Wind Energy

64 Stefan Emeis and Matthias Türk
are matched. For the logarithmic profiles a roughness length of 0.0001 m has
been assumed. For neutral stratification no fit of the logarithmic profile to the
measured data was possible because this profile is fixed through the inevitable
choice L∗ = ∞ for the Monin–Obukhov length.
The fits are satisfying over the whole height range only for stable stratification.
The logarithmic profile from (11.1) is closer to the measurements
than the power law profile from (11.2). For neutral conditions and unstable
conditions below 50 m the fits are not so well. The measured profile for neutral
conditions below 81 m is more slanted to the right than the truly neutral
logarithmic profile indicating that we are already in the upper part of the
surface layer. Above 81 m the measured wind speeds under neutral and stable
conditions increase slower with height. Obviously, we reach here already
the Ekman layer. Under unstable stratification the surface layer is higher and
thus no drop in the wind speed increase with height can be observed below
102.5 m.
11.4 Conclusions
Within the height range of their validity (i.e. the surface layer of the atmospheric
boundary layer) a power law wind profile can only approximate
a logarithmic wind profile over a wider height range in case of stable thermal
stratification for certain surface roughnesses (see (11.3)). For neutral and
unstable stratification this approximation is possible only for very smooth
surfaces.
There is an indication that for neutral and stable thermal stratification of
the air offshore wind profiles in heights above about 80 m above the sea are
already above the surface layer within which (11.1) is valid. Nevertheless a
description of offshore profiles by (11.1) and (11.2) seem to be possible at least
under stable conditions. But it remains open whether the Monin–Obukhov
length L∗ used here to fit the logarithmic profile in 51 to 61 m height to the
measured profile resembles to L∗ in the true surface layer in the first ten or
twenty meters above the sea surface.
References
1. Stull RB (1988) An Introduction to Boundary Layer Meteorology. Kluwer,
Dordrecht, pp. 666
2. Sedefian L (1980) On the vertical extrapolation of mean wind power density.
J Appl Meteorol 19:488–493
3. Emeis S (2005) How Well Does a Power Law Fit to a Diabatic Boundary-Layer
Wind Profile? DEWI Magazine 26:59–62