Geoscience Reference
In-Depth Information
flows with and without floodplain vegetation, the friction slope due to inter-
facial shear and eddy viscosity are evaluated by using the flow structure
simulated from the three-dimensional (3D) numerical model developed by
Kang.
2
Finally, the impact on the backwater computations is discussed.
2. 1D Mathematical Model
Yen
et al.
3
proposed backwater equations for compound open-channel flows,
which take into account the flow exchange between main channel and flood-
plain as well as the shear force between them. For steady and gradually var-
ied flows in compound open-channel, the respective backwater equation for
the main channel (subscript
m
) and the vegetated floodplain (subscript
f
)
can be written as
S
fm
−
L,R
S
sm
+
L,R
S
em
1
S
0
−
d
H
m
d
x
=
,
(1)
−
Fr
2
m
d
H
f
d
x
S
0
−
(
S
ff
−
S
sf
−
S
ef
+
S
v
)
=
,
(2)
1
−
Fr
f
where
x
is the longitudinal distance,
H
the flow depth,
Fr
the Froude
number,
S
0
the bottom slope,
S
f
the friction slope,
S
s
the friction slope
due to interfacial shear,
S
e
the friction slope due to flow exchange, and
S
v
is
the friction slope due to vegetation. The friction slope due to vegetation in
the floodplain is expressed as
1
2
βc
D
aF r
f
h
p
,
S
v
=
(3)
where
β
is the momentum correction factor,
c
D
the volume averaged drag
coecient of cylinder,
h
p
the vegetation height, and
a
is the vegetation
density of unit [L
−
1
]. Detailed procedures to obtain
S
f
,
S
s
,and
S
e
are
found in Ref. 3.
3. Impact of Floodplain Vegetation
We applied the 3D model by Kang
2
to Tominaga and Nezu's
4
experiment.
The flow depths in the main channel and floodplain are 0.08 and 0.04 m,
respectively. The width of the main channel (
B
m
) is 0.2 m, which is the
same as that of the floodplain (
B
f
). The discharge,
Q
=0
.
0088 m
3
/s,
S
0
=
0
.
00064, and the resulting Reynolds number is 54,500.
