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Short grass
Tall crop
4
4
3
3
Figure 19.6 Observed
profiles of average wind speed
over short grass and tall crops
demonstrating that the
position of zero wind speed
as deduced from
measurements above the crop
is elevated by the zero plane
displacement.
2
2
1
1
d
0
0
0
1
2
3
0
1
2
3
Wind speed (m s 1 )
Wind speed (m s 1 )
while, on the basis of mixing length theory, the general expression for eddy
diffusion coefficients applicable in neutral conditions in the surface layer of the
ABL is:
(19.24)
KKKkuz d
===
(
)
*
M
V
H
The friction velocity u * may be substituted into Equation (19.24) from Equation
(19.21) to give:
zd
KKKk uz d z
(
)
(19.25)
2
1
===
(
)ln
M
V
H
0
or substituted from Equation (19.23) to give:
u
KKKk z d z
=== −
(19.26)
2
(
)
2
M
V
H
Thus, in conclusion, in neutral conditions in the surface layer, substituting the
value of eddy diffusivity from Equation (19.26) can be used in Equations (19.4),
(19.5), and (19.6) to give the required first order local turbulent closure equations:
u
uuwkuz d z
(19.27)
2
−τ
= −
=
¢¢
= −
(
)
*
*
k
q
(19.28)
v
H
=
q¢ ¢
w
= −
ku z
(
d
)
*
k
v
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