9THEME C: Compound Channels-1

MIXING STRUCTURE AND F LOW EVOLUTIONRESULTING FROM VARIATION IN THE DENSITYOF RIPARIAN VEGETATION ALONG THE BANKS
OF A MAIN CHANNEL IN A COMPOUND CHANNEL
1

Watanabe A. and Fukuoka S. 2
Associate Professor, Department of Civil and Environmental Engineering
2 Professor, Department of Civil and Environmental Engineering, Hiroshima University,
1-4-1 Kagamiyama, Higashi-Hiroshima City, 739-8527, Japan,
Telephone 081-824-24-7821, fax number 0824-24-7821
1

Abstract: This research elucidated the process of change in mixing mechanisms associatedwith change in vegetation density, as well as the process of change directly upstream anddownstream from the vegetation, and considered flow field transition distance. It was foundthat immediately downstream from the vegetation, the abrupt inflow of the floodchannel flow
into the main channel resulted in extensive horizontal mixing that exceeded the mixing between
flows inside and outside of the vegetation. Another important characteristic was that thevigorous mixing immediately downstream from the vegetation is diffused by large-scale
horizontal eddies. As with cases of density that is greater downstream, the process of mixing
development is one in which the development of large-scale eddies changes the main channel
layer’s velocity distribution, resulting in vertical mixing.
Keywords: Riparian vegetation, compound channel, Reynolds stress, large horizontal eddy,transition distance

1. INTRODUCTION
The vegetation that often grows along the banks of the main channel of a compoundwatercourse presents the issue of flood-flow resistance that lowers the river’s transport capacity
during flooding. Flood control and environmental management therefore necessitate a fullunderstanding of the flow properties of compound waterways where riparian vegetation grows.1)
For compound watercourses having riparian vegetation, Fukuoka and Fujita, et al., 2) havedeveloped a quasi-two-dimensional analysis method that utilizes a boundary mixing coefficientand that has been used in actual flood control planning in Japan. Nadaoka and Yagi, 3) as well as
Fukuoka and Watanabe et al., 4) have published researches on horizontal two-dimensional
analysis; Fukuoka et al. have reproduced the large-scale horizontal eddies and horizontal flow
field resulting from vegetation in actual flooding in the Tone River.

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XXX IAHR Congress

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Although vegetation normally varies longitudinally in density and growth pattern, resulting in athree-dimensional flow structure, the evolution of three-dimensional flow fields accompanying
vegetation has not been studied adequately. This research investigates, for cases of abruptchanges in vegetation density in the downstream direction, the three-dimensional structure of theflow field, its process of change, and the downstream distance required for the mean flow todevelop.

2. EXPERIMENTAL PROCEDURES AND CONDITIONS
The cross-section and planform of the experimental waterway are shown in Figures 1 and 2,
respectively. This single-sided compound straight waterway was 28 m long and 0.8 m wide, witha main channel width of 0.5 m, a floodchannel width of 0.3 m, and a floodchannel height of
0.057 m. The simulated vegetation was 0.035 m wide and was placed in a continuous strip along
the main channel’s bank.
Vegetation

x0=0.0mxc=12.2m

w
5.7cm

Flood
channel
30.5cmu
3.5cm

xFlood channel

Vegetation I

v

Flow

Vegetation II
Main channel

46cm

yFig.1 Cross-section of the experimental channel

Fig.2 Plan view of the experimental channel

Table 1 Experimental condition

Case

Vegetation I

Vegetation II

Exp. DExp. NExp. ND
Exp. SD
Exp. DS
Exp. DN1
Exp. DN2
Exp. DN3

dense
no vegetation
no vegetationdense
sparsedense
sparsedense
dense
no vegetation
dense
no vegetation
dense
no vegetation

Discharge

Bed
slope

23 ("/s)

1/550
28 ("/s)
30 ("/s)

D: Dense, S: Sparse, N: Nothing

To determine the effect of longitudinal changes in vegetation density, each experimental case(see Table 1) tested a different combination of vegetation conditions in the upstream anddownstream sections of our experimental channel—dense (D) simulated vegetation, sparse (S)vegetation, or no (N) vegetation. The transition from one vegetation condition to anotherTHEME C: Compound Channels-1

11

occurred at the section where xc = 12.2 m. Velocity through the vegetation can be expressed withthe permeability coefficient K, which is defined as  = KIe1/2, where  is velocity inside thevegetation and Ie is the energy gradient. K is 1.74 m/s for the sparse vegetation and 0.45 m/s forthe dense vegetation.
Under uniform flow conditions, a depth of 6.5–9.9 cm was maintained throughout the entire
watercourse so as not to completely submerge the simulated vegetation.
A Laser Doppler Velocimeter (LDV) with a 100-Hz sampling frequency and an I-type
electromagnetic velocimeter with a 20-Hz sampling frequency were used to measure velocity.

