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10
0
10
−1
10
−2
10
−3
10
−4
10
−5
10
−6
10
−7
10
−8
10
−9
10
−1
10
0
10
1
f, Hz
Figure 5.29 Illustration. JONSWAP spectrum
(2.7)
is shown with solid line (peak enhancement of
γ
=
7 is chosen for clarity), zero-breaking saturation level with dashed line, 5% breaking level
with dotted line and 100% breaking level with dash-dotted line. The breaking limits are drawn qual-
itatively for illustration purposes only and must not be used for estimates. Figure is reproduced
from
Babanin & van der Westhuysen
(
2008
)
©
American Meteorological Society. Reprinted with
permission
σ
threshold
can be established,
the dimensional threshold can then be obtained at every frequency:
Since a universal dimensionless saturation-threshold value
2
g
2
4
σ(
f
)
threshold
f
5
F
(
f
)
threshold
=
.
(5.37)
(
2
π)
The meaning of the dimensional threshold is illustrated in
Figure 5.29
.
In this figure, JONSWAP-spectrum parameterisation (
2.7
, solid line) and arbitrary
breaking limits are used for illustration purposes, but the real spectra and breaking threshold
exhibit qualitatively similar behaviour (
Babanin & Young
,
2005
;
Babanin
et al.
,
2007c
;
Babanin & van der Westhuysen
,
2008
). The dashed line indicates the dimensional threshold
(5.37)
, and the dash-dotted line is the imagined ultimate spectral limit in saturation terms
- i.e. the spectral density cannot physically reach over this limit because the steepness of
waves will be such that all the waves will be breaking (
Babanin
et al.
,
2007c
;
Stiassnie
,
2010
). If the spectral density drops below the dashed level, there will be no breaking in the
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