Geoscience Reference
In-Depth Information
boundary-layer resistance to momentum exchange by the form drag exchange
mechanism per unit area of leaf, is given by:
⎛
⎞
1
bb
(21.5)
R
≈ ⎜
⎟
⎜
⎟
M
cU
⎝
⎠
f
Note that Equation (21.5) has been written to give the resistance per unit area of
leaf assuming the leaf has two sides. If the canopy air stream velocity is 1 m s
-1
and
c
f
= 0.2,
R
M
bb
is 5 s m
-1
, which is about an order of magnitude less than the
boundary-layer resistance would be if momentum were transferred solely by
skin friction.
In the case of momentum transfer, it is convenient to combine the effect of skin
friction and bluff body transfer processes in a single drag coefficient,
c
d
, which,
given the form of Equations (21.3) and (21.5), should have the approximate form:
c
≈+
c U
−
0.5
(21.6)
d
f
where
n
is a constant.
R
M
, the corresponding boundary-layer resistance per unit
area of leaf for momentum transfer
by both skin friction and bluff body transfer
, is
then given by:
⎛
1
⎞
R
≈
⎜
(21.7)
⎟
M
cU
⎝
⎠
d
On the basis of the above discussion, it is clear that the drag coefficient,
c
d
, will
be a strong function of the orientation of the leaf with respect to the wind, a
result that has been demonstrated for model leaves in wind tunnels, see Fig. 21.2,
for example.
The boundary-layer resistance for exchanges other than momentum is deter-
mined by molecular diffusion through a boundary layer. Taking sensible heat, for
example, if the 'effective' boundary-layer thickness through which heat has to diffuse
from a leaf to the canopy air stream is
d
, the boundary-layer resistance per unit area
of leaf for sensible heat,
R
H
, is given by:
d
R
=
(21.8)
H
D
H
where
D
H
is the molecular diffusivity for heat. However, because
d
is not a
measureable quantity, it is preferable to estimate boundary-layer resistance based
on a measureable characteristic dimension,
d
, of the vegetation instead. For this
reason, the boundary-layer resistance for sensible heat is more conveniently
parameterized in terms of the '
Nusselt number'
(
Nu
), defined to be the ratio of a
characteristic dimension of vegetative element,
d
, to the
effective
boundary-layer
thickness,
d
, see Fig. 21.3. In terms of the Nusselt number, the boundary-layer