3. RESULTS OF EXPERIMENT
3.1. Evolution of the Three-Dimensional Structures of Mean Flow and Turbulence
Downstream from Abrupt Change in Vegetation
3.1.1. Longitudinal Change in Flow Structure in Experiment ND
Figures 3 (a), (b), and (c) respectively show mean velocity distribution ( u ) and Reynolds stress
distributions ( u' v ' , u' w' ). Because flow field properties in a compound flow differ above andbelow the floodchannel bottom, the authors divided the channel into upper and lower layers andcalculated the vertical mean for each. Because of flow field changes, the velocity distributionchanges from one characterized by an inflection point roughly at the main channel–floodchannelboundary to one characterized by velocity reduction caused by the vegetation. At the section 1.4
m from the transition point, velocity had slowed primarily in the upper layer of the main channel,
but by the point 2.2 m downstream, both the upper–lower layer differential and the longitudinalvariation in velocity had diminished, indicating a nearly stable flow. Reynolds stress distribution( u'v' ) is such that in sections upstream from the vegetation, a stress value was registered only inthe upper layer. This is because of the mixing between the main channel and floodchannel flows
in the upper layer. At points farther downstream, Reynolds stress ( u'v' ) in the neighborhood ofvegetation increases in both the upper and lower layers, then changes to a negative value in thefloodchannel. This is interpreted as follows: The flow around the vegetation is significantly
slowed in the upper and lower layers by the strong resistance arising from the vegetation, so thatmixing around the vegetation occurs uniformly in the vertical direction. Furthermore, mixing in
the upper layer comprises not just mixing between flows inside and outside of the vegetation but
also mixing between the main channel and floodchannel flows through the vegetation, which is
why the value of u'v' is larger than that for the lower layer.
The value of u' w' around the vegetation is small at the transition point but increases at points
farther and farther downstream. This is due to the vertical difference in velocity that arises

XXX IAHR Congress

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Lower layer

Upper layer-0.2

AUTh, Thessaloniki, Greece(a) Mean velocity distribution

Lower layer

Upper layer

Distance from the transition point (m)
0.6
1.4
2.2
3.0

Distance from the transition point (m)
3.8

-0.2

0.6

1.4

2.2

3.0

3.8

(cm/sec)u(cm/sec)(a) Mean velocity distribution

2

u

2

(cm /sec )(b) Reynolds stress distribution

22(b) Reynolds stress distribution

 u cv c22(cm /sec )(c) Reynolds stress distribution

2(cm /sec ) u cv c

2(cm /sec ) u cwc(c) Reynolds stress distribution

 u cwc

-1.0

1.0

0

0

10

10

20

20

30

30

40

40

50

50

60

60

70

70

80

80
-1.5

-1.0

-0.5

0

0.5

Distance from the transition point (m)

1.0

1.5

10(cm/sec)

-1.5

-0.5

0

0.5

Distance from the transition point (m)(d) Velocity vector distribution(d) Velocity vector distribution
50(cm/sec)

Fig.3 Experiment ND

Fig.4 Experiment DN

1.510(cm/sec)
50(cm/sec)

THEME C: Compound Channels-1

13

from the development of large-scale horizontal eddies. In the transition to a vegetation-affected
flow, the mechanism of flow mixing changes extensively because of the abrupt onset of the effectof resistance at the upstream end of the vegetation. In addition, the main channel flow isaccelerated when it strikes the upstream front of the vegetation and flow direction is bent. Largescale horizontal eddies form and grow larger as the flow travels downstream, resulting in a flow
characterized predominantly by horizontal mixing in the upper layer. The resultant upper–lower
layer velocity differential in the main channel produces vertical mixing.

