy topmigrated upward with vegetation density. Howev-er, the stream-wise peak point variation range of peak values (urms, vrms,

t the seven positions under a vegetation density of 90 stems/m2.

Fig. 8. Vertical distribution profiles of turbulence intensity (urms, vrms, wrms) at positions 1, 2, 4, 5, 6, and 7 under the five vegetation densities. The dotted line represents z = Hv. (a) to(f) represent the values of turbulence intensity for P1, P2, P4, P5, P6, and P7, respectively.

320 Y. Li et al. / Geomorphology 204 (2014) 314–324

wrms) was different. For example, peak urms along the vegetation areamigrated upward ranging from z/Hv = 0.7 to 1.0 for small vegetationdensities (10, 30 stems/m2), and alternatively from z/Hv = 1.0 to 1.3 forlarge vegetation densities (50, 70, 90 stems/m2). However, the peakvrms migrated upward ranging from z/Hv = 0.5 to 0.7 and z/Hv = 0.5 to

Fig. 9. Calibration of the relationship betweenManning coefficient and vegetation densityat each flow rate. The plot of Manning coefficients displayed a log law with vegetationdensity for uo = 24 cm/s, while it displayed a parabolic curve with vegetation densityfor uo = 10 cm/s.

1.3 for vegetation densities of 10 and 30 stems/m2 and 50, 70 and90 stems/m2 (except position 5), respectively. The range of peak valuefor urms was higher than vrms, and peak points increased with vegetationdensity. For wrms, the turbulence intensities were nearly constant atthe upstream of vegetation area from positions 1 to 3, gradually formedpeak points at the downstream of vegetation area from positions 4to 6 for all vegetation densities. At position 6, the peak point locatedat z/Hv = 1.3.

The variation of turbulence intensity in three dimensions (urms, vrms,wrms) with vegetation density was quite distinct at position 6, whereturbulence intensity became stable at the downstream area, similar tovelocity and Reynolds stress. There existed a demarcation point ofzero turbulence intensity above and below which the flow was dis-turbed. The peak turbulence intensities above and below the demarca-tion points increased with vegetation density. But for a vegetationdensity of 10 stems/m2, the turbulence intensities (urms, vrms, wrms)were nearly constant (close to zero) for the entire flow depth.

3.4. The Manning roughness coefficient

TheManning roughness coefficient, n, was expressed as a function offlow rate and vegetation density. The inclusion of vegetation could

Table 2Calibration results of Eq. (5) with the coefficients a and b, and function C(x) for fitting theupper layer velocity profile for the five vegetation densities and the five measuringpositions within the vegetation area. Here, x = z/hp.

Density (stems/m2) Eq.(5) Position

2 3 4 5 6

90 a 0.791 0.521 0.517 0.757 0.460b 0.857 1.462 1.311 0.748 0.679C(x) ln x/x2 ln x/x ln x/x ln x/x2 ln xR2 0.983 0.936 0.859 0.947 0.966

70 a 0.836 0.562 0.540 0.408 0.363b 0.333 2.594 1.053 3.055 1.504C(x) ln x/x2 ln x/x2 ln x/x ln x/x2 ln x/xR2 0.750 0.961 0.884 0.910 0.992

50 a 0.883 0.624 0.552 0.739 0.374b 0.198 2.366 2.232 0.237 1.436C(x) ln x/x2 ln x/x2 ln x/x2 x0.5 ln x ln x/xR2 0.400 0.987 0.812 0.872 0.959

30 a 0.873 0.945 0.604 0.712 0.640b −0.018 −0.008 0.869 0.285 0.845C(x) x2 ln x x2 ln x ln x/x ln x ln x/xR2 0.829 0.240 0.949 0.965 0.919

10 a 0.825 0.624 0.767 0.788 0.720b 0.005 1.463 0.338 0.002 0.186C(x) x2 ln x ln x/x2 ln x/x2 x2 ln x ln x/xR2 0.108 0.939 0.346 0.145 0.631

321Y. Li et al. / Geomorphology 204 (2014) 314–324

certainly increase the flow resistance irrespective of density, flexibilityor type, which in this studywas determined by calculating theManningroughness coefficient due to vegetation. By using Eqs. (2) to (4), the re-lationship between n and vegetation density for each flow rate wasobtained (Fig. 9).

