Energy dissipation across the wave spectrum - Breaking and Dissipation of Ocean Surface Waves - page 233

crest and then spreads laterally, and the turbulence produced by the breaking is essen-
tially three-dimensional. Such fluid-mechanics approaches, in principle, are available, but
dedicated efforts are needed to combine and further develop them for the wave-breaking
application.
Therefore, experimental estimates of the breaking dissipation, both for monochromatic
and spectral waves, have so far mostly concentrated on bulk energy loss or energy/
momentum flux change, by measuring waves before and after breaking commenced and
finished. These are purely empirical approaches, and they also need some empirical time
scale in order to convert the results into dissipation rates. Such methods are necessary and
very helpful in practical requirements, particularly if parameterised in statistical terms, but
they reveal little about the physics of breaking in progress, and correspondingly about the
control mechanisms of energy dissipation.
Theories on wave-breaking dissipation, correspondingly, have also primarily focused on
interpreting properties of the wave fields by means of their state before and after the break-
ing takes place, usually in statistical terms. These will be summarised in Section 7.1 for
the spectral models and in Section 7.2 for phase-resolvent models. Section 7.1.2 describes
an interesting approach which is a combination of both. Experimental measurements of
the wave-breaking dissipation in wave trains and fields with a continuous spectrum are not
many, and they will be depicted in Section 7.3 . Section 7.4 is dedicated to the implemen-
tation of spectral-dissipation functions in wave-forecast models. In this regard, that is, as
far as modelling the wave energy dissipation is concerned, dissipation does not cease in
the wave field if the breaking is not present. Therefore, we have found it relevant to outline
non-breaking dissipation mechanisms in the last section of this chapter.

7.1 Theories of breaking dissipation

This section will provide a brief review of analytical theories of dissipation in wave fields
with a continuous wave spectrum. Older theoretical models, based on the probability,
quasi-saturated and negative-input approaches, have received substantial attention in the
literature, and here we have combined them into a single subsection (7.1.1) and will accom-
modate the most recent updates, but will largely follow revisions by Donelan & Yuan
( 1994 ), Babanin et al. ( 2007e ) and Babanin ( 2009 ). A new kinetic-dynamic approach will
be described in a separate subsection (7.1.2) .
In a general case, the spectral dissipation S ds (

f , k ,θ) in (2.61) is a function of frequency

, but the theories so far only deal with omni-directional
frequency-dependent dissipation which is assumed to be a function of spectrum F

f , wavenumber k and direction θ

( f ) :

n

S ds ( f ) ∼ F ( f ) . (7.1)

Even in this relatively simple setup, the diversity of outcomes is such that proposed expo-
nents n vary in the range n

1-5, that is from the dissipation being a linear function of
the wave spectrum to being highly nonlinear.

=