laboratory experiments for 3d characteristics of depth-limited open-channel...

Laboratory Experiments for 3D Characteristics of

Depth-Limited Open-Channel Flows with Submerged Vegetation

Sung-Uk Choi1, Wonjun Yang

2, and Jaekook Shin

3

1Professsor, Primary author, School of Civil and Environmental Engineering,

Yonsei University, 134 Seodaemun-gu, Shinchon-dong, Seoul, Korea; Tel.: +82-2-

2123-2797; Fax.:+82-364-5300; email: [email protected] 2Post Doctoral Research Fellow, School of Civil and Environmental Engineering,

Yonsei University; email: [email protected] 3M.S. Student, School of Civil and Environmental Engineering, Yonsei University

; email: [email protected]

ABSTRACT

This paper presents laboratory experiments for 3d characteristics of depth-limited

open-channel flows with submerged vegetation. Both flexible and rigid stem are

used in the experiments. Laser Doppler anemometer is used to sample the

velocities. Streamwise mean velocity is provided, showing the flow concentration

in the sidewall region. This occurs because the counter-clockwise rotating vortex

moves high-momentum fluids from the center towards the sidewall. The estimated

pattern of the secondary currents supports this phenomenon. The turbulence

statistics are also given and the impact of the secondary currents is discussed.

Keywords: open-channel flow, submerged vegetation, 3D characteristics, secondary currents

INTRODUCTION

Due to increasing awareness of vegetation in hydraulic engineering, the mean

flow and turbulent structures of the flow with vegetation have been unveiled

significantly. In the laboratory experiments, researchers used either rigid stems

(Lopez and Garcia, 1998; Ghisalberti and Nepf, 2002; Huai et al., 2009) or

flexible stems (Ikeda and Kanazawa, 1996; Tsujimoto et al., 1996; Nepf and

Vivoni, 2000; Jarvela, 2002; Armanini et al., 2005). They sometimes use mimic

plants with foliage in the experiments (Shi et al., 1996; Wilson et al., 2003;

Velasco et al., 2003). However, most of previous attempts were restricted to the

two-dimensional case, i.e., for a wide channel case.

Recently, Kang and Choi (2007) reported the flow concentration in the

sidewall region using the numerical simulations (see Figure 1). The phenomenon

of the flow concentration in the vegetated flow has never been observed in neither

in the laboratory experiments nor through numerical simulations. This motivated

the present study.

The purpose of the present study is to investigate the three-dimensional

characteristics of the depth-limited open-channel flow with submerged vegetation.

For this, laboratory experiments were carried out and velocity data were collected

using laser Doppler Anemometer (LDA). Three-dimensional data sets of the mean

33rd IAHR Congress: Water Engineering for a Sustainable Environment

Copyright c© 2009 by International Association of Hydraulic Engineering & Research (IAHR)

ISBN: 978-94-90365-01-1


flow and turbulence statistics are provided. The impact of secondary currents is

also investigated and discussed.

LABORATORY EXPERIMENTS

Laboratory experiments were carried out in a 0.45 m wide and 8.0 m long

recirculating open-channel facility. Model vegetation, 0.035 m high, was planted

at the bottom in a staggered manner at a density of 2.78 m-1

, forming a 6.0 m long

vegetated zone from the downstream end. Both flexible and rigid stems were

employed. Flexible model vegetation is made with polyethylene film (0.002 m �

0.0002 m) whose modulus of elasticity is 4.0�10-6

N�m, and rigid model

vegetation is made with wooden dowels (0.002 m diameter). Streamwise and

vertical velocity components (u, w) were measured by Laser Doppler

Anemometer (LDA). The measuring points are shown in Figure 2, indicating that

more points were taken along the vertical lines close to the sidewall. This feature

of LDA measurement is discussed in Wang and Chen (2005).

Flow conditions employed in the experiments are given in Table 1.

Starting letters “F” and “R” in the title of the experimental case denote the use of

flexible and rigid stems, respectively. For flexible stems, two discharges with two

flow depths were generated. The channel slope is varied to render desirable flow

conditions. For flexible stems, since the degree of bending depends on the flow

condition, the depth ratio (H/h1) is changed within the range between 2.73 and

3.55. According to Raupach et al. (1996), who proposed that the flow with a depth

ratio exceeding 5 - 10 is a terrestrial canopy flow. This ensures that the flows

generated in the present study are depth-limited flows with submerged vegetation.

