Definitions for wave breaking - Breaking and Dissipation of Ocean Surface Waves - page 28

which charac-
terises the speed of propagation of wave energy. The difference is significant, and for linear
waves in deep water the ratio is

The phase speed c (ω) of waves is different to the group velocity c g (ω)

g
k =

d dk = 1

2

1
2 c

1
2

g
ω .

c g = = (2.19)

Group velocity is another most important characteristic to be employed in wave-breaking
studies as it describes the speed of wave envelopes (e.g. Yefimov & Babanin , 1991 ). The
dominant waves exist as wave groups whose elevation envelope decays away from the peak
magnitude close to the centre of the group. Thus, the individual waves propagate through
the group at a relative speed 2 c and correspondingly change their height as they propagate.
Close to the centre of the group their height/steepness is largest, and that is where they
most frequently break.

2.7 Breaking severity

Breaking severity is another most important characteristic of wave breaking. By breaking
severity, or breaking strength, we mean the amount of energy lost in an individual breaking
event. Note that in the spectral wave environment the breaking of a wave of a certain scale
can mean or involve loss of energy, or sometimes gain of energy by waves of other scales.
Here, we will be interested in defining this property in such a way that, taken together with
the breaking probability from Section 2.5 , they will determine the wave energy dissipation
rate. This way, if both the breaking probability and breaking severity can be measured
experimentally, whitecapping dissipation can be estimated experimentally including the
spectral distribution of the dissipation. So far, spectral dissipation functions employed in
wave models remain, to a large extent, speculative formulations.
Note also that in the case of breaking severity a breaking event does not comprise a
breaking wave only, but rather the wave group which the breaking waves are propagating
through. Such detail is essential and will be discussed in the current section. As with the
breaking probabilities in Section 2.5 , however, there are further uncertainties even within
such a simple and general definition. In the case of breaking severity, these uncertainties are
even deeper due to the fact that this property has received far less attention, and the energy
loss in the course of breaking is a much less studied process compared to the phenomena
leading to breaking occurrence.
Difficulties in studying breaking severity are indeed serious. While hydrodynamic
theories, even simplified versions of them such as those based on irrotational wave
motion and assumptions of small initial amplitudes and disturbances, can be employed to
investigate the probability of a breaking onset, they are clearly not applicable once the
onset happens. On their own, no such theories can describe in detail the process of wave
collapse and the associated energy loss in the generation of turbulence, entraining the air
bubbles and pockets into the water and emitting spray into the air. In the absence of a
theory, the numerical modelling of breaking strength suffers obvious limitations too. With