Geoscience Reference
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Instead, other issues which are non-existent in the case of dominant breaking become
important.
These waves can potentially be breaking because of two reasons. First of all, one would
expect them to break due to inherent physical processes that lead surface waves to break
in any scenario. Secondly, their breaking is induced by the longer waves. This is either
the straining action of longer waves (
Longuet-Higgins & Stewart
,
1960
;
Phillips
,
1963
;
Donelan
,
2001
;
Donelan
et al.
,
2010
) or forced breaking (
Babanin &Young
,
2005
;
Young &
Babanin
,
2006a
). The straining action takes place because of the modulation of short wave
trains by the underlying large waves which causes the short-wave steepness to increase at
the forward faces of longer waves, resulting in their frequent breaking. Forced breaking is
the breaking of short waves in a wake or on the top of large-wave breaking triggered by the
large breaker. One way or another, but similarly to the subsequent breaking of dominant
waves on top of their groups described above, sequential or simultaneous breaking of short
waves is expected in this case on top of longer waves. This sequence is linked to the phase
of the longer waves (i.e. it happens on the front face, at the top or in the wake of the long
wave). By analysing this phase link, Filipot (2010, private communication) concluded that
the induced breaking dominates at frequencies
f
>
3
f
p
.
λ
short
, frequencies
f
short
) are also coupled in a
nonlinear sense, then, similarly to definition
(2.32)
for groups of dominant waves, the short-
breaker severity
s
short
needs to be defined in terms of a value averaged over the period of
the dominant wave:
If these short breakers (wavelengths
λ
long
8
λ
long
2
dx
E
s
short
=
s
short
η
short
(
x
)
.
(2.42)
0
Here,
E
s
short
(
)
λ
long
is the length
f
is the energy lost due to the breaking of short waves,
of the modulating underlying wave, and
are surface elevations just before the
breaking started, but with the low-frequency/wavenumber oscillations of the mean surface
(
η
short
(
x
)
λ
long
is also not a constant value of, for
example, dominant waves with frequency
f
p
. There has to be
λ>λ
short
,
f
<
f
short
) filtered out. Wavelength
λ
long
(
f
long
)
λ
short
(
f
short
),
(2.43)
f
long
f
short
,
but other than that
λ
long
and
f
long
can take on any scale.
We should note that the severity of breaking of short waves may depend on their scale
f
short
and therefore
E
s
short
can be treated as a spectral function
E
s
short
(
. Like the break-
ing probability of
Section 2.5
, in practical terms frequency
f
implies some spectral band
f
f
)
±
η
short
(
)
in
(2.43)
are bandpassed into this band.
The outcome of induced breaking is the so-called cumulative effect (
Babanin & Young
,
2005
;
Young & Babanin
,
2006a
;
Babanin
et al.
,
2007c
, see also
Section 7.3.4
), accumula-
tion of breaking energy losses at smaller scales which are coupled with the behaviour of
longer waves. Further from the spectral peak, the cumulative energy loss grows and tends
f
(2.5)
such that surface elevations
x
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