In experiments, bent heights of each individual stem are different, and change

with time. Thus, the height of the vegetation layer, denoted by h1, is the vegetation

height for the rigid stems and the height averaged over the canopy and the time

for the flexible stems. In order to measure h1 for flexible stems, ten different stems

were selected arbitrarily, and the maximum and the minimum heights were

measured for about 1 min. The shear velocity u* at the interface near h1 is

estimated from the Reynolds shear stress distribution (= [max.(-uw)]0.5

). The

Froude numbers (Fr = U/(gH)0.5

) and the Reynolds numbers (Re = UH/�) of the

generated flows ranged between 0.15 - 0.41 and 15,700 - 26,300, respectively,

indicating that the flows are subcritical and turbulent. For rigid stems, two

experiments were carried out with different discharges.

EXPERIMENTAL RESULTS

Streamwise mean velocity

The distribution of the streamwise mean velocity is given in Figure 3. It can be

seen that a velocity maximum occurs near the sidewall, i.e., near y/B = 0.05, as

well as near the center. This occurs for both flexible and rigid stems. This is a

unique feature of the flow with submerged vegetation which is distinguished from

the flow without vegetation. Thus, a purpose of the present study is to explore

what causes the flow concentration to the sidewall.

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Secondary currents

To obtain the pattern of the secondary currents, the lateral component of the mean

velocity (V) is estimated using the continuity relationship. This is because the

LDA used in the experiment is a two-dimensional device that only samples U and

W. This procedure, as reported by Wang and Cheng (2005), may overestimate the

lateral component of the velocity due to small magnitudes of V and W compared

with U.

Figure 4 shows the resulting secondary current vectors, clearly depicting a

vortex rotating in the counter-clockwise direction in the vicinity of the sidewall.

This vortex is originated from the bottom vortex near the corner, which grows

significantly as the vegetation density increases (Kang, 2004). In the central

region, velocity vectors laterally flowing towards the sidewall are observed. This

is thought to be errors amplified due to the coarse grid in the measurements.

From previous studies, for example, Naot and Rodi (1982), Demuren and

Rodi (1984), Nezu and Nakagawa (1984), it is known that the secondary currents

locate the velocity maximum below the free surface in open-channel flows, which

is called the velocity dip. This is achieved by the secondary currents which

transport low momentum fluids at the upper corner near the sidewall to the center

of the channel near the free surface. A similar phenomenon also occurs in the

present vegetate flow. That is, the secondary currents transport high momentum

fluids at the channel center near the free surface to the sidewall region. This is the

mechanism how another velocity maximum occurs near the sidewall. The impact

of the downflows seen in Figure 3 is that the isovels are bulged towards the

bottom since the secondary currents move the high-momentum fluids downwards.

The impact of the upflows is also noticed in the same figure, i.e., the isovels are

bulged towards the free surface at about y/B = 0.16. Therein, the secondary

currents move the low-momentum fluids upward. The phenomenon described so

far appears to be responsible for the three-dimensional flow observed near the

sidewall and will affect the turbulence structures as well.

Reynolds shear stress

Figure 5 presents the vertical distribution of the Reynolds shear stress at various

lateral locations. The solid line in the figure denotes a linear profile, connecting

zero at the free surface and the value of �u*2 at h1 in the upper region. In general,

the Reynolds shear stress increases from zero at the bottom, showing the

maximum near h1, and decreases towards the free surface. In the central part of

the cross section, i.e., y/B > 0.22, the Reynolds shear stress follows well the linear

profile, showing the maximum slightly above h1. However, near the sidewall, i.e.,

y/B < 0.16, where the secondary currents are present, the Reynolds shear stress

does not show a linear profile. Specifically, at y/B = 0.02, the Reynolds shear

stress shows smaller values than the linear profile, forming a concave curve. This

is due to the downflows near the sidewall which transport high momentum fluids

downwards, making the larger velocity gradient. Near the free surface, at y/B =

0.02, the Reynolds shear stress shows a negative value, which is a direct effect of

the velocity dip. In contrast, in the upflows region, i.e., y/B = 0.16, the Reynolds

shear stress is larger than the linear profile, forming a convex curve, with uplifting

of the maximum Reynolds shear stress. This is a direct effect of the upflows. That

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is, the low momentum fluids in the vegetation layer are transported upward by the

secondary currents, reducing the velocity gradient. The deformations of the

Reynolds shear stress in the upflow and downflow regions are consistent with

those described for the flow over ridges and troughs in Nezu and Nakagawa

(1993). For rigid stems, similar phenomenon is clearly observed, showing the

maximum at h1 and linearly decreasing towards the free surface and the bottom.

