Geoscience Reference
In-Depth Information
Fig. 3.5 Three normalised neutral wind profiles extrapolated from the 50 m wind speed for
increasingly smooth terrain (from left to right). Full lines: logarithmic profiles from (
3.6
)
(uppermost number gives z/z
0
), dashed lines: power profiles from (
3.22
) (number at bottom line
gives the exponent a). The middle curve has been shifted to the right by 0.5 and the right curve
has been shifted to the right by 1.0 for better visibility
when a tends to zero. Thus, for neutral stratification, a power law with a slope and
curvature that fits the logarithmic profile over a larger height range can never be
constructed. Such a fit would be possible only if the power law exponent were not
constant but varied with height according to (
3.28
).
The use of (
3.27
) for calculating the exponent a of a power wind profile that is
an approximation to the logarithmic wind profile is better the larger z/z
0
is, i.e. the
smoother the surface is. For complex terrain on the other hand, the power law with
an exponent a given by (
3.27
) is not a good approximation to the true wind profile.
This is demonstrated in Fig.
3.5
where we present wind profiles computed from
(
3.6
) and (
3.22
) for three different height-to-roughness ratios z/z
0
. The height
where the profiles should be identical is chosen to be 50 m and the wind profiles
have been normalized to the wind speed in this height. The wind speed difference
between the logarithmic profile and the power law profile at 100 m height is 1.3 %
for z/z
0
= 50 [power law exponent a = 0.2556 from (
3.27
)] and 0.3 % for
z/z
0
= 5,000 (a = 0.1174). The relative difference between the two profiles at
10 m height is 11.2 and 2.0 % respectively.
Usually—except for very strong winds—the atmosphere is not stratified
neutrally. For non-neutral stratification the slope of the logarithmic profile (
3.16
)is
determined by:
W
1
u
ð
z
Þ
z
o
u
oz
¼
ln
z
z
0
z
L
1
x
z
L
\0
for
ð
3
:
29
Þ
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