Agriculture Reference
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second-order closure models are developed and then applied to the problem. Recently, several
papers have been published focusing on the closure problem, particularly within forest
canopies [26-28]. However, because the traditional K-theory approach can be applied
successfully within tall grass canopies [21], we shall stay with it.
A number of assumptions are offered about the variation of
K
s
within tall grass canopies
[29,30]. Among those, we chose the approach where
K
s
is proportional to wind speed,
u
, i.e.,
K
s
=
σ
u
,
(17)
where the scaling length,
σ
, is an arbitrary, unknown
constant. Combining Eqs. (11) and (17)
produces an equation for the wind speed inside the canopy
(
)
2
2
2
d
u
2
C
L
H
−
h
d
d
=
u
.
(18)
2
σ
H
dz
A particular solution of this equation can be found in a form that approximates the wind
profile within the tall grass canopy fairly well [31]:
⎡
⎤
1
⎛
z
⎞
u
(
z
)
=
u
(
H
)
exp
−
β
1
−
(19)
⎝
⎠
⎣
⎦
2
H
where
u
(
H
) is the wind speed at the canopy height and
β
is the extinction parameter, defined
as
(
)
2
L
H
−
h
H
2
d
d
β
=
,
(20)
σ
where
σ
still remains an unknown constant. Its value can be determined as a function of the
morphological and aerodynamic characteristics of the underlying tall grass canopy in the
following manner. We shall use the lower boundary condition at the canopy bottom
z = h
in
terms of the shear stress,
τ
, just above and below the indicated level. Therefore,
2
τ =
ρ
u
,
(21)
dg
h
h
where
C
dg
is the leaf drag coefficient estimated from the size of the roughness elements of the
ground [21], i.e.,
2
k
C
=
,
(22)
dg
2
⎡
⎤
h
ln
⎢
⎣
⎥
⎦
z
⎢
⎥
g
where
k
is the von Karman constant, taken to be 0.41, and
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