Civil Engineering Reference
In-Depth Information
(3.10)
(
z
h
is usually taken as zero over the ocean.)
The implicit nature of the relationship between
z
0
(or
κ
) and
Ū
10
in Equations (3.9) and
(3.10) makes them difficult to apply, and several simpler forms have been suggested.
Garratt (1977) examined a large amount of experimental data and suggested a value
for
a
of 0.0144. Using this value for
a,
taking
g
equal to 9.81 m/s
2
and
k
equal to 0.41, the
relationship between
z
0
and
Ū
10
given in Table 3.2 is obtained.
The values given in Table 3.2 can be used in non-tropical cyclone conditions. Mean
wind profiles over the ocean in tropical cyclones (typhoons and hurricanes) are discussed
in a following section.
Table 3.2
Roughness length over the ocean as a function of
mean wind speed
Ū10(m/s)
Roughness length (mm)
10
0.21
15
0.59
20
1.22
25
2.17
30
3.51
3.2.4
Relationship between upper level and surface winds
For large-scale atmospheric boundary layers in synoptic winds, dimensional analysis
gives a functional relationship between a
geostrophic drag coefficient, C
g
=
u
*
/Ug,
and the
Rossby number, Ro=U
g
/fz
0
. u
*
is the friction velocity and
U
g
is the geostrophic (Section
1.2.3) or gradient wind;
f
is the Coriolis parameter (Section 1.2.2) and
z
0
is the roughness
length (Section 3.2.1). Lettau (1959) proposed the following relationship based on a
number of full-scale measurements:
C
g
=0.16
Ro
−0.09
(3.11)
Applying the above relationship for a latitude of 40°(
f
=0.935×10
−4
s
−1
), a value of
U
g
equal to 40 m/s and a roughness length of 20 mm gives a friction velocity of 1.40 m/s
and, from Equation (3.2), a value of
Ū
10
of 21.8 m/s. Thus, in this case, the wind speed
near the surface is equal to 0.54 times the geostrophic wind—the upper level wind away
from the frictional effects of the earth's surface.
