14
Stable
φm = 1 + 7 ζ
12
10
φm 8
=1+5ζ
6
4
= (1 + 4.5 ζ)3/4
2
= 1 + 0.7 ζ + 0.75 ζ (6 0.35 ζ) exp (0.35 ζ)
0
0
0.5
1.0
1.5
2.0
ζ = z/L
Figure 5. Various suggestions for the functional form
of the nondimensional wind speed (φm) and scalar (φh)
gradients for stable conditions.
decrease monotonically. This means, according to eq
is, the profiles are basically semi-logarithmic as in eq
78, that the vertical gradients of wind speed, tempera-
72, 75 and 77, but each has an additional additive term
that depends on ζ. φm and φh would, thus, have the form
ture and humidity get weaker as the instability
increases. The vertical exchange that the increasing
φm (ζ) = φh (ζ) = 1 + γ sζ.
buoyancy fosters homogenizes the profiles.
(80)
In contrast to the situation for unstable stratification,
The constant γs is generally reported to be in the range
for an ASL that is stably stratified there are a host of
suggestions as to the forms of φm and φh. Figure 5 shows
from 5 (Webb 1970, Dyer 1974, Large and Pond 1981)
some of these functions.
to 7 (Wieringa 1980, Large and Pond 1982, Hgstrm
Often the wind speed and scalar profiles are assumed
1988).
to be log-linear in stable conditions (Webb 1970). That
From wind speed and temperature profiles at the South
12
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