For Q = 0.06 m3/s (uo = 24 cm/s), the n values increased sharplywith small vegetation densities (10 and 30 stems/m2) and increasedslightly over larger vegetation densities (50, 70, and 90 stems/m2).The plot ofManning coefficients was logarithmicwith vegetation densi-ty. For this flow rate, the range of Manning coefficients was from 0.01 to0.05. However, for Q = 0.025 m3/s (uo = 10 cm/s) the trend of nvalues was quite different. The peakManning coefficient value occurredat the vegetation density of 50 stems/m2, and the plot of Manning coef-ficient displayed a parabolic curve with vegetation density. For this flowrate, n values ranged from 0.03 to 0.07. In general, the Manning coeffi-cientwas larger at the smallerflow rates. However,when the vegetationdensity was 90 stems/m2, the Manning coefficient for Q = 0.06 m3/swas larger than that for Q = 0.025 m3/s.

The relationship betweenManning coefficient and vegetation densi-ty can be described by Eqs. (6) and (7):

uo ¼ 24 cm=s n ¼ 0:018 lnρ−0:031 R2 ¼ 0:955 ð6Þ

uo ¼ 10 cm=s n ¼ −0:00002ρx2 þ 0:001ρxþ 0:015 R2 ¼ 0:914

ð7Þ

where n is Manning coefficient, ρ is vegetation density, and uo is themean flow velocities of fully developed non-vegetated flow.

The functions of Manning coefficient and vegetation density fit thelogarithmic relationship (R2 = 0.955) with a flow rate of Q =0.06 m3/s (uo = 24 cm/s) and the parabolic curve (R2 = 0.914) witha flow rate of Q = 0.025 m3/s (uo = 10 cm/s).

4. Discussion

4.1. Mean velocity profiles

The velocity profile can be roughly divided into three layers, thestructure of which is highly related to the vegetation height andlocations of canopy and sheath (Fig. 2c). The velocity profile in the

upper non-vegetated layer followed the log law with the minimumvalues located at the bottom where the canopy top was; this profileshape was similar to the shape of a velocity profile in a river or channelwithout the presence of vegetation. Thus, the canopy top acted as anew “soft riverbed” for the flow in the upper non-vegetated layer,and the vertical movement of water through the “soft riverbed” de-creased with increasing vegetation density. For large vegetation densi-ties (e.g. N50 stems/m2), the dense leaves formed a relatively solidboundary preventing the upper flow from penetrating into the “softriverbed”. Therefore, more flowwould be forced up from the lower veg-etated layers to travel through the upper non-vegetated area, increasingthe velocity above the canopy top. However, this was not observedfor the case of 10 stems/m2 vegetation density, as the velocityprofile exhibited a relatively uniform distribution similar to the non-vegetated conditions. The minimum velocity values were located atthe bottom of the flume. The velocity profiles had minimum points inthe canopy area (0.7Hv) within themiddle canopy layer, andmaximumpoints in the sheath section (0.2Hv), suggesting that the flow structureswithin the vegetation area were quite complex, associated with vegeta-tion density, canopy frontal width and location of sheath section. Theleaves hindered the flow to a greater extent than the sheath (Fig. 5),resulting in relatively more unstable flow and higher turbulence in themiddle canopy layer compared to the lower sheath layer.

Many researchers have found that the velocity profile could be di-vided into two or three layers (Cheng, 2007; Huai et al., 2009a; Pietriet al., 2009; Chen et al., 2011). Klopstra et al. (1997) divided the velocityprofile into two parts: the vegetation part and the surface partwith sub-merged tall vegetation reeds. Huai et al. (2009a) divided the flow intofour regions: external region, upper vegetated region, transition regionand viscous region with submerged rigid vegetation. Chen et al. (2011)mentioned three layers based on the stream-wise velocity distributionprofile: the upper layer was from the inflection point (where the mini-mum velocity occurred) to the surface: the middle layer was from thelocation ofmaximumvelocitywithin the sheath section to the inflectionpoint: and the lower sheath layer was from the bed towheremaximumvelocity occurredwithin the sheath section. Our results showed that thevelocity profiles could be roughly divided into three layers based on thecurrent vegetation properties and flume apparatus. In general, differentdivisions of layers may result from different vegetation configurations,heights (short or tall) and vegetation types (rigid or flexible).

