Vertical Profiles Over Flat Terrain - Wind Energy Meteorology: Atmospheric Physics for Wind Power Generation - page 47

u ð z = L Þ¼ð 1 þ b z/L Þ 1 = 4

ð 3 : 71 Þ

and the stability correction function in ( 3.69 ) and ( 3.70 ) becomes (Peña et al.
2010b ):

T ð z = L Þ¼ W m ð z/L Þ ð 3 : 72 Þ

In stable situations the differential form u of the correction function W m ( 3.15 )
for stable stratification reads:

u ð z = L Þ¼ 1 þ a z/L

ð 3 : 73 Þ

and the stability correction function in ( 3.69 ) and ( 3.70 ) becomes (Peña et al.
2010b ):

T ð z = L Þ¼ W m ð z/L Þ 1 z
2z i

ð 3 : 74 Þ

As above, b is chosen around 15 or 16 and a is chosen to be around 4.7 and 5.
The work on such unified profiles is ongoing, see. e.g., Sathe et al. ( 2011 ).
Measurement methods that are needed to determine the mixed layer height are
described in Appendix B.

3.3 Spectra

Power spectra (or shortly spectra) describe the frequency dependence of the power
of turbulent fluctuations, while the standard deviations of the wind components
given in the relations ( 3.9 ) and ( 3.17 )to( 3.20 ) are integral values over the entire
turbulence spectrum. The frequency dependence of the standard deviations is
needed for load calculations for wind turbines. This desired information can be
obtained from turbulence spectra only. Kaimal et al. ( 1972 ) give universal func-
tions for the turbulence spectra for neutral stratification over flat terrain:

nS u ð n Þ
u 2

f
1 þ 33f

¼ 105 ð 3 : 75 Þ

Þ 5 = 3

ð

nS v ð n Þ
u 2

f
1 þ 9 : 5f

¼ 17 ð 3 : 76 Þ

Þ 5 = 3 ð

nS w ð n Þ
u 2

f
1 þ 5 : 3f 5 = 3

¼ 2 ð 3 : 77 Þ

ð Þ

with the spectral power density S(n), frequency n, and normalized frequency
f = nz/U. The functions ( 3.75 )-( 3.77 ) follow Kolmogrov's -5/3 law for the
inertial subrange between the low-frequency production range and the high-