3.1.2. Longitudinal Change in Flow Structure in Experiment DN
Figures 4 (a), (b), and (c) respectively show mean velocity distribution ( u ) and Reynolds stress
distributions ( u'v' , u' w' ) for experiment DN. Here, at the transition from dense vegetation toan absence of vegetation, the velocity distribution changes from one characterized bydeceleration at the main channel–floodchannel boundary to one characterized by acceleration of
the floodchannel flow by the main channel flow. That u'v' is significantly greater than u' w'
indicates the predominance of transverse mixing, and its high value also suggests vigorous
mixing between the main channel and floodchannel flows in the upper layer.
As seen in Figures 4 (b) and (c), Reynolds stress downstream from the vegetation (both u'v'
and u' w' ) exceeds that in the range of the vegetation. As Figure 4 (d) shows, this is due to thevigorous mixing that occurs when floodchannel flows that had been slowed by the vegetation
abruptly enter into the main channel, and when very slow flows inside the vegetation exit thevegetation into the downstream waters. As the water travels downstream, the effect of thisvigorous mixing is diffused transversely in the form of convection from the floodchannel andlarge-scale horizontal eddies. The structure of this mixing is evident in the longitudinal change inu'v ' . Horizontal mixing at the boundary decreases farther downstream, and mixing gradually
gives way to a structure characteristic of compound flows in a waterway lacking vegetation.

3.2. Downstream Distance Required for Flow Field Development
This section considers the downstream distance required for development of the mean flow field.
Distance L from the flow field transition point to where mixing reaches equilibrium can bethought of as the flow field transformation distance. The change in mean flow field in thisexperiment is clearly apparent in the Reynolds stress distribution ( u' v ' ); the change in u' v 'associated with this transformation is particularly great at the floodchannel–main channelboundary and the vegetation boundary. Therefore, development of the mean velocity field isdetermined as longitudinal change in the Reynolds number Re’, which is calculated using a
representative velocity defined as the square root of u' v ' acting on the upper layer at theboundary, and a representative length defined as the transverse width B over which u' v ' occurs

AUTh, Thessaloniki, Greece

XXX IAHR Congress14

in the upper layer of the main channel. This value of Re’ is referred to in this paper as theboundary Reynolds number.
Figure 5 (a) shows the longitudinal change in Re’ for experiments DS, DN1, DN2, and DN3;
Figure 5 (b), that for experiments SD and ND. The values of L (i.e., distance required for flow
field development) were LSD = 1.4 m, LND = 2.2 m, LDN1 = 4.4 m, LDN2 = 5.2 m, and LDN3 = 5.8m (LDS was not calculated because of the inability to determine a clear transition section). The
results show that in cases of abrupt change in the flow field (as in DN and ND), the downstream
distance required to reach equilibrium is longer. A comparison of LND and LDN1 shows that
despite the considerable change in both flow fields, the transformation distance was longer in thelatter case because of the considerable effects of mixing at the end of the vegetation. A
comparison of LDN1, LDN2, and LDN3 reveals a relationship whereby transformation distanceincreases with discharge. This is because under these experimental conditions, an increase indischarge intensifies mixing at the end of the vegetation, requiring a greater distance to diffuse its
effects.
LND

6
5
4
3
2
1
0

LSD

DN1
DN2
DN3
DS

Re’ number x10-4

Re’ number x10

-4

LDN3
LDN2

LDN1

3
2
1

SD
ND

0
-2

-1

3
2
4
5
6
0
1
Distance from the transition point (m)

7

8

-2

-1

3
2
4
5
6
7
1
0
Distance from the transition point (m)(a) Experiment DS, DN1, DN2, DN3(b) Experiment SD, ND

Fig.5 Longitudinal change in boundary Reynolds number Re c

3.3. Deriving an Equation for Transition Distance

Distance L from the end of the vegetation to where mixing achieves equilibrium is considered

the transition distance. An equation of motion for the transition section in the x- direction isderived thus:

wu wu wu
wt wx wy

gi 

w 2u
1
Fu 2  H 2
2h
wy

(1)
1

where u: main velocity, h: depth, F: friction loss coefficient ( Feddy viscosity.

