Civil Engineering Reference
In-Depth Information
where
z
ref
is a reference height at which the two 'laws' are matched.
z
ref
may be taken as
the average height in the range over which matching is required or half the maximum
height over which the matching is required.
Figure 3.2 shows a matching of the two laws for a height range of 100m, using
Equation (3.8), with
z
ref
taken as 50m. It is clear the two relationships are extremely
close, and that the power law is quite adequate for engineering purposes.
3.2.3
Mean wind profiles over the ocean
Over land the surface drag coefficient,
κ,
is found to be nearly independent of mean wind
speed. This is not the case over the ocean, where higher winds create higher waves, and
hence higher surface drag coefficients. The relationship between
κ
and
Ū
10
has been the
subject of much study, and a large number of empirical relationships have been derived.
Charnock (1955), using dimensional arguments, proposed a mean wind profile over
the ocean, which implies that the roughness length,
z
0
,
should be given by:
(3.9)
where
g
is the gravitational constant and
a
an empirical constant.
Figure 3.2
Comparison of the logarithmic
(
z
0
=0.02m) and power laws (
α
=0.128) for
mean velocity profile.
Equation (3.9), with the constant
a
lying between 0.01 and 0.02, is valid over a wide
range of wind speeds. It is not valid at very low wind speeds, under aerodynamically
smooth conditions and also may not be valid at very high wind speeds, during which the
air-sea surface experiences intensive wave breaking and spray.
Substituting for the surface drag coefficient,
κ,
from Equation (3.6) into Equation
(3.9), Equation (3.10) is obtained:
