Geoscience Reference
In-Depth Information
As mentioned above, the individual waves and the group propagate with different speeds.
In the case of deep-water waves of 1
5 Hz frequency shown in Figure 6.3 , and in a close-
to-linear scenario, according to (2.19) the relative speed of wave propagation within the
group is c relative =
.
0
.
52m
/
s and the relative position of a wave over 1
.
04 s will be shifted
by 0
69m. That is, in
the absence of breaking, each wave would move approximately one position ahead, and the
highest wave in the solid-lined group would become the second highest (in front of it) in
the dash-lined group. Because of this, the height of the highest wave would be significantly
reduced without any breaking.
Since breaking does occur, the pattern is more complicated. The breaking was quite
gentle visually, and indeed its impact on the individual wave that broke (now the sec-
ond wave in each dash-lined group) is not that large. It is quite significant, however, over
the entire group because of, obviously, nonlinear coupling between different waves in the
course of the breaking event. Other details of such a breaking impact will be discussed in
Chapter 6 ; here we would like to highlight the fact discussed above: that is, in the case of
wave breaking within a wave-group structure, estimating the breaking strength in terms of
measurements of the breaking wave only is ambiguous and even misleading.
This is even more valid for strong breaking, when two or more subsequent waves break
one after another. This is demonstrated in Figure 6.2 . Again, wave series immediately
before and after the breaking are compared. Breaking of the three incipient breakers seen
in the solid-lined wave train happened (started and finished) between the two probes. The
wave that is seen following the incipient breaker at the second probe also broke between the
two probes. These breakings happened in a period of 1
.
5m. This is comparable with one wavelength of such waves,
λ =
0
.
2 s, the time required by the waves
to travel the distance between the probes. Therefore, the dash-lined record is time-shifted
by 1
.
2 s in an attempt to superimpose the two wave trains.
Now that a strong breaking has occurred, the correlation between the two time series
is quite poor. The incipient breaker and wave following it practically disappeared, as well
as the entire modulation. The number of waves in the segment has also changed. This is
a collapse of the wave group which from this point in time and space should restart its
evolution in hydrodynamic terms, from the new initial conditions. Again, further details
will be examined in Chapter 6 , but it is apparent that the severity can only be estimated in
terms of the wave group (2.32) rather than in terms of individual waves.
The third reason for (2.27) -like constant-fraction estimates of the severity coefficient
s being not general is the influence of various environmental conditions on real wave
fields. Ocean waves are directional (i.e. three-dimensional), wind-forced and experience
many sorts of interactions with background currents, turbulence and other phenomena
that may affect the breaking strength, with or without alterations of the breaking prob-
ability. For example, Babanin et al. ( 2009a , 2010a ) demonstrated that the presence of
wind increases the breaking probability due to modulational instability of nonlinear wave
groups, but decreases the breaking severity. This reduction extends to the severity becom-
ing virtually zero at reasonably strong wind forcing, which effectively means that the wind
may essentially impair or even erase breaking caused by the evolution of wave groups.
.
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