A commonly used log equation for the fully developed velocity in theupper non-vegetated layer is Prandtl's log law modified by Nikuradse(Stephan and Gutknecht, 2002):

uu�

¼ 1kln

zks

þ C ð8Þ

where u is the mean point velocity, u* is the shear velocity, k is the VonKarman constant, z is the vertical coordinate, ks is the roughness scaleand C is a constant. Järvelä (2005) mentioned that the approach ofStephan and Gutknecht (2002) appears to be a suitable method for cal-culating the upper non-vegetated layer velocity profile for submergedvegetation with a wide range of flexibility. Based on this equation, pre-vious studies (e.g. Temple, 1986; El-Hakim and Salama, 1992; Stephanand Gutknecht, 2002; Järvelä, 2005; Liu et al., 2010; Hossein et al.,2011) had obtained equations for their specified vegetation types andexperimental conditions, which are reviewed in Table 3. However, wefound that the measured data from this study barely fit the commonlyused Prandtl's log law and couldn't be extended to equations given inother previous works. Irrespective of vegetation type and flow dis-charge, all studies listed in Table 3 extended log law equations basedon Prandtl's log law with limiting factors, owing to different vegetationtypes and flow rates. A common feature of those experiments was thatthey used relatively more dense vegetation stems compared to ours.The highest vegetation density in our study is actually somewhatlower than that used in previous works included in Table 3. It was

Table 3Equations for velocity profiles above vegetation canopy, with natural or artificial material, from this and previous research with experimental conditions listed.

Author Vegetation type Density(stems/m2)

Discharge(m3/s)

Equation

Temple (1986) Bermuda grass Thickly dotted Q = 0.03–1.7 uu�

¼ 1k lnyþ C

Stephan and Gutknecht (2002) Three kinds of natural plant Thickly dotted Q = 0.13/0.23/0.3 uu�

¼ 1k ln y−yp;m

yp;mþ 8:5

Järvelä (2005) Wheat 12000 Q = 0.04/0.1/0.143 uu�

¼ 1k ln y−yp;m

yp;mþ 8:5

Hossein et al. (2011) Wheat sprout 45604 Q = 0.037/0.055 uu�

¼ 1k ln y−yp;m

yp;mþ 8:5

El-Hakim and Salama (1992) Branched plastic strip 1667 Q = 0.0313/0.0486/0.0501/0.0612 uu�

¼ 1k ln y

ypþ C

Liu et al. (2010) Acrylic dowel 6759 Q = 0.0114 uu�

¼ 1k ln z−dh

ksþ 8:5

This research Flexible plastic bundle 10, 30, 50, 70, 90 Q = 0.025/0.06 uu0

¼ aþ b×C zhp

� �

322 Y. Li et al. / Geomorphology 204 (2014) 314–324

confirmed that the velocity profiles under lower density configurationsdo not display a single logarithmic profile, which suggested that thehigher density plant stems acted as “soft riverbed” just like the channelbottom. It was confirmed that themodified log laws for velocity profilesabove the vegetation canopy were only suitable for dense vegetationstems. Hence, it was argued that the velocity profile above the vegeta-tion canopy with low vegetation densities in this work can't be easilydescribed by Prandtl's log law.

4.2. Flow turbulence

The flow turbulence (both Reynolds stress and turbulence intensity)experienced large fluctuations within the vegetation area, suggestingthat the presence of vegetation induced unevenflow. The three direction-al Reynolds stresses, which were calculated from the pulse velocity, hadpeak values at approximately the canopy top (z/Hv = 1.0) at the down-stream vegetation area.While the three directional turbulence intensitieshad peak values at the sheath section (z/Hv = 0.1–0.4) and canopy top(z/Hv = 0.7–1.3) for all vegetation densities within the vegetation area.This showed that the uneven flow mainly fluctuated above the canopytop region and around the bottom plant stems, resulting from the densevegetation leaves at the canopy top and bottom boundary at the flumebed, respectively. The turbulence characteristics were greatly influencedby vegetation density. Flows with high vegetation densities generatelarge turbulence values because the shear at theflow-vegetation interfaceincreases due to the higher flow resistance in the vegetated area (Nezuand Onitsuka, 2001). The non-isotropic fluctuation of flow induced bythe vegetation density resulted in different magnitudes of peak Reynoldsstress values with the greatest peak value occurring at the largest vegeta-tion density. The turbulence intensities of urms, vrms, and wrms reach peakvalues at canopy tops with dense leaves (e.g. Huai et al., 2009a; Stoesseret al., 2009; Wang, 2009; Hossein et al., 2011). The turbulence intensityincreasedwith vegetation density. Thiswas similar to the findings report-ed by Stoesser et al. (2009). It was also found by Nezu and Onitsuka(2001) that the degree of flow instability increases with an increase ofthe vegetation density due to large scale of plant stems.

The turbulence was induced by vortices that came from flow insta-bility. Presence of vegetation caused variation of stream-wise velocitywith faster and slower flow generating velocity mixing regions. Trailingand horseshoe vortices (longitudinal coherent vortices) were generatedwithin the velocity-mixing regions. The horseshoe vortices at the bot-tom boundary could be explained as the turbulent length scale migrat-ing downward because of wake turbulence generation at the stem scale(Nepf et al., 1997). Also the trailing vortices at the canopy top resultedfrom the higher velocity flow merging with the lower velocity flowwhich causes the flow to fold and generate instabilities (Raupachet al., 1996). The large number of continuous vortices, whichwas gener-ated by Kelvin–Helmholtz (K–H) instabilities, dominates the momen-tum exchange and has an impact on turbulence characteristics(Finnigan, 2000; Okamoto and Nezu, 2009). The K–H instabilities in-duce momentum transfer from the non-vegetated layer above the can-opy to within the vegetation (Ghisalberti and Nepf, 2005). Therefore,

momentum exchange mainly occurred at the interface of the uppernon-vegetated layer and the vegetation canopy area which is mostlythe unstable region where vegetation greatly absorbs the momentumfrom the flow and transfers parts of the flow momentum into theplant stems (Wang et al., 2009). Meanwhile, plant swaying also trans-ferred a proportion of the plant momentum into the flow. Hence,momentum exchange caused the interaction between flow and vegeta-tion which controls the vertical exchange of mass, affecting both veloc-ity and turbulence intensity (Ghisalberti and Nepf, 2005; Chen et al.,2011). This interaction was uniform when the flow became stable atthe downstream end of the vegetation area. The area between theupper and lower horizontal lines in Fig. 7 represents the upper and bot-tom boundaries of themomentum exchange region. This represents thearea where the velocity mixing layer is created as a result of merging offlows from the vegetation and non-vegetation zones. It can be seen thatthe bottom boundary seldom varied along the flume, indicating thatmomentum exchange mainly happened in the upper canopy layerirrespective of longitudinal addition of plant stems. On the other hand,variation of the upper boundary height indicated that the momentumexchange region enlarged along vegetation area. The transversal effectsgradually became negligible towards the water surface, with no furtherobstruction to the flow (Wang et al., 2009).

4.3. Effects of vegetation density on flow structures

Vegetation density greatly affected flow structures. Higher vegetationdensity resulted in larger velocity above the vegetation canopy and small-er velocity within the vegetation area. As vegetation density increased,more water would pass above the canopy since the large volume ofleaves and stemswithin the vegetation hinders flow through it. To reflectthe contribution of the submerged vegetation on the flow pattern, flowrates were calculated in two layers: the upper non-vegetated layer (Qu)and the lower vegetation layer (Qd). The relationship between vegetationdensity (ρ) and the ratio of flow rate above and within the vegetationarea was investigated (Table 4), which can be described by Eq. (9)(Fig. 10).

Qu

Qd¼ 1:331e0:011ρ; R2 ¼ 0:988 ð9Þ

whereQu andQd are theflow rates in the upper non-vegetated layer andthe lower vegetation layer, respectively, and ρ is the vegetation density.

