Geoscience Reference
In-Depth Information
1
þ
1
¼
C
jx
z
0
h
z
0
h
z
0
ln
ð
3
:
94
Þ
where x is the distance from the onset of the IBL, z
0
is the maximum of the
upstream and downstream roughness, j = 0.4 is von Kármán's constant and C is a
constant which Floors et al. (
2011
) put to 2.25. Following Troen and Petersen
(
1989
), the wind profile over the IBL can be written as:
8
<
:
ln
z
z
0u
ln
c
1
h
z
0u
u
u
z
c
1
h
Þ
ln
z
u
d
þ
u
u
u
d
ð
c
2
h
ln
c
c
2
c
2
h
z
c
1
h
u
ð
z
Þ¼
ð
3
:
95
Þ
ln
z
z
0d
ln
c
2
h
z
0d
u
d
z
c
2
h
where z
0u
is the upstream roughness length, z
0d
is the downstream roughness
length, u
u
is the wind speed at the height c
1
h computed from (
3.6
) using the
upstream roughness length and friction velocity, and u
d
is the wind speed at the
height c
2
h computed from (
3.6
) using the downstream roughness length and
friction velocity. Floors et al. (
2011
) suggest c
1
= 0.35 and c
2
= 0.07, because
this gives the best fit to their data measured at Horns Rev. The various plots in
Savelyev and Taylor show that the height h of the IBL is roughly one tenth of the
distance from the step change. This infers that the height of the equilibrium layer is
roughly of the order of one hundredth of the distance from the step change. This
fits well to the usual rule of thumb which says that a measurement made at a mast
at a given height is representative for the surface properties in an upstream dis-
tance of about 100 times the measurement height. The advantage of the simple
model (
3.94
) and (
3.95
) is, that after C, c
1
, and c
2
have been specified, only u
*d
,
z
0u
, and z
0d
have to be known to describe the wind profile (Floors et al.
2011
).
3.6 Wind and Turbulence Profiles Over Forests
In recent years, forests have become an interesting site option for wind turbines
since these sites are usually away from larger settlements. Forest-covered surfaces
are a special form of vegetated surfaces. The special features of the forest
boundary layer decisively depend on the spacing of the trees. If trees grow very
close together, their crowns form a rough surface which has much in common with
an impervious rough grass land (Raupach
1979
) as depicted in Fig.
3.1
, having a
rather large displacement height [see (
3.6
)] in the order of two to three thirds of the
canopy height. The displacement height substitutes the real Earth's surface in all
profile laws for flows over forests. If the trees grow sparser, then the rough surface
at the displacement height has to be considered as pervious which is indicated by
the bold bended vertical arrow shown in Fig.
3.22
. Therefore, the main difference
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