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Vertical structure of the marine boundary layer over a wavy sea surface. p
+
and p
-
Fig. 5.1
indicate positive and negative pressure perturbations close to the waves
Fig. 5.2 Roughness length of the sea surface in m (left) and friction velocity in m/s (right) using
Charnock's relation (
5.1
) and the neutral logarithmic wind profile (
3.6
)
for two different values of
the Charnock parameter (bold line: 0.011, thin line: 0.020)
Many studies on the wind-driven roughness of the sea surface already exist.
Charnock (
1955
) presented a relation between roughness length, z
0
and friction
velocity, u
*
based on a small dataset collected under near-coastal conditions at a
measurement height of eight metres:
aj
2
u
ð
z
Þ
2
z
0
¼
au
2
g
¼
ð
5
:
1
Þ
2
z
0
W
ð
L
Þ
z
g ln
where z
0
is the surface roughness length, u
*
the friction velocity and g the
acceleration of gravity. The term behind the second equal sign in (
5.1
) has been
derived by using the formula for the diabatic wind profile (
3.16
). This latter
relation has to be solved iteratively. The empirical constant, a is called today the
Charnock parameter. For the open ocean Smith (
1980
) suggests a = 0.011 while
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