Based on the formula Q = V ∗ A, the average velocity ratio of theupper layer and lower vegetation layer (Vu=Vd)was obtained by rewrit-ing Eq. (9) as:

Vu

Vd¼ 1:331

Ad

Aue0:011ρ; R2 ¼ 0:988 ð10Þ

where Vu and Vd are the average velocity in the upper non-vegetatedlayer and the lower vegetation layer, respectively. Au and Ad are the

Table 4Flow rates of the upper non-vegetated layer and the lower vegetation layer for a dischargeof 0.06 m3/s from positions 2 to 6 within the vegetation area.

Vegetation density(stems/m2)

Flow rate(m3/s)

Positions Average flowrate(m3/s)

2 3 4 5 6

90 Qu 0.022 0.021 0.020 0.021 0.019 0.021Qd 0.009 0.008 0.008 0.009 0.005 0.008Qu/Qd 2.392 2.574 2.472 2.413 3.930 2.638

70 Qu 0.021 0.023 0.019 0.020 0.018 0.020Qd 0.008 0.008 0.007 0.006 0.006 0.007Qu/Qd 2.779 2.981 2.616 3.255 2.872 2.890

50 Qu 0.022 0.023 0.021 0.021 0.018 0.021Qd 0.010 0.007 0.007 0.008 0.008 0.008Qu/Qd 2.255 3.123 2.844 2.716 2.270 2.618

30 Qu 0.020 0.022 0.020 0.020 0.020 0.021Qd 0.011 0.010 0.008 0.011 0.010 0.010Qu/Qd 1.782 2.168 2.340 1.799 1.938 1.985

10 Qu 0.020 0.020 0.020 0.019 0.018 0.019Qd 0.010 0.010 0.009 0.011 0.012 0.011Qu/Qd 1.980 2.026 2.140 1.667 1.509 1.840

323Y. Li et al. / Geomorphology 204 (2014) 314–324

cross-sectional area for the upper non-vegetated layer and the lowervegetation layer, respectively, and ρ is the vegetation density.

Since (Au / Ad) = 34/16 in this experiment, when the flow becomessteady, it was calculated that the average velocity in the upper non-vegetated layer and the lower vegetation layer will be the same whenvegetation density reaches 43 stems/m2. For lower vegetation densities(b43 stems/m2), Qu (or Vu) was smaller than Qd (or Vd), suggesting arelatively larger volume of flow going through the vegetation areawhich causes substantial channel bottom scour. This could greatly influ-ence the extent of sediment erosion. Alternatively, the average velocityin the lower vegetation area was smaller than that in the upper non-vegetated layer when the vegetation density was greater than the criti-cal value of 43 stems/m2, and at this point the effect of the “soft river-bed” formed by the submerged vegetation would become muchstronger. At higher densities, this would lead to a reduced scour effectof flow on the bottom, and hence decreased sediment erosion rate(Stephan andGutknecht, 2002), but this would also lead to an increasedwater level which could affect flood frequency.

For large vegetation densities, the dense leaves highlight anisotropy.Leaf surfaces have different morphologies and orientations, changingflow directions around leaves and branches and increasing flow resis-tance. Hence the Reynolds stress and turbulence intensity both increasedwith vegetation density. Vegetation can reduce the conveyance of waterthrough fluvial channels by increasing flow resistance (Wu et al., 1999).The Manning's vegetation roughness was computed for differentflow rates and vegetation densities. Our results showed that theManning's coefficient followed the logarithm law and parabolic curve

Fig. 10. Calibration of the relationship between vegetation density and flow rate ratio. Qu

means the average flow discharge in the non-vegetated layer, and Qd means the averageflow discharge in the vegetated layers.

with vegetation density at high and low flow rates, respectively. Sincemodeling of shallowflows often requires theManning's coefficient to ad-dress the influence of bed roughness/vegetation, it is essential to selectan appropriate Manning's value. In addition, it is also known that riverchannel conditions can alter significantly in the presence of vegetation,thus the corresponding Manning's coefficient may change based on thecharacteristics of vegetation and flow rate in the river, which makes itmore difficult to choose an accurate coefficient value for river modeling(Kouwen, 1992; Wu et al., 1999). Furthermore, it is inaccurate to set asingle value of the Manning's coefficient in numerical models for ariver channel having submerged vegetation with different densities(Noarayanan et al., 2011). Hence, the Manning's coefficient wasexpressed as a function of flow rate and vegetation density in thisstudy to describe the complex conditions.

