Offshore Winds - Wind Energy Meteorology: Atmospheric Physics for Wind Power Generation - page 95

at shallow or near-coastal sites a is a little larger with values about 0.016-0.02
(Garratt 1977 ;Wu 1980 ). Garratt ( 1977 ) summarized sea surface drag coefficients
from 17 experiments and supported Charnock's relation. Using a friction velocity
of 0.33 m/s and a = 0.018 gives z 0 = 0.00018 m.
The determination of the sea surface drag coefficient, C D is another way of
looking at sea surface roughness. The drag coefficient for neutral atmospheric
stability and 10 m height is defined as:

C DN10 ¼ u 2
u 10

ð 5 : 2 Þ

where u * is the friction velocity defined in ( 3.16 ) and u 10 is the 10 m wind speed
defined in ( 3.1 ). Despite conflicting evidence in the past (Garratt 1977 ), it is now
accepted that the drag coefficient in the MABL is an increasing function of the
wind speed (Sullivan and McWilliams 2010 ) for moderate wind speeds (see
Fig. 5.4 ). This becomes obvious when inserting the logarithmic wind profile ( 3.6 )
for the denominator of ( 5.2 ) using ( 5.1 ) for the determination of the roughness
length:

2

j
ln

C DN10 ¼ ð 5 : 3 Þ

gz
au 2

where z = 10 m. At higher wind speeds, however, most data sets suggest that the
drag coefficient tends toward a constant value (Anderson 1993 ; Donelan et al.
2004 ; Black et al. 2007 ). A few, e.g., the HEXOS data (Janssen 1997 , triangles in
the left frames of Figs. 5.3 and 5.4 ) do not show this levelling off. The exact
equation that describes the relationship between the drag coefficient and wind
speed is dependent on the author (Geernaert 1990 ). Although an universal con-
sensus does not exist, the most widely cited relationships are possibly those pro-
posed by Smith ( 1980 ):

C DN10 ¼ 0 : 00061 þ 0 : 000063u 10 ð 5 : 4 Þ

said to be valid for a wind speed range between 6 and 22 m/s, the one proposed by
Large and Pond ( 1981 ):

0 : 00114 for 4 m/s\u 10 10 m/s

C DN10 ¼

ð 5 : 5 Þ

0 : 00049 þ 0 : 000065u 10 for 10 m/s\u 10 \26 m/s

and the one by Yelland et al. ( 1998 ):

C DN10 ¼ 0 : 00050 þ 0 : 000071u 10 ð 5 : 6 Þ

said to be valid for a wind speed range between 6 and 26 m/s. Similar wind speed
dependencies come from the Coupled Ocean-Atmosphere Response Experiment
(COARE) algorithm by Fairall et al. ( 1996 , 2003 ).