Geoscience Reference
In-Depth Information
For flexible vegetation, such as trees and bushes, the foliage, whether broad or
needle-like, is the major contributor to the total drag. For example, in Jarvela's (2002)
experiments on willows, the drag coefficient for leafy willows was three to seven times
that of the leafless willows, depending primarily on flow velocity. Considering this
fact, Jarvela (2004) suggested the use of the leaf area index (
i
la
) in determining the
friction factor. The leaf area index is conventionally defined as the ratio of the upper-
side projected area of the leaves in canopy to the area of the surface under the canopy,
i.e., the one-sided area of foliage per unit bed area. The developed relation of the
friction factor for partially submerged vegetation is
i
la
U
U
χ
m
χ
h
h
v
λ
=
4
C
d
χ
(10.31)
where
C
d
χ
is a species-specific drag coefficient,
U
χ
is a reference velocity, and
m
χ
is
an exponent. The coefficients in Eq. (10.31) for several species are listed in Table 10.2.
Table 10.2
Coefficients in Eq. (10.31) for various vegetation species (Jarvela, 2004)
U
χ
(m
·
s
−
1
)
Species
C
d
χ
m
χ
i
la
Data source
Cedar
0.56
−
0.55
0.1
1.42
Fathi-Maghadam (1996)
Spruce
0.57
−
0.39
0.1
1.31
Fathi-Maghadam (1996)
White pine
0.69
−
0.50
0.1
1.14
Fathi-Maghadam (1996)
Austrian pine
0.45
−
0.38
0.1
1.61
Fathi-Maghadam (1996)
Willow
0.43
−
0.57
0.1
3.2
Jarvela (2002)
Eqs. (10.29) and (10.31) are valid for situations where the trees just cover the channel
bed in plan view. In nature, trees may cover only a part of the bed, or the leaves of
adjoining trees may overlap. As pointed out by Raupach
et al
. (1980) and confirmed
by Fathi-Maghadam (1996), the pattern or distribution of the trees does not have a
significant effect on the friction factor, but the vegetation density is always a dominant
parameter. Kouwen and Fathi-Maghadam (2000) suggested the following correction
method to consider the effect of vegetation density:
A
tv
A
t
λ
=
λ
(10.32)
m
where
is the friction factor estimated using
Eq. (10.29) or (10.31),
A
tv
is the total top-view area of the channel covered by trees,
and
A
t
is the total top-view area of the channel.
Freeman
et al
. (2000) conducted experiments on the resistance due to shrubs and
woody vegetation in a large 2.44 m-wide flume and a small 0.46 m-wide flume. A total
of 20 different species of broadleaf deciduous vegetation commonly found in flood-
plains and riparian zones were evaluated. It was observed that the plant leaf mass
trailed downstream forming a streamlined, almost teardrop-shaped profile. The leaf
shape changed with velocity and became more streamlined with increasing veloc-
ity, yielding a significant decrease in the drag coefficient and resistance coefficient
with velocity. On the other hand, the resistance increased with depth for partially
λ
m
is the corrected friction factor,
λ