5. Conclusions

This study investigated variation in flow characteristics with differ-ent densities of submerged flexible vegetation, simulated by artificialplastic material, in an open-channel flume using 3D ADV. Vertical pro-files of flow structure are affected markedly by the presence of the veg-etation, associated with the vegetation density and height. The velocityprofile could be roughly divided into three layers. The upper layer veloc-ity profile followed the log lawmentioned by Chen et al. (2011), but didnot fit the commonly used Prandtl's log law (Stephan and Gutknecht,2002). By comparing the experimental conditions for different works,we confirmed that the differences may be attributed to the vegetationdensities. With increasing vegetation density, the velocity and corre-sponding flow rate increased in the upper non-vegetated layer, and de-creased within themiddle canopy layer and the lower sheath layer. Theratio of average flow discharge in the upper non-vegetated layer (Qu)and the other two layers (Qd) with vegetation followed an exponentialfunction law based on the vegetation density. The ratio (Qu/Qd) in-creased with vegetation density, suggesting that more water couldpass through the channel from the top of submerged vegetation withthe increasing vegetation density, resulting in less scouring of the bot-tom. Hence, vegetation density was the main factor contributing toflood or bed scour in river channels.

Reynolds stress and turbulence both peaked at the canopy top. Themagnitude of Reynolds stress and turbulence increasedwith vegetationdensity. The interaction between flow and vegetation induced instabil-ity, generating vortices and impacting the momentum exchange andturbulence characteristics. TheManning's coefficient was highly relatedto vegetation density and inflow discharge, and new empirical equa-tions were proposed to describe their relationships.

NomenclatureHv undisturbed vegetation height (cm)x, y, z stream-wise, span-wise and vertical coordinates, respectivelyQ flow discharge (m3/s)uo mean stream-wise velocity of fully developed non-vegetated

flow measured at 7 m from the upstream inlet (cm/s)n Manning's coefficientR hydraulic radiusn(veg) Manning's n due to vegetation onlyuu(veg + wall) upstream velocity measured with vegetationuu(wall) upstream velocity measured without vegetationhu(veg + wall) depth of flow at the upstream location with vegetationhu(wall) depth of flow at the upstream location without vegetationud(veg + wall) downstream velocity measured with vegetationud(wall) downstream velocity measured without vegetationhd(veg + wall) depth of flow at the downstream locationwith vegetationhd(wall) depth of flow at the downstream location without vegetationS(veg + wall) energy slope with vegetationS(wall) energy slope without vegetationBG length of the vegetation area

324 Y. Li et al. / Geomorphology 204 (2014) 314–324

u, v, w mean velocity components in stream-wise, span-wise andvertical directions, respectively (cm/s)

u′, v′, w′ turbulent velocity components in stream-wise, span-wiseand vertical directions, respectively (cm/s)

−u′v′ Reynolds stress in the vertical direction (z) on a plane perpen-dicular to the stream-wise direction (cm2/s2)

−v′w′ Reynolds stress in the stream-wise direction (x) on a planeperpendicular to the span-wise direction (cm2/s2)

−u′w′ Reynolds stress in the span-wise direction (y) on a plane per-pendicular to the stream-wise direction (cm2/s2)

urms, vrms, wrms root mean squared (rms) velocity (also named turbu-lence intensity) in stream-wise, span-wise and vertical direc-tions, respectively (cm/s)

h water depth (cm)hp distance from the bed surface to the inflection point (cm)Qu, Qd flow rate of the upper layer and the vegetation layer, respec-

tively (m3/s)Au, Ad area of the upper layer and the vegetation layer, respectively

(m2)hu, hd height of the upper layer and the vegetation layer, respectively

(m)Vu, Vd average velocity of the upper layer and the vegetation layer,

respectively (m/s)ρ vegetation density (stems/m2)Wd frontal width of a plant clump (cm)

Acknowledgments

The research was supported by the Chinese National Science Foun-dation (51379061, 51009049, 51109061, 51179053); Qing Lan Project,Excellent Innovation Talents in Hohai University and grant numbers2010CB951101, 40911130507, and BE2010672.

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