Wind Energy

4
Mean Wind and Turbulence
in the Atmospheric Boundary Layer
Above the Surface Layer
S.E. Larsen, S.E. Gryning, N.O. Jensen, H.E. Jørgensen and J. Mann
Summary. Most wind energy related boundary layer formulations derive from the
atmospheric surface boundary layer. The increasing height of modern wind turbines
forces meteorologists to use relations more appropriate for greater heights. Such
expressions are not as well established as the surface layer formulations. Data from
the new Danish wind energy test site at Høvsøre is used to illustrate similarities and
differences.
4.1 Atmospheric Boundary Layers at Larger Heights
For wind energy, the atmospheric boundary layer is normally considered surface
layer with neutral thermal stability.
The surface layer wind profile can be written:
u(z) = u∗
� � �
z
�
z
�
ln − ψ
κ z0 L
�
, (4.1)
where u∗ is the friction velocity, z the measuring height and z0 the roughness
length, κ the v. Karman constant, ψ the stability function and L is the length
scale of thermal stratification:
z
L
= −wθ
u 3 ∗
gκz
, (4.2)
T
with T and θ being temperature and potential temperature respectively. Neutral
conditions correspond to ψ(z/L ∼ 0) ∼ 0, i.e. when z is small and or
|L| is large. Conversely for z large, L has to be even larger to ensure that
the atmosphere can be considered neutral. For |z/L| � 0.5 one will expect
the stability term in (4.1) to be important. The scales, u∗ and wθ, reflect the
stress and heat-flux conditions at the surface.
The surface layer approximation of the atmospheric boundary layer demands
that z0 ≪ z ≪ h, where h denotes the boundary layer height. Since
typically, 100 � h � 1,000 m, the assumption becomes unrealistic with wind