Geoscience Reference
In-Depth Information
ω 6 exp
2 g 2
(ω) =
F
C
(8.12)
2 U 2
ω
s 3 is a dimensional constant. The parameterisation of Burling
( 1955 ) was measured in the range of wave fetches X
10 3 cm
where C
=
1
.
4
·
/
=
400-1350m and wind speeds
U 10 =
s and stated the fact that, even though the spectra themselves were clearly
developing, with the spectrum peak and the total energy evolving, the tails
5-8m
/
“obtained in different conditions very nearly coincide and become apparently independent of the
fetch and of the strength of the wind”:
ω 5
10 3
F
(ω) =
7
.
0
·
.
(8.13)
Bretschneider ( 1958 ) produced a parameterisation which is already remarkably familiar
(see (2.7) ):
ω 5 exp
4
657 2
π
g 2
F
(ω) = α
0
.
(8.14)
T
ω
where T is
“a 'mean wave period' which depends upon wind speed and the state of development of the sea”.
10 3 , obtained from observations of
Bretschneider ( 1958 ) found that constant
α =
7
.
4
·
Burling ( 1955 ), was consistent with his spectra.
Phillips ( 1958 ) rightly argued that for the spectrum parameterisation to be physically
sound, its dimension has to be correct. He produced a rather long list of physical dimen-
sions to be considered, i.e. air and water densities
ρ a and
ρ w
, friction velocity u
, surface
roughness length z 0 , acceleration g , water surface tension
σ
and viscosity
ν
, together with
the relevant spectral scales k and
.
In different parts of the spectrum, different combinations of the dimensional properties
may be valid and/or significant, but when it comes to the gravitational range of surface
waves, it was u which represented the wind stress and gravitational acceleration g that
remained. If talking about the spectrum tail, which clearly exhibited some level of satura-
tion in the spectra of Burling ( 1955 ), Phillips ( 1958 ) argued that this saturation signifies
some limiting shape of the wave crests which is apparently due to the waves breaking and
not being able to grow any further.
With respect to the breaking, Phillips ( 1958 ) argued that
ω
“the geometry of the limiting shape near the sharp crests is determined by the condition that the
downward acceleration should not exceed g , so that the asymptotic forms
...
would not be expected
to involve u
.Anincreasein u
...
should not influence the geometry of such a sharp crest itself”.
Phillips ( 1958 ) even made a footnote remark that
“we have excluded a different possible type of surface instability in which the sharp crests may be
'blown off' by very high winds”.
 
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