Physics of Wind Parks - Wind Energy Meteorology: Atmospheric Physics for Wind Power Generation - page 140

Fig. 6.3 Normalised reduction of wind speed (above) and available wind power (below)athub
height in an indefinitely large wind park as function of atmospheric instability (h/L* = 1: strong
instability, 0: neutral stability, ? 1: stable stratification) and surface roughness (z0 = 0.0001 m:
very smooth sea surface, 0.001 m: rough sea surface, 0.1 m: smooth land surface, 1.0 m: rough
land surface)

6.3 Analytical Model for Wind Park Wakes

The estimation of the length of the wakes of large wind parks is essential for the
planning of the necessary distance between adjacent wind parks. This estimation
can be made using the same principal idea as in the subchapter before: the missing
momentum in the wake of an indefinitely broad wind park can only be replenished
from above (Fig. 6.4 ). If we imagine to move with an air parcel, then we feel the
acceleration of the speed of this parcel, u hn from u hn0 at the rear end of the park to
the original undisturbed value, u h0 , which had prevailed upstream of the park
(neglecting the Coriolis force):

o u hn
ot

¼ o ð s = q Þ
oz

ð 6 : 28 Þ

Substituting the differentials by finite differences and using ( 6.8 ) leads to: