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3), agreement of the two dissipations
at the spectral peak is reasonable for the Melville-Matusov value of b br
At this stage of wave development ( U 10 /
c p
=
1
.
10 3 .
=
8
.
5
·
10 5 suggested by Gemmrich ( 2005 ) gives much lower dissipation
values across the entire spectral band. As discussed by Tsagareli ( 2009 ), however, there is
a dimensional issue in comparing the b br coefficients of Melville & Matusov ( 2002 ) and
Gemmrich ( 2005 ), due to the normalisation by
The value of b br
=
2
·
3 . If this issue is accounted for,
the agreement between the experimental outcomes of the two studies at the peak of the
dissipation function (7.58) at U 10 /
(
/
U 10 )
10
3 is quite good (not shown here).
Thus, to summarise this section on the whitecap-dissipation function for spectral mod-
els, we can conclude that new developments are being seen in almost every regard lately.
The substantial experimental progress which led to direct estimates of the breaking dissi-
pation and finding new features of its behaviour in recent years, has produced a number of
different formulations and parameterisations. These are converging qualitatively and quan-
titatively, if compared within ranges of their expected performance and applicability. And
the most encouraging fact is that newly advanced and proposed spectral-dissipation source
terms are now being adopted in spectral models, all the way to operational wave-forecast
modelling.
It is also worth mentioning in conclusion that there is a growing discussion not only on
what the model-dissipation has to damp, but also on what it should not and what it may
in fact produce. For example, Lavrenov ( 2004 ) showed that, if the dissipation function in
wave models is not forced to suppress the low-frequency spectral energy, this may result in
return energy fluxes from the waves into the atmospheric boundary layer, up to a quarter of
the total wind-to-wave flux in magnitude. Such a considerable additional source of energy
for the atmosphere may prove a significant factor in weather and climate forecasts (see also
Hanley et al. , 2010 ).
An interesting feature which the dissipation can also produce is downshifting of the
spectral energy. Such a downshift does appear a consistent outcome of the breaking due
to modulational instability (see Section 8.1 ) and attempts have been made to attribute
this behaviour to the dissipation function (e.g. Schneggenburger et al. , 2000 , and papers
presented at WISE meetings by Donelan and Meza).
c p =
1
.
7.5 Non-breaking spectral dissipation
This topic is dedicated to wave breaking and the dissipation of ocean waves, and as far as
the latter is concerned most attention is paid to whitecapping dissipation, i.e. that due to
wave breaking. There is a good rationale for this of course, as once the waves break, most
of the dissipation in such wave trains/fields is due to the breaking.
There are many other sources of dissipation, however, and some of them have already
been outlined in Section 7.3.4 (see eq. 7.26 ). Compared to the whitecapping dissipation,
their efficiency may be small or even negligible, but once the wind forcing drops down or
ceases, or in case of swell, the breaking subsides or stops, these become a major sink of
energy in the wave system.
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