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φ
m
φ
m
k = 0.35
k = 0.40
7
1.4
1.6
1.4
1.2
6
1.0
0.8
0.8
0.6
5
0.6
0.4
0.4
ζ
k = 0.40
0.2
0.2
4
-0.10
-0.05
0.05
0.10
-0.10
-0.05
0
0.05
0.10
ζ
k = 0.35
3
φ
m
= (1 - 15
ζ
)
-1/4
2
φ
4
m
- 9
ζ
φ
3
m
=1
φ
m
= 1 + 4.7
ζ
1
-2.5
-2.0
-1.5
-1.0
-0.5
0
ζ
0.5
1.0
1.5
2.0
Figure 3.14
Example of a similarity relationship as obtained from an experiment.
Here
φ
m
as found in the Kansas 1968 experiment is given (vertical axis), as a function
of
ζ
(or
z/L
). (From Businger et al.,
1971
). Note that the functions given in the graph
are slightly different than those used here (see
Section 3.5.3
). (© American Meteoro-
logical Society. Reprinted with permission.)
in
Section 3.3.5
. Indeed, if we approximate the wind shear
∂
∂
u
z
by
u
κ
, the Richardson
number appears to be equivalent to
z/L
(see also
Section 3.5.6
). Thus, the same limit-
ing cases hold for
z/L
as for
Ri
f
(see
Figure 3.15
):
*
z
•
Positive values of
Ri
f
and
z/L
indicate stable conditions (suppression of turbulence by
buoyancy).
Negative values of
•
Ri
f
and
z/L
indicate unstable conditions (enhancement of turbulence
by buoyancy).
•
Ri
f
or
z/L
equal to zero indicate neutral conditions in which buoyancy does not play a role.
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