Wave-breaking severity - Breaking and Dissipation of Ocean Surface Waves - page 223

0.04

0.02

0

−0.02

−0.04

0 2 4 6 8 10 12 14 16

time, sec

Figure 6.3 As in Figure 6.2 , with wind forcing. A segment of the time series with IMF = 1 . 5Hz ,
IMS = 0 . 30 , U / c = 3 . 9. Solid line - surface elevations at the second probe prior to breaking. Dashed
line - same waves 1.04 s later at the third probe. The waves propagate from right to left (shifted back
and superposed). Figure is reproduced from Babanin et al. ( 2010a ) by permission

Again, the wave time series are compared immediately before and after breaking. The
solid line shows the waves of IMF

9 at the second probe
and the dashed line at the third probe. Breaking of the four incipient breakers seen at
probe 2 occurred between the two probes. The breaking was very gentle when observed
visually, and there was no double-breaking. With IMF

= 1 . 5Hz , IMS = 0 . 30 , U / c = 3 .

= 1 . 5 Hz, the time necessary to

travel the distance between the two probes is estimated as 1 . 04 s and therefore the record

made on the third probe is shifted back correspondingly.
As was analysed in Section 2.7 , because of the difference of the phase speed and group
velocity each of the solid-lined waves would move approximately one position ahead
within the envelope, and the highest wave should become the second highest (in front of
it) in the dash-lined group. Because of this, the height of the wave which was the highest
at the previous probe would be significantly reduced even without breaking, but the overall
picture of the wave group would remain the same.
Breaking, even though gentle, however, happened and comparison of the breaking impacts
in Figures 6.2 and 6.3 is quite instructive. In Figure 6.2 , the incipient breaker and the wave
following it practically disappeared, as well as the entire modulation. In Figure 6.3 ,they
are all present and each wave in the modulation can be tracked at the third probe. The
energy loss was minimal and could not have been quantified within the confidence limits
of the respective spectra.
In contrast to Figure 6.2 , after the breaking in Figure 6.3 the number of waves did
not change and no downshifting is visible. As seen in the figure, the breaking resulted
in some truncation of the crest of the highest wave in the group, and in smoothing of the
modulation.
The latter, we believe, is a most essential observation. The fact that the wind influ-
ence reduces the modulational-instability growth and smears the modulation has already
been noticed (i.e. Figure 5.2 , Section 5.1.3 ). It was also seen that the wind impact on the
wave breaking as such, at the wave-breaking time scale, is always small or even negligible