Publishers version - DTU Orbit

1000CDN
3
2
1
0
10 20 30
U(10 m) [m s−1 ]
Figure 36: The neutral drag coefficient CDN as a function of mean wind speed at z = 10 m.
The broad line is from Charnock’s relation Eqs. (64) and (62). The thin lines are empirical
relations from Geernaert (1987) and the dotted line is from NDP (1998), see Eq. (73).
30 m Eq. (62) is a good approximation to Eq. (63). Throughout this comparison we use
f = 10 −4 s −1 .
Charnock (1955) argued that over the sea the roughness length is related to g = 9.8 m s −2
the acceleration due to gravity and the friction velocity by
z0 = A u2 ∗
g
where A, the Charnockconstant,must be determinedexperimentally. On basis ofan extensive
literaturestudyofoceandataGarratt (1977)foundthatthebestfitofEq.(64)isA = 0.0144.
A slightly newer value is given by ESDU International (1982):
(64)
A = 0.0167, (65)
which will be used here. Over the ocean the neutral drag coefficient
2 u∗
CDN =
U(10 m)
increases monotonicly with U as can be seen by solving Eqs. (64) and (62). This is shown
in Figure 36 as a broad line together with several recent empirical relations. The figure gives
a good impression of the uncertainty in estimates of drag coefficients. Among the various
reasons for this variability are atmospheric stability, surface currents, ‘wave age’, length of
the fetch over water, and water depth (Garratt, 1977; Geernaert, 1987; Brown and Swail,
1991). The spectral density of velocity fluctuations is in general proportional to the drag
coefficient so the uncertainty of the former is probably of the same order of the latter.
3.5.1 Code and textbook spectra
Surface layer scaling is used in many spectral models, implying that length scales are proportional
to z and that variances are proportional to u2 ∗. Therefore, it is convenient to normalize
the spectra with u2 ∗ and present them as functions of either n ≡ fz/U or k1z. All spectra in
this paper are ‘two-sided’ implying −∞
∞ S(f)df is equal to the variance2 .
The spectra of Kaimal are (Kaimal et al., 1972; Kaimal and Finnigan, 1994)
fSu(f)
u 2 ∗
= k1Fu(k1)
u 2 ∗
fSv(f)
u 2 ∗
=
=
52.5n
(1+33n) 5/3,
8.5n
(1+9.5n) 5/3,
2 ∞
The so-called ‘one-sided’ spectra, where 0 S(f)df is equal to the variance, are probably more commonly
used.
62 DTU Wind Energy-E-Report-0029(EN)
(66)
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