Energy dissipation across the wave spectrum - Breaking and Dissipation of Ocean Surface Waves - page 243

(here, we have diverged from the original symbols employed by Iafrati ( 2009 ) for consis-
tency throughout this topic). Decay of both E K and E P , as well as of the total energy

E T = E K + E P (7.12)

were scrutinised.
For non-breaking waves of

= . = .

3, the total-energy decline is well described
by theoretical expectations due to the action of viscosity (e.g. Landau & Lifshitz , 1987 ).
Once the breaking threshold (7.9) for background steepness is exceeded, the energy
dynamics becomes much more interesting.
Unfortunately, only one spilling-breaking case (

0 2 and 0

35) is analysed in Iafrati ( 2009 ),
and therefore it is impossible to draw conclusions about the trends and dependences for
this class of dissipation. Compared to viscous decline, the rate of energy drop is much
larger, and some 25% of additional loss is observed. It is interesting that in dimensional
terms, the time history of this spilling-breaking dissipation eventually leads to the same
energy level as in the threshold case of no breaking (steepness

= 0 .

3). If it is confirmed
that there is a consistent outcome, whatever the mean steepness, if it results in a spilling
breaking, then the energy will be reduced to the (7.9) -threshold level - then parameterising
the spilling dissipation would be a relatively straightforward task, for example, by means of
probability models described in Section 7.1.1 . This guess would need further investigation,
particularly important as spilling breaking is the most frequent breaking occurrence at sea,
at least for energetic waves (see Section 2.8 ).
The plunging breaking in Iafrati ( 2009 ) is essentially stronger, but dissipation, instead of
approaching some constant dimensional level ultimately, with some scatter asymptotes to
some constant dimensionless level of approximately 45-55%. Such a result, if confirmed,
first of all provides a very apparent distinction between the spilling- and plunging-breaking
dissipation. Secondly, the outcome is in excellent agreement with the experimental esti-
mates of Rapp & Melville ( 1990 ).
The latter fact, however, may outline limits on the conclusions drawn as a result of
breaking simulations by Iafrati ( 2009 ). As discussed in Sections 2.7 and 6.1 , the certain-
percentage loss of initial wave energy to breaking is a feature of breaking caused by the
linear superposition of waves. Modulational-instability breaking may result in any amount
of loss, from virtually 0% to 100% when the breaker disappears. Since the latter breaking
cause appears more likely in field conditions ( Babanin et al. , 2011a ), the topic needs further
research, specifically into dissipation due to modulational-instability breaking.
This further research would need to be extended to simulations of breaking within wave
groups, rather than of single waves, as the depth of the nonlinear-group modulation appears
to be at least one of the properties well correlated with modulational-breaking severity
( Section 6.1 , Galchenko et al. , 2010 ). Alternatively, the individual waves can be simulated
as before, but the initial conditions for the surface elevations and velocity distributions
should be taken as those characteristic of the breaking onset brought about by modulational
instability. This can be achieved, for example, by coupling the output of the Chalikov &
Sheinin ( 2005 ) model with the input of the Iafrati ( 2009 ) model.

= 0 .