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These spectral consequences of the breaking will be discussed in Section 7.3.2 . Cumulative
effect, an important feature of dissipation in wave fields with full spectrum, is described in
Section 7.3.4 . And finally, wind-forcing and directional-distribution issues pertinent to the
spectral dissipation will be attended to in Sections 7.3.5 and 7.3.6 , respectively.
7.3.1 Laboratory measurements
A lot of laboratory effort, if not most of it with respect to wave-energy dissipation, has
concentrated on the total energy loss in a wave train where a breaking occurs. These can
be trains of monochromatic waves (e.g. Manasseh et al. , 2006 ), or quasi-monochromatic
waves (e.g. Babanin et al. , 2007a ), or spectral waves (e.g. Rapp & Melville , 1990 ). In
this regard, we also see a recent experimental study complemented with an eddy-viscosity
model which investigated the dissipation rates, rather than the total loss, and associated
temporal and spatial scales in unsteady plunging breaking ( Tian et al. , 2010 ).
The output of the breaking, however, as we have just mentioned above, is always spec-
tral. That is, the energy is never lost from a particular Fourier scale, i.e. frequency or
wavenumber, but is rather distributed across a range of scales, or at least has an impact
at a number of scales.
Experiments dedicated to the investigation of this spectral impact are much fewer,
and here we shall highlight two of them. Both were most thoroughly conducted in con-
trolled laboratory conditions, but produced quite different, in fact directly opposite in some
regards, conclusions.
In Tulin & Waseda ( 1999 ), evolution of nonlinear deep-water wave groups was tested
in a 50m-long tank. Waves were produced mechanically by a sensitive programmable
wave generator. Experiments were conducted for waves of 1-4m in length, with the initial
steepness of primary waves varying in the range
=
.
.
28. For such wavelengths
and steepnesses, the tank is long, but not long enough for the Benjamin-Feir instabili-
ties to grow and lead to the breaking. Therefore, small sidebands were initially imposed
over a steeper carrier wave, in order to speed up the development of instability and to
study the outcomes of modulational-instability breaking. The sidebands broadly covered
the expected instability range which, in terms of the inverse modulational index M I (2.12) ,
was
0
10-0
δ = δω/ω =
4. An array of eight high-resolution wire wave probes were
deployed along the tank in order to obtain evolution of the spectrum of such wave trains,
including the breaking effects.
Without breaking, the energy was dynamically exchanged between the primary wave and
sidebands in the course of evolution, but the exchange was reversible and near-recurrence
occurred at some stage (see Figure 7.1 reproduced from Figure 18 of Tulin & Waseda
( 1999 )). When breaking happened, it was always plunging. The ultimate dynamics in this
scenario was quite different (also in this figure). There was no recurrence, and rather the
wave energy was shifted down the spectral scales.
Tulin & Waseda ( 1999 ) provide an interesting and detailed account of the generation
of both new free components and bound harmonics, as well as the behaviour of the
0
.
2-1
.
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