Wind Energy

24 S.E. Larsen et al.
2.5
2.25
2
σ 1.75
w
u* 1.5
1.25
1
0.75
σ u
u*
4
3.5
3
2.5
2
1.5
1
−2
West
0 2
z/L
10 m
20 m
40 m
60 m
80 m
100 m
2.5
2.25
2
σ 1.75
w
u* 1.5
1.25
1
0.75
East
4 6 −2 0 2
z/L
10 m
20 m
40 m
60 m
80 m
100 m
−2 0 2
z/L
4 6 −2 0 2
z/L
4 6
West
4
3.5
East
10 m
3
10 m
20 m
40 m
60 m
σu u*
2.5
2
20 m
40 m
60 m
80 m
100 m
1.5
1
80 m
100 m
4 6
Fig. 4.3. Scaled standard deviations: σw/u∗ and σu/u∗ vs. z/L for z ∼ 10–100 m for
West and East flows. Local scaling has been used, see (4.3). Broken lines: Analytical
forms [2]
In Fig. 4.3 we present finally the scaled standard deviations of velocity,
σw/u∗ and σu/u∗ vs. z/L, forz between 10 and 100 m. For σw/u∗ analytical
expressions are shown as a broken line. No general simple form exists for σu/u∗
vs. z/L. For unstable conditions it becomes a function of h/L and for stable
condition it growths slowly with z/L. We believe that use of local scaling is
partly responsible for the some of behavior with z/L since h varies somewhat
systematically with z/L.
4.3 Discussion
We have considered mean flow and turbulence over land and water based on
data from Høvsøre, above the surface layer proper. We have seen that thermal
stability cannot be neglected for these heights, neither over land nor water,
that the wind profiles adapt to the standard models for internal boundary
layers, and that the wind aloft has a tendency to increase more than logarithmic,
either due to the boundary length scale of [1] or due to the influence
of stability and a length scale based on the Brunt–Vaisala frequency [4]. For
neutral to stable conditions it is understood that these two scales may be
related.
Additionally, we have found that the scaled σw/u∗ vs. z/L largely follows
standard formulations, while σu/u∗ is less well behaved. Some of the behavior
of σw/u∗ and σu/u∗ can be explained by that the plots are based on local