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stratified in the mean, it becomes obvious from the above calculations why the
power law approach has been so successful in many cases.
For high wind speeds which are most favourable for wind energy conversion
the stratification of the boundary-layer usually becomes nearly neutral. The above
considerations then show that only for very smooth terrain (offshore and near the
coasts) the power law is a good approximation to the real surface layer wind
profile. Extrapolations of the wind profile above the height of the surface layer
(80-100 m) by either law ( 3.6 )or( 3.22 ) should be made with very great care
because both laws are valid for the surface layer only (Emeis 2001 ).
3.1.4 Vertical Wind Profile with Large Wind Speeds
Wind profiles for strong winds are nearly always close to the neutral wind profiles,
because the Obukhov length defined in ( 3.11 ) takes large absolute values and the
correction terms in the profile law ( 3.16 ) remain small. Vertical gust profiles look
different. Wieringa ( 1973 ) derives profile exponents for gusts which are about
45 % lower than those for the mean wind. This implies that the gust factor G(z)
(i.e., the ratio of the gust wind speed to the mean wind speed, see equation A.33 in
Appendix A) must decrease with height which has been confirmed by Davis and
Newstein ( 1968 ). The decrease can be explained by the decrease of the vertical
wind speed shear with height which leads to a decreasing mechanical production
of turbulence. Wieringa ( 1973 ) gives an empirical relation for the height depen-
dence of the gust factor by stipulating D/t = 86.6 in Eq. (A.36) in Appendix A:
G ð z Þ¼ 1 þ 1 : 42 þ 0 : 3013 ln ð 990 vt Þ 4 Þ
ln ð z = z 0 Þ
ð 3 : 39 Þ
The numerical value 990 m (86.6 times 11.5 m/s / 1 s) represents the turbulent
length scale underneath which the majority of the turbulence elements are found.
This results in G = 1.37 for a roughness length of 0.03 m.
3.2 Profile Laws Above the Surface Layer
Modern large wind turbines with upper tip heights of more than about 100 m
frequently operate at least partly in the Ekman layer. Therefore, wind resource and
load assessment cannot be done solely with the vertical profile relations and laws
given in Sect. 3.1 . The more complicated wind regime in the Ekman layer is to be
considered as well.
The equilibrium of forces changes when moving upward from the surface layer or
Prandtl layer into the Ekman layer. In addition to the pressure gradient force and the
surface friction, the Coriolis force due to the Earth's rotation becomes important here
as well. This means that in a stationary Ekman layer the three terms III, V, and VII in
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