Geoscience Reference
In-Depth Information
Figure 5.30 Breaking probabilities (from left to right) for frequencies of
f
p
,1
.
2
f
p
,1
.
4
f
p
,1
.
6
f
p
,
and 1
.
8
f
p
in the
±
0
.
1
f
p
frequency range. Asterisks are experimental points. The solid line in all
plots identifies the linear dependence obtained in the first panel. Dashed lines, from left to right, are
b
T
5
.
Circles in the higher-frequency bins are estimates of the breaking probability based on account-
ing the cumulative effect
(5.41)
. Figure is reproduced from
Babanin
et al.
(
2007c
) (public domain
site http://www.waveworkshop.org/ sponsored by Environment Canada, the U.S. Army Engineer
Research and Development Center's Coastal and Hydraulics Laboratory, and the WMO/IOC Joint
Technical Commission for Oceanography and Marine Meteorology)
2
,
b
T
3
,
b
T
4
,and
b
T
∼
(
F
−
F
threshold
)
∼
(
F
−
F
threshold
)
∼
(
F
−
F
threshold
)
∼
(
F
−
F
threshold
)
What happens if the cumulative effect is disregarded, as it is now in most breaking/
dissipation parameterisations? As seen in
Figure 5.30
, it would still be possible to draw a
linear dependence in each frequency bin, but at higher frequencies such dependence will
become steeper and the intercept will move further from the origin (i.e. the threshold value
will be growing). This is similar to what was done, for example, in
Banner
et al.
(
2002
).
In the case of
Figure 5.30
, the universal threshold value has already been subtracted at
the bottom scale, and therefore all the dependences have to go through zero. If we now
try to fit a best power function at each frequency, this will result in a quadratic function at
f
=
1
.
2
f
p
, a cubic function at
f
=
1
.
4
f
p
, a fourth power at
f
=
1
.
6
f
p
, and a fifth power
at
f
8
f
p
as shown in the figure.
Thus, fitting some functions expressed in terms of local spectral density at each fre-
quency can be done across the spectrum as a matter of tuning, but as a matter of physics
=
1
.
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