Wind Energy

11
Comparison of Logarithmic Wind Profiles
and Power Law Wind Profiles and their
Applicability for Offshore Wind Profiles
Stefan Emeis and Matthias Türk
11.1 Wind Profile Laws
Two types of wind profile laws are often used for the vertical extrapolation of
wind speeds u(z) in the atmospheric surface-layer [1]: the theoretically derived
logarithmic profile with stability corrections Ψ
u(z) =
� �
u∗
κ
� �
z
ln
z0
�
− Ψ
� z
L∗
��
(11.1)
with height z, roughness length z0, Monin–Obukhov length L∗, friction
velocity u∗, and von Kármán’s constant κ =0.4and the empirical power
law
� �n z
u(z) =u(zA)
(11.2)
with reference height zA and Hellmann exponent n. Due to its mathematical
simplicity (11.2) is widely used for wind energy purposes. The first part of
this study (Chap. 11.2) investigates the possible approximation of (11.1) by
(11.2), the second part (Chap. 11.3) compares (11.1) and (11.2) to measured
offshore wind profiles.
11.2 Comparison of Profile Laws
In extension to existing studies (e.g. [2]) the slope and the curvature of the
logarithmic and the power law profiles should coincide in a selected height simultaneously
in order to give a good fit over a wider height range. The surface
roughness and thermal stratification conditions for which such a simultaneous
coincidence is possible are calculated analytically (see the full equations in [3]).
It turns out that for neutral and unstable conditions slopes and curvatures
of the two profiles (11.1) and (11.2) cannot coincide simultaneously. Only an
approximate coincidence is found in the limit z0 → 0 for very smooth surfaces.
zA