Energy dissipation across the wave spectrum - Breaking and Dissipation of Ocean Surface Waves - page 244

With these potential limitations in mind, we shall return to other very interesting conclu-
sions of Iafrati ( 2009 ) regarding the rate of wave-breaking dissipation. In temporal domain
t , from start to finish of the plunging-breaking active phase, the total energy appears to
follow the dependence of

t − 1

E T ( t )/ E T ( 0 ) ∼ . (7.13)

Again, if confirmed as a general feature of wave-breaking dissipation, such a function can
provide a principal transition in understanding and presenting the dissipation function. Like
other source/sink functions in (2.61) , the dissipation term can then be approached in physi-
cal terms of the gradual evolution of a wave spectrum due to such dissipation, rather than in
empirical-parameterisation terms of what was with the spectrum/wave-energy before and
after a breaking event.
Iafrati ( 2009 ) then follows on to elucidate what processes contribute to the observed
plunging-breaking dissipation, and to quantify their relative importance. Immediately after
the jet impacts the free surface, two additional active subsurface phenomena appear. The
first is a strong rotational flow in the water caused by the large air cavity entrapped, and
associated viscous dissipation. The second is work against the buoyancy forces (see also
Lammarre & Melville , 1991 , 1992 ; Blenkinsopp & Chaplin , 2007 ).Asfarasthewave
energy dissipation is concerned, these two processes can be regarded as independent and
studied separately.
Therefore, the efficiency and magnitude of different terms in the total-energy balance
equation are investigated. The viscous dissipation rate, in the most severe cases, grows up
to an order of magnitude following the breaking onset. This high dissipation level can last
for about one wave period. After that, the viscous dissipation itself adopts a t − 2 decay rate.
The overall contribution of the viscous dissipation, however, was only about 15% of the
initial energy, which is just one third of the 45-55% energy loss (about one half is spent on
work against buoyancy as mentioned above). At the opening stage of the wave breaking,
i.e. during the first half-wave-period, the viscous dissipation is even less and only accounts
for some 2% of the energy loss. The bulk of the energy in these early times is spent on
work done in accelerating the air phase of the fluid mixture, which has been still before
breaking. For the rest of the dissipation sources, Iafrati ( 2009 ) concludes that the role of the
normal and tangential stresses at both sides of the interface is essential too, but the model
in its presented version was not able to provide reliable estimates in this regard.
In physical space, the dissipation is mainly localised in a narrow layer below the surface
around small air bubbles produced by the collapse of the large air cavity captured by the
plunger.

“Sharp velocity gradients are induced by the interaction of the rotating structures with the surround-
ing fluid at rest”.

The simulations of Iafrati ( 2009 ) were two-dimensional, and analyses of three-
dimensional breaking by means of two-phase models are also available. Most of such
modelling efforts are dedicated to shallow waters, which are apparently more interesting