Geoscience Reference
In-Depth Information
Fig. 4.6 Vertical wind profiles over the ridge shown in Fig.
4.2
for L = 1,000 m, H = 200 m,
z
0
= 0.2 m and u
*?
= 0.25 m/s at x/L =-2, -0.5, 0 (crest line), 0.5 and 2. Full line from
Eq.
4.15
, dashed line for horizontally flat terrain
l
z
P
0
ð
z
Þ¼
1
þ
ln
exp
z
z
0
l
ð
4
:
16
Þ
l
z
0
ln
and:
0
@
1
A
0
@
1
A
2
z
z
0
z
z
0
ln
ln
P
d
ð
z
Þ¼
exp
2
ð
4
:
17
Þ
l
z
0
l
z
0
ln
ln
Figure
4.6
shows sample results from (
4.15
) using (
4.9b
) for a ridge with half-
width L = 1,000 m and aspect ratio H/L = 0.2. x/L =-2 is upstream of the ridge
closely before the minimum of the shape function r (see Fig.
4.2
). x/L =-0.5 and
0.5 are at the positions where the shape function r has its largest gradients.
x/L = 0 is on the crest of the ridge and x/L = 2 has been chosen symmetrically to
the first point. We see the largest speed-up over the crest itself at the top of the
inner layer at the height of the length l which was at roughly 16.5 m above ground
in this example (see Fig.
4.3
). The vertical wind shear is enhanced below this
height l compared to the undisturbed logarithmic profile (dashed line) and the
shear is reduced above this height. The two frames to the right show the influence
of the wake. This influence leads to a reduced wind speed near the height l,
although this analytical model is not able to produce flow separation which should
set in for aspect ratios larger than about 0.2.
In the outer layer, the solution is still symmetrical to the hill crest, but in the
inner layer a considerable asymmetry becomes visible. In this respect, solution
(
4.15
) is more realistic than the pure potential flow solution in
Sect 4.2.1
. Nev-
ertheless it has to be noted that the analytical model (
4.15
) can only be used for
shallow hills with aspect ratios smaller than 0.2 and a cross-wind elongation which
is much larger than the width of the ridge cross-section parallel to the wind
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