However, compared with the previous figures for flexible stems, the measured

data are less scattered, showing an excellent agreement with the linear profile.

This seems to be caused by the swaying motions of the flexible stems that are

irregular with time and space. The three profiles at y/B = 0.02, 0.09, and 0.16

show the distribution in the region close to the sidewall. At y/B = 0.02, the

downflows clearly affect the Reynolds shear stress, which is consistent with cases

for flexible stems. However, in the upflow region, i.e., at y/B = 0.16, the

deformation of the Reynolds shear stress is not clearly seen.

Turbulent intensity

Figure 6 shows the vertical distribution of turbulent intensity at various lateral

locations. Both streamwise and vertical components are presented. The lines in

the figure denote the regressed formulas for the turbulent intensities under wide-

channel condition given in Yang and Choi (2009). It can be seen that both

components of the turbulent intensity increases from the free surface, showing the

maximum near h1, then decreases towards the bottom. It can be seen that the

secondary currents affect the x-turbulence intensity, but rarely do the z-turbulence

intensity. Regarding, the x-turbulent intensity, it is noteworthy that the measured

data are in good agreement with the proposed relationships in the region away

from the sidewall, namely for y/B � 0.22. The extent of the region without the

sidewall effect is consistent with that for the Reynolds shear stress. However, in

the region close to the sidewall, the impact of the secondary currents on the x-

turbulent intensity is noticed. That is, the profile at y/B = 0.16 appears to be lifted

upward by the upflows. Similarly, the profile at y/B = 0.02 seems to be pushed

downward by the secondary currents although their impact on the z-component

turbulent intensity is not so clear. For rigid stems, the impact of secondary

currents on the turbulent intensity is similar to that for flexible stems. That is, the

deformation of the x-turbulent intensity profile in the downflow region is clearly

observed, however, their impact in the downflow region appears to be weak. This

is consistent with the Reynolds shear stress profiles described in previous section.

CONCLUSIONS

This paper presents laboratory experiments to investigate 3d characteristics of

depth-limited open-channel flows with submerged vegetation. Flume experiments

were performed with both flexible and rigid stems and velocity data were

collected by LDA measurements.

In the distribution of the streamwise velocity, the flow concentration is

observed in the vicinity of the sidewall. Thus, a velocity maximum occurs near

the sidewall as well as near the center. This is due to the counter-clockwise

rotating secondary currents originated from the bottom vortex. The impact of

secondary currents is noticed in the profiles of Reynolds shear stress and turbulent

465


intensity. That is, the secondary currents make the Reynolds shear stress or

turbulent intensity profiles deviated from the 2d profiles, i.e., concave and convex

in the downflow and upflow regions, respectively.

ACKNOWLEDGEMENTSThis research was supported by a grant (06B01) from the Technical Innovation of Construction Program funded by Ministry of Land, Transport, and Maritime Affairs of Korea government.

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in Fully Vegetated Open-Channel Flows.” Journal of KSCE, 39(B), 237-

245(in Korean).

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vegetation: suspended sediment transport modeling.” Water Resources

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conduit.” Journal of Hydraulic Engineering, ASCE, 110(1), 173-193.

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467


Table 1. Experimental conditions

Case Q

(m3/s) H

(m) H/h1

(-)

S

(-)

u*

(m/s)

FH2Q1 0.0075 0.075 2.73 0.00151 0.0265

FH2Q2 0.0105 0.075 3.00 0.00266 0.0361

FH3Q1 0.0075 0.110 3.24 0.00070 0.0229

FH3Q2 0.0105 0.110 3.55 0.00079 0.0247

RH2Q1 0.0075 0.075 2.14 0.00141 0.0235

RH2Q2 0.0105 0.075 2.14 0.00269 0.0325

(a) Streamwise mean velocity contour (b) Secondary flow pattern

Figure 1. Simulation results form Kang and Choi (2007)

