Geoscience Reference
In-Depth Information
The subsection begins from outlining the physics that makes small-scale breaking
different to the dominant breaking and from formulating the cumulative-effect concept.
Experimental estimates of the breaking probability are then described, and the problem
of the count of the small waves riding larger waves is discussed. The important spec-
tral wave-breaking property, the dimensionless and dimensional threshold which identifies
spectral levels below which breaking does not occur, is introduced and quantified. Formu-
lations are suggested for breaking probability and breaking dissipation which account for
the threshold and for the cumulative effect. The transition frequency between the inherent-
and induced-breaking domination in the spectrum is identified quantitatively. Finally, an
alternative method of approaching breaking probability in terms of breaking-wave-height
distributions is described.
Lately, the frequency distribution of the breaking probability
b
T
(
(2.4)
has been a
sought after function (
Ding & Farmer
,
1994
;
Phillips
et al.
,
2001
;
Banner
et al.
,
2000
,
2002
;
Melville & Matusov
,
2002
;
Babanin & Young
,
2005
;
Gemmrich
,
2006
;
Manasseh
et al.
,
2006
;
Babanin
et al.
,
2007c
;
Filipot
et al.
,
2008
,
2010
;
Babanin
,
2009
). There is a rea-
sonable expectation in the wave-modelling community that, once some universal function
for
b
T
(
f
)
is obtained, such a parameterisation will provide a major step forward towards
an experimental, rather than speculative dissipation function.
Breaking of small-scale waves, however, apart from inherent reasons such as modulation-
al instability or linear focusing, can be affected by longer waves (e.g.
Longuet-Higgins
&Stewart
,
1960
;
Phillips
,
1963
;
Donelan
et al.
,
2010
). As a result, parameterisation of
the breaking rates at short wavelength is problematic, if not impossible in terms of the
steepness of the short waves or spectral density at the respective wavelength. Here, by
short/small-scale we mean waves with temporal and spatial relative scales smaller than
those of the dominant waves in a wave field.
There are a number of ways in which the long waves can affect the breaking of shorter
waves. One of them is modulation of the train of the short waves riding the underlying
large-scale waves. The latter compress the short wavelengths at their front face and extend
those at the rear face. As a result, the front-face small waves become steeper and frequently
break (
Donelan
,
2001
). In the absence of underlying long waves, the breaking, due to the
regular reasons only, would be much less frequent. This mechanism must be most essential
in deep water and finite depths outside the surf zone, as for every sequence of shorter waves
such a modulation inevitably occurs over every period of any underlying longer wave.
Another effect is due to breaking of the large waves (
Banner
et al.
,
1989
;
Tulin &
Landrini
,
2001
;
Manasseh
et al.
,
2006
;
Young & Babanin
,
2006a
). This is how
Tulin &
Landrini
(
2001
) describe the short waves in such circumstances:
f
)
“As we have observed in our large wind-wave tank, the growth of these waves is much effected by
the existence of breaking energetic waves, which not only modulate the microbreakers, but virtually
eliminate them as the microbreaker train is overcome by the energetic breaker at the peak of the wave
group. It would seem, observing this striking phenomenon, that it is the action of the energetic break-
ers which causes the microbreakers to disappear, and that they begin growing again from very short
waves. Their eventual length is thus determined by the effective fetch between energetic breakers.”
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