Geoscience Reference
In-Depth Information
Roughness of flexible vegetation
According to Kouwen and Li (1980), the resistance to flow by flexible vegetation in
channels can be determined using a relative roughness approach similar to the widely
accepted resistance relationships developed for rigid roughness in pipes and channels.
Because flexible vegetation bends when subjected to shear, its roughness height is
a function of vegetation properties and flow parameters. The significant vegetation
properties are the stem density
M
and the flexural rigidity in bending, given by
J
EI
.
Here,
E
is the stem's modulus of elasticity and
I
is the second moment of inertia of the
stem area. The stem density
M
is defined as the ratio of the stem count to a reference
number of stems per unit area. The reference number is arbitrary, but for convenience
it is taken to be 1 stem per square meter, thus yielding
M
=
=
N
a
. Note that
M
is
dimensionless.
Based on laboratory experiments on flow over flexible plastic strips, Kouwen and
Li (1980) showed that the roughness height
k
s
would vary as a function of the amount
of drag exerted by the flow and the parameter
MEI
:
0.14
h
v
1.59
0.25
(
MEI
/τ
b
)
k
s
=
(10.25)
h
v
m
2
. Tsujimoto and Kitamura
(1998) conducted numerical analysis using a hydrodynamic model coupled with a can-
tilever beam model describing bending of vegetation, and obtained a similar formula
for the flexible vegetation height under the shear of flow.
Kouwen and Li (1980) suggested the use of the semi-logarithmic resistance equation
to determine the Darcy-Weisbach friction factor
m
−
2
, and
MEI
is in N
τ
b
is in N
·
·
where
h
v
is in meters,
λ
:
b
log
R
k
s
1
√
λ
=
a
+
(10.26)
where
R
is the hydraulic radius of the channel; and
a
and
b
are two fitted parameters,
depending on the relative magnitude of the shear velocity
U
and a critical value
U
crit
.
∗
∗
In a numerical model test, Darby (1999) used the form of Hey's (1979) equation:
2.03 log
a
s
R
k
s
1
√
λ
=
(10.27)
)
−
0.314
,
where
a
s
is a dimensionless shape correction factor, given by
a
s
=
11.1
(
R
/
h
max
with
h
max
being the maximum flow depth in the cross-section.
The key aspect of successful application of Eq. (10.25) appears to lie in the measure-
ment of
MEI
. This parameter can be measured directly for different species using the
“board drop” test. In this test, a standard wooden board is dropped onto a vegetated
surface to impart a frictional force that deflects the stems in a manner similar to flow-
ing water. The distance between the ground and the bottom edge of the fallen board,
which reflects the ability of the vegetation to resist bending under flow conditions,
