Page 53 - Wind Energy Handbook

TURBULENCE 27

30m height, 25m/s, z = 0.010m, 50 latitude
0
0.3

Eurocode
0.25
DS 472
0.2
Normalized spectrum 0.15 Kaimal
IEC 1400-1

IEC 1400-1
von Karman

0.1
Improved von
Karman

0.05

0
0.001 0.01 0.1 1
Frequency (Hz)

Figure 2.7 Comparison of Spectra at 25 m/s

described by ‘coherence’ functions, which describe the correlation as a function of
frequency and separation. The coherence C(˜r, n) is defined by

jS 12 (n)j
C(˜r, n) ¼ p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (2:33)
S 11 (n)S 22 (n)

where n is frequency, S 12 (n) is the cross-spectrum of variations at the two points
separated by ˜r, and S 11 (n) and S 22 (n) are the spectra of variations at each of the
points (usually these can be taken as equal).
Starting from von Karman spectral equations, and assuming Taylor’s frozen
turbulence hypothesis, an analytical expression for the coherence of wind-speed
fluctuations can be derived. Accordingly for the longitudinal component at points
separated by a distance ˜r perpendicular to the wind direction, the coherence
C u (˜r, n) is:

C u (˜r, n) ¼ 0:994(A 5=6 (ç u ) ç A 1=6 (ç u )) (2:34)
1 5=3
2 u
j
Here A j (x) ¼ x K j (x) where K is a fractional order modified Bessel function, and