Civil Engineering Reference
In-Depth Information
wind stress in
x
-direction has the strongest disturbance in the
y
-direction, and so he
defined the wind stress in two forms. The first is an assumption of a wind stress that
is homogenous in the
x
-direction (Eq.
4.1
), and the second is a more realistic one
(Eq.
4.2
) with a two-dimensional wind pattern (Brostr
¨
m
2008
). This leads to the
following formulation of wind stress:
2
ðÞ
2
y
L
τ
x
¼ τ
x
0
Δ
τ
x
e
ð
4
1
Þ
:
x
L
2
ð
2
y
Þ
ðÞ
1
x
L
τ
x
¼ τ
x
0
Δ
τ
x
e
max e
,0
ð
4
:
2
Þ
0
8
Lþ
0
2
x
:
:
with
τ
x
0
:
¼
windstress outside the influence of wind farm
Δ
τ
x
:
¼
change in the wind stress induced by wind farm
L
:
¼
characteristic size of wind farm
The advantage of this description is a cushy application. Here, a wind stress field
with a mean wind stress of 0.012 N/m
2
, which is based on reference wind speed of
METRAS wind field simulation without wind farm operation and geostrophic wind
speed of ug
¼
8 m/s, is supposed. Investigation area is based on simulation TOS-01
of 240
6 km in the middle of
this area. The changes of such wind stress field due to a wind farm are shown in
Fig.
4.1
for two different wind directions, westerly and southwesterly. A westerly
flow is even used by Brostr
¨
m, while here a southwesterly wind direction is added
due to its frequent incidence in the German part of the North Sea (Loewe
2009
). The
reduction of wind stress by wind farm impact after Brostr¨m has an elliptical form
with a maximum at wind farm
'
s end of 0.0054 N/m
2
deficit, followed by a slightly
wind stress increase in flow direction. Minimal values are 0.0064 N/m
2
for westerly
flow and 0.0068 N/m
2
for southwesterly flow. Transverse to flow direction the wind
farm changes the wind pattern in a symmetric way with the strongest deficit within
OWF. The form of the wake is nearly independent of flow direction. Faint aberra-
tions are attributed to the grid and so in flow direction into the front side of wind
farm boxes and into the corner; see illustration at Table
4.1
under the line
240 km with a wind farm of characteristic size of
L¼
inflow of
'
wind farm.
In sum, the wake shows a maximal reduction of 45-46 % with
x
-
dimension of 39-42 km and
y
-dimension of 18-24 km. Here,
x
-dimension means
the spread in flow direction and
y
-dimension, orthogonal to flow direction. The
impact of the relative small wind farm of an area of 36 km
2
extends to an area of
702-1,008 km
2
, so influencing a field, which is 20-28 times bigger than the OWF
itself. For comparison,
'
the city of Hamburg is measured around 755.3 km
2
(Haffmans
2005
).
Brostr¨m
s equations for wind stress changes give an estimation of how strong
the impact of a wind farm can be. It is a quick test but a pure manipulation of wind
stress, not based on physical principles; owing to these limitations, this method does
not provide an optimal description of wind farm wakes. Considering this method,
'
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