Page 50 - Wind Energy Handbook

24 THE WIND RESOURCE

The length scales are dependent on the surface roughness z 0 , as well as on the
height above ground (z); proximity to the ground constrains the size of turbulent
eddies and thus reduces the length scales. If there are many small obstacles on the
ground of typical height z9, the height above ground should be corrected for the
effect of these by assuming that the effective ground surface is at a height z9 2:5z 0
(ESDU, 1975). Far enough above the ground, i.e., for z . z i , the turbulence is no
longer constrained by the proximity of the surface and becomes isotropic. Accord-
x
ing to ESDU (1975), z i ¼ 1000z 0:18 and above this height L u ¼ 280 m, and y L u ¼
0
z
x
z L u ¼ L v ¼ L v ¼ 140 m. Even for very small roughness lengths z 0 , the isotropic
region is well above the height of a wind turbine and the following corrections for
z , z i should be applied:
x 0:35
L u ¼ 280(z=z i )

y 0:38
L u ¼ 140(z=z i )
z 0:45
L u ¼ 140(z=z i ) (2:28)

x 0:48
L v ¼ 140(z=z i )
z 0:55
L v ¼ 140(z=z i )

x
y
y
z
together with L w ¼ L w ¼ 0:35z (for z , 400 m). Expressions for L v and L w are not
x
x
x
given. The length scales L u , L v and L w can be used directly in the von Karman
x
spectra. For the Kaimal spectra we already have L 1u ¼ 2:329 L u , and to achieve the
same high frequency asymptotes for the other components we also have
x
x
L 1v ¼ 3:2054 L v , L 1w ¼ 3:2054 L w .
Later work based on measurements for a greater range of heights (Harris, 1990;
ESDU, 1985) takes into account an increase in length scales with the thickness of the
boundary layer, h, which also implies a variation of length scales with mean wind
speed. This yields more complicated expressions for the nine length scales in terms

of z=h, ó u =u and the Richardson number u =( fz 0 ).
Note that some of the standards used for wind turbine loading calculations
prescribe that certain turbulence spectra and/or length scales be used. These are
often simplified compared to the expressions given above. Thus the Danish
standard (DS 472, 1992) specifies a Kaimal spectrum with
L 1u ¼ 150 m, or 5z for z , 30 m
(2:29)
L 1v ¼ 0:3L 1u
L 1w ¼ 0:1L 1u

while the IEC standard (IEC, 1999) recommends either a Kaimal model with