Definitions for wave breaking - Breaking and Dissipation of Ocean Surface Waves - page 34

In the case of a single breaker, they can be approximately related to severity s through the
number n g of waves in the group:

s = n g s g . (2.34)

The number n group is different to the number n of breaking waves in (2.4) and (2.21)
because typically there is more than one individual wave breaking within a wave group
in close proximity in time and space (e.g. Donelan et al. , 1972 ; Babanin et al. , 2009a ,
2010a ; Galchenko et al. , 2010 , among many others). As has already been mentioned, field
observations by Donelan et al. ( 1972 ) revealed several consecutive waves breaking at the
peak of the group envelope. This was interpreted in a quasi-linear sense: that is, subsequent
waves propagate with their phase speeds within the group according to (2.19) , exceed a
limiting height/steepness as they approach the peak of the group and keep breaking until
sufficient energy is lost from the group. Babanin et al. ( 2009a , 2010a ), in a laboratory
experiment with two-dimensional wave breaking due to modulational instability, found
that the number of one-after-another breaking waves in a wave group can be one or more,
depending also on wind forcing and breaking severity. They showed that subsequently
breaking waves are strongly coupled if the breaking strength is large enough.
Therefore, subsequent breaking of a number of waves on the top of the wave group is
effectively a single breaking event in the dynamics of groups. Although different individual
waves are breaking, they cannot be separated in order to measure the wave-group energy
loss (2.32) for each of the breakers. Thus, a typical scenario for a breaking event is

n group = 1 ,

(2.35)

n ≥ 1 .

In this regard, it is helpful to introduce a group-breaking probability b Tg in terms of the
relative number of wave groups containing one or more breaking waves coupled in such a
way that they can be treated as a single breaking event:

n group T g
t

n group
N group

b Tg = = (2.36)

where T g is the period of the wave group and N group is the total number of wave groups in
the wave record.
These issues of individual waves breaking within the group can be illustrated by means
of Figures 6.2 and 6.3 in Chapter 6 . Starting from Figure 6.3 , we can see what happens with
waves propagating through the group without breaking or with only gentle breaking. The
time series are compared immediately before (solid line) and immediately after breaking
(dashed line). Breaking of the four incipient breakers (highest waves in each solid-lined
wave group) started and ended between the two probes. The breaking was very gentle
when observed visually and the wave following this gentle incipient breaker did not break.
The time necessary to travel the distance between the two probes was estimated as 1 . 04 s

and therefore the dash-lined record was shifted back by 1 . 04 s in order to superpose the

two wave trains.