2 gn 2 / h 3 ), H: coefficient of8

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THEME C: Compound Channels-1

In equation (1), the hydraulic quantities for each point can be divided into equilibrium quantities
and deviation thusu f ( y )  u~ ( x, y ) , h( x)u ( x, y )~hf  h , H ( x) ef  H~

Separating equation of motions—one for the equilibrium flow field and another for the deviationfrom equilibrium, and giving following approximations

w 2 u~| 0,
wy 2

uf !! ũ ,(hf  h ) | hf

thereby simplifying the equation of motion for the transition to derive the following equation:

uf 

wu
wx



F
w 2 u~
u f  u~  2H f 2
hf
wy

(2)

Upon nondimensionalizing x and y in equation (2) with transition distance L and width of mixing
in the equilibrium range 'Y§x· § y ·X ¨ ¸ Y¨¸
© L ¹ © 'Y ¹uand realizing X, X’, Y, Y’ and Y” to be determined solely with respect x and y,
the following proportional relationships are valid.

Hf
('Y)

2

D

H
u F  ufF  uf uf
D f 2 , fD,
L
L ('Y)
hf
hf

From this, the following relational equation is derived:
L D

hf
F

(3)

Transition distance L is proportional to (depth)/(friction loss coefficient), and proportionality
constant D is a coefficient that is determined by the nondimensional quantities represented by
H(x), 'Y, and equilibrium velocity uf, which depend on large-scale horizontal eddies and thevegetation permeability coefficient. Because of the pronounced effect of flow field transition in
the main channel, the main channel friction loss coefficient Fm and mean depth hm at equilibrium
were substituted into equation (3), andTable-2 Numerical values of Eq (3)proportionality constant D was determined
D
Case
hm
Fm
L
so as to agree with measured transition
Exp ND
8.4
0.0050220
0.130
distance L as determined from the
Exp SD
8.43
0.0050140
0.083
Exp DN1
6.97
0.0052440
0.328
longitudinal change in boundary Re number
Exp DN2
8.01
0.0050520
0.324(Re’). Under these experimental conditions,Exp DN3
8.61
0.0049580
0.330
the values shown in Table 2 were obtained

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XXX IAHR Congress

AUTh, Thessaloniki, Greece

for D. In all three DN cases, a value of 0.33 was obtained for D, indicating that under these
conditions (i.e., a relative depth of 0.18–0.33), transition distance is proportional to(depth)/(friction loss coefficient) downstream at equilibrium.

4. CONCLUSIONSThis research elucidated the process of change in mixing mechanisms associated with change in
vegetation density, as well as the process of change directly upstream and downstream from thevegetation, and considered flow field transition distance. It was found that immediately
downstream from the vegetation, the abrupt inflow of the floodchannel flow into the main
channel resulted in extensive horizontal mixing that exceeded the mixing between flows insideand outside of the vegetation. Another important characteristic was that the vigorous mixing
immediately downstream from the vegetation is diffused by large-scale horizontal eddies. As
with cases of density that is greater downstream, the process of mixing development is one inwhich the development of large-scale eddies changes the main channel layer’s velocity
distribution, resulting in vertical mixing.
Thus flows are three-dimensionally complex, with strong nonlinearity, at the points where
vegetation permeability changes longitudinally and in the flow field transition areas that occur atthe upstream and downstream ends of the vegetation. Consequently, numerical analysis methods
are an effective means of predicting hydraulic phenomena in a channel having various types ofvegetation growth. The next step is to develop a highly accurate three-dimensional analysis
model capable of predicting the resistance properties and transition distance of a channel having
varying vegetation permeability an d hydraulic conditions.

REFERENCES[1]

Fukuoka, S., Watanabe, A and Tsumori, T.: Structure of Plane Shear Flow in River with
Vegetations, Journal of Hydraulic, Coastal and Environmental Engineering, No.491/II-27,
pp.41-51, 1994.
[2] Fukuoka, S., Fujita, K and Niida, H.: Prediction in Flood Water Level of River Courses
with Vegetation, Japan Society of Civil Engineers, Hydraulic and Sanitary Engineering,
No.447/II-19, pp.17-24, 1992.
[3] Nadaoka, K and Yagi H.: Horizontal Large-eddy Computation of River Flow withTransverse Shear by SDS & 2DH Model, Journal of Hydraulic, Coastal and Environmental
Engineering, No.473/II-24, pp.35-44, 1993.
[4] Fukuoka, S., Watanabe, A., Uesaka, T and Tsumori T.: Structure of Flood Flow in the Tone
River with Vegetation Clusters Along Low-water Channel Bank, Journal of
Hydraulic, Coastal and Environmental Engineering, No.509/II-30, pp.79-88, 1995.