Geoscience Reference
In-Depth Information
Height above
ground
Inertial sublayer
Constant flux layer
Crop height,
h
Roughness sublayer
Zero plane
displacement,
d
Figure 22.6
Location of the
roughness sublayer within the
constant flux layer above a stand
of vegetation.
transfer. The layer over which such modification occurs is referred to as the
'
roughness sublayer
,' see Fig. 22.6.
A realistic description of turbulent transport in the roughness sublayer requires
higher order closure representation, but in K Theory the approach adopted is to
treat the effect of the nearby surface on turbulence by re-defining the similarity
relations near the surface such that Equation (20.2), (20.5) and (20.8) respectively
become:
kzdu zd zd
u
(
−∂
)
−
−
⎛
⎞
⎛
⎞
(22.10)
=
f
j
⎜
⎟
⎜
⎟
M
∂
z
⎝
L
⎠
⎝
z
*
⎠
*
kz d
(
−
)
z d z d
−
−
⎛
⎞
⎛
⎞
∂
q
(22.11)
v
=
f
j
⎜
⎟
⎜
⎟
H
z
⎝
L
⎠
⎝
z
⎠
q
∂
*
*
kz d
(
−
)
∂
q
z d z d
−
−
⎛
⎞
⎛
⎞
(22.12)
=
f
j
⎜
⎟
⎜
⎟
V
q
∂
z
⎝
L
⎠
⎝
z
*
⎠
*
On the basis of observations over tall crops and trees, it has been suggested that
over a height range
z
<
z
*
the empirical correction function
j
has the form:
⎡
⎤
⎛
⎞
⎛
⎞
zd
−
−
≈− −
zd
(22.13)
j
exp
0.7 1
⎢
⎥
⎜
⎟
⎜
⎟
z
z
⎝
⎠
⎝
⎠
⎢
⎥
⎣
⎦
*
*
where
z
*
is an empirical height range. It is assumed that
j
=
1 above
z
=
z
*
, although
this gives an unrealistic discontinuity in
at this level. The value of (
z
*
/
z
0
) is very
poorly defined but has an order of magnitude of 50.
The net effect of the factor
j
is to enhance the eddy diffusivities for turbulent
transfer near the surface and, in this way, reduce the overall aerodynamic resistance
j