0.0 0.1 0.2 0.3 0.4 0.5

y/B

0.0

0.2

0.4

0.6

0.8

1.0

z/h

Channel center at y/B = 0.50

Figure 2. Measuring points

y/B

z/H

0.0 0.1 0.2 0.3 0.4 0.50.0

0.5

1.0U (m/s): 0.00 0.15 0.31

y/B

z/H

0.0 0.1 0.2 0.3 0.4 0.50.0

0.5

1.0U (m/s): 0.00 0.18 0.36

(a) For Case FH2Q1 (b) For Case FH2Q2

Figure 3. Contour map of streamwise mean velocity

468


y/B

z/H

0.0 0.1 0.2 0.3 0.4 0.50.0

0.5

1.0U (m/s): 0.00 0.10 0.20

y/B

z/H

0.0 0.1 0.2 0.3 0.4 0.50.0

0.5

1.0U (m/s): 0.00 0.13 0.26

(c) For Case FH3Q1 (d) For Case FH3Q2

y/B

z/H

0.0 0.1 0.2 0.3 0.4 0.50.0

0.5

1.0U (m/s): 0.00 0.13 0.26

y/B

z/H

0.0 0.1 0.2 0.3 0.4 0.50.0

0.5

1.0U (m/s): 0.00 0.22 0.44

(e) For Case RH2Q1 (f) For Case RH2Q2

Figure 3. (Continued)

y/B

z/H

0.0 0.1 0.2 0.3 0.4 0.50.0

0.2

0.4

0.6

0.8

1.00.01 m/s

y/B

z/H

0.0 0.1 0.2 0.3 0.4 0.50.0

0.2

0.4

0.6

0.8

1.00.01 m/s


y/B

z/H

0.0 0.1 0.2 0.3 0.4 0.50.0

0.2

0.4

0.6

0.8

1.00.01 m/s

y/B

z/H

0.0 0.1 0.2 0.3 0.4 0.50.0

0.2

0.4

0.6

0.8

1.00.01 m/s


y/B

z/H

0.0 0.1 0.2 0.3 0.4 0.50.0

0.2

0.4

0.6

0.8

1.00.01 m/s

y/B

z/H

0.0 0.1 0.2 0.3 0.4 0.50.0

0.2

0.4

0.6

0.8

1.00.01 m/s


Figure 4. Secondary currents for open-channel flows

469


0 0.001

-uw (m2/s2)

0.0

1.0

2.0

3.0

z/h

1

0 0.001 0 0.001 0 0.001 0.002

0 0.001

-uw (m2/s2)

0.0

1.0

2.0

3.0

z/h

1

0 0.001 0 0.001 0 0.001 0.002

y/B = 0.02 y/B = 0.09 y/B = 0.16 y/B = 0.22

y/B = 0.29 y/B = 0.36 y/B = 0.42 y/B = 0.49

0 0.001

-uw (m2/s2)

0.0

1.0

2.0

3.0

z/h

1

0 0.001 0 0.001 0 0.001 0.002

0 0.001

-uw (m2/s2)

0.0

1.0

2.0

3.0

z/h

1

0 0.001 0 0.001 0 0.001 0.002

y/B = 0.02 y/B = 0.09 y/B = 0.16 y/B = 0.22

y/B = 0.29 y/B = 0.36 y/B = 0.42 y/B = 0.49


-0.0005 0 0.0005

-uw (m2/s2)

0.0

1.0

2.0

3.0

4.0

z/h

1

0 0.0005 0 0.0005 0 0.0005 0.001

0 0.0005

-uw (m2/s2)

0.0

1.0

2.0

3.0

4.0

z/h

1

0 0.0005 0 0.0005 0 0.0005 0.001

y/B = 0.02 y/B = 0.09 y/B = 0.16 y/B = 0.22

y/B = 0.29 y/B = 0.36 y/B = 0.42 y/B = 0.49

-0.0005 0 0.0005

-uw (m2/s2)

0.0

1.0

2.0

3.0

4.0

z/h

1

0 0.0005 0 0.0005 0 0.0005 0.001

0 0.0005

-uw (m2/s2)

0.0

1.0

2.0

3.0

4.0

z/h

1

0 0.0005 0 0.0005 0 0.0005 0.001

y/B = 0.02 y/B = 0.09 y/B = 0.16 y/B = 0.22

y/B = 0.29 y/B = 0.36 y/B = 0.42 y/B = 0.49


0 0.001

-uw (m2/s2)

