Offshore Winds - Wind Energy Meteorology: Atmospheric Physics for Wind Power Generation - page 97

Nevertheless, a wind speed-dependent drag coefficient is not desirable, because
usually a drag coefficient for a fully turbulent flow should be only object-dependent
and independent of the flow speed above this object. Only then flows at different
speeds are similar to each other. A wind speed-dependent drag coefficient indicates
that the state of flow is changing with wind speed. Most probably, the flow over the
very smooth sea surface is not fully turbulent for 10 m wind speeds of less than about
8 m/s. The drag coefficient should be a constant above this wind speed.
Therefore, a new functional form of the neutral drag coefficient for moderate to
high wind speeds in the MABL for a range of field measurements as reported in the
literature has been proposed by Foreman and Emeis ( 2010 ). This new form is
found to describe a wide variety of measurements recorded in the open ocean,
coast, fetch-limited seas, and lakes, with almost one and the same set of param-
eters. It is the result of a reanalysis of the definition of the drag coefficient in the
marine boundary layer, which finds that a constant is missing from the traditional
definition of the drag coefficient. The constant arises because the neutral friction
velocity over water surfaces is not directly proportional to the 10 m wind speed, a
consequence of the transition to rough flow at low wind speeds below about 8 m/s.
Within the rough flow regime, the neutral friction velocity is linearly dependent on
the 10 m wind speed; consequently, within this rough regime, the newly defined
drag coefficient is not a function of the wind speed. The magnitude of the newly
defined neutral drag coefficient represents an upper limit to the magnitude of the
traditional definition.
In order to derive this new wind speed independent drag coefficient, Foreman
and Emeis ( 2010 ) start with an analysis of the relation between the friction
velocity and wind speed. Solving ( 5.2 ) for the friction velocity gives:
u ¼

p

C DN10 u 10 ð 5 : 7 Þ

( 5.7 ) does not depict the reality, especially not for higher wind speeds. A better
relation is (straight line in Fig. 5.3 left and bold line in Fig. 5.3 right):
u ¼

p

C mN10 u 10 þ b ð 5 : 8 Þ

with C mN10 = 0.0026 and b =-0.14 m/s. The straight line described by ( 5.8 )
does not meet the origin, thus it is valid only for the fully turbulent regime above
8 m/s wind speed. Inserting ( 5.7 ) into ( 5.1 ) yields:

2

p

C mN10

u 10 þ b

C DN10 ¼ ð 5 : 9 Þ

u 10

This new relation ( 5.9 ) is depicted as bold curves in Fig. 5.4 . For high wind
speeds, the classical drag coefficient C DN10 from ( 5.9 ) converges against C mN10 .
C mN10 = 0.0026 is shown as dashed horizontal line in Fig. 5.4 left.