Wind Energy

62 Stefan Emeis and Matthias Türk
z/z 0
10 7
10 6
10 5
10 4
10 3
10 2
n =
0.07
0.10
0.15
0.20
0.30
0.40
0.50
0.70
10 1
−0.4 −0.2 0.0 0.2 0.4 0.6 0.8 1.0
Fig. 11.1. Diagram showing the solution of (11.3) (bold line). Roughness decreases
along the y-axis and stable stratification increases along the x-axis. Thin lines towards
the upper right indicate power law and logarithmic profiles with equal slope,
lines towards the lower right those profiles with equal curvature. Asterisks mark
positions for Fig. 11.2
A perfect coincidence is possible in stably stratified flow, if the following relation
between roughness and stratification holds (see Fig. 11.1):
� �
z
1
ln =2+ . (11.3)
4.7(z/L∗)
z0
The practical result is that (11.2) offers a nearly perfect fit to (11.1) under
stable conditions for certain surface roughness conditions and a good approximation
under neutral and unstable conditions in the limit of very smooth
surfaces.
z/L *
11.3 Application to Offshore Wind Profiles
Offshore wind and turbulence profiles from the 100 m mast on the FINO1
platform in the German Bight 45 km off the coast are currently processed at
our lab (project OWID, funded by the German Ministry of the Environment,
BMU by grant no. 0329961). Measurement heights are 33.5, 41, 51, 61, 71,
81, 91, and 102.5 m. For comparison with (11.1) and (11.2) wind data from
2004 have been used. According to the difference between air temperature in
41 m height and water temperature the profiles have been lumped into several
stability classes. Figure 11.3 shows exemplary annual mean profiles for very