0.0

1.0

2.0

3.0

z/h

1

0 0.001 0 0.001 0 0.001 0.002

0 0.001

-uw (m2/s2)

0.0

1.0

2.0

3.0

z/h

1

0 0.001 0 0.001 0 0.001 0.002

y/B = 0.02 y/B = 0.09 y/B = 0.16 y/B = 0.22

y/B = 0.29 y/B = 0.36 y/B = 0.42 y/B = 0.49

0 0.001

-uw (m2/s2)

0.0

1.0

2.0

3.0

z/h

1

0 0.001 0 0.001 0 0.001 0.002

0 0.001

-uw (m2/s2)

0.0

1.0

2.0

3.0

z/h

1

0 0.001 0 0.001 0 0.001 0.002

y/B = 0.02 y/B = 0.09 y/B = 0.16 y/B = 0.22

y/B = 0.29 y/B = 0.36 y/B = 0.42 y/B = 0.49


Figure 5. Vertical distribution of Reynolds shear stress

470


0 0.05

u', w' (m/s)

0.0

1.0

2.0

3.0

z/h

1

u' (m/s)

w' (m/s)

0 0.05 0 0.05 0 0.05 0.1

0 0.05

u', w' (m/s)

0.0

1.0

2.0

3.0

z/h

1

0 0.05 0 0.05 0 0.05 0.1

y/B = 0.02 y/B = 0.09 y/B = 0.16 y/B = 0.22

y/B = 0.29 y/B = 0.36 y/B = 0.42 y/B = 0.49

0 0.05

u', w' (m/s)

0.0

1.0

2.0

3.0

z/h

1

u' (m/s)

w' (m/s)

0 0.05 0 0.05 0 0.05 0.1

0 0.05

u', w' (m/s)

0.0

1.0

2.0

3.0

z/h

1

0 0.05 0 0.05 0 0.05 0.1

y/B = 0.02 y/B = 0.09 y/B = 0.16 y/B = 0.22

y/B = 0.29 y/B = 0.36 y/B = 0.42 y/B = 0.49


0 0.05

u', w' (m/s)

0.0

1.0

2.0

3.0

4.0

z/h

1

u' (m/s)

w' (m/s)

0 0.05 0 0.05 0 0.05 0.1

0 0.05

u', w' (m/s)

0.0

1.0

2.0

3.0

4.0

z/h

1

0 0.05 0 0.05 0 0.05 0.1

y/B = 0.02 y/B = 0.09 y/B = 0.16 y/B = 0.22

y/B = 0.29 y/B = 0.36 y/B = 0.42 y/B = 0.49

0 0.05

u', w' (m/s)

0.0

1.0

2.0

3.0

4.0

z/h

1

u' (m/s)

w' (m/s)

0 0.05 0 0.05 0 0.05 0.1

0 0.05

u', w' (m/s)

0.0

1.0

2.0

3.0

4.0

z/h

1

0 0.05 0 0.05 0 0.05 0.1

y/B = 0.02 y/B = 0.09 y/B = 0.16 y/B = 0.22

y/B = 0.29 y/B = 0.36 y/B = 0.42 y/B = 0.49


0 0.05

u', w' (m/s)

0.0

1.0

2.0

3.0

z/h

1

u' (m/s)

w' (m/s)

0 0.05 0 0.05 0 0.05 0.1

0 0.05

u', w' (m/s)

0.0

1.0

2.0

3.0

z/h

1

0 0.05 0 0.05 0 0.05 0.1

y/B = 0.02 y/B = 0.09 y/B = 0.16 y/B = 0.22

y/B = 0.29 y/B = 0.36 y/B = 0.42 y/B = 0.49

0 0.05

u', w' (m/s)

0.0

1.0

2.0

3.0

z/h

1

u' (m/s)

w' (m/s)

0 0.05 0 0.05 0 0.05 0.1

0 0.05

u', w' (m/s)

0.0

1.0

2.0

3.0

z/h

1

0 0.05 0 0.05 0 0.05 0.1

y/B = 0.02 y/B = 0.09 y/B = 0.16 y/B = 0.22

y/B = 0.29 y/B = 0.36 y/B = 0.42 y/B = 0.49

(a) For Case RH2Q1 (b) For Case RH2Q2

Figure 6. Vertical distribution of turbulent intensity

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