Detection and measurement of wave breaking - Breaking and Dissipation of Ocean Surface Waves - page 71

In reality, however, breaking is principally unsteady, and this brings about a proportion-
ality coefficient broadly called the breaking parameter b br . Measurements within realistic
unsteady-breaking conditions in the laboratory and in the field have seen b br varying by
some two to four orders of magnitude (see Section 7.4 for more details). Some studies
pointed out its dependence on wave steepness ak (e.g. Melville & Matusov , 2002 ; Drazen
et al. , 2008 ), others argue that it is not the average steepness (1.1) , but rather local variations
of the steepness, that is wave slope, crest-to-wavelength ratio, along with other character-
istics such as density of the whitecapping foam, relative orbital velocity (with respect to
the phase speed) that form such a breaking parameter b br ( Gemmrich et al. , 2008 ).
If we identify a range of open ocean-sea-lake peak frequencies very broadly as f p

=

10 3
according to (3.27) , which is only two orders of magnitude. That is, the predicted range of
change of the dissipation based on the Duncan ( 1981 ) hypothesis is comparable or even less
than the range that can be inflicted by uncertainties brought about by the 'proportionality
coefficient' b br . Given the fact that hypothesis (3.27) has been widely exploited in the
wave-dissipation literature lately, it should be emphasised that its practical significance
appears in fact rather low in the light of the enormous variability of this proportionality
coefficient.
Besides, the connection of dissipation in a breaking wave with its phase speed is clearly
not applicable in the case of induced breaking, i.e. the breaking of short waves caused by
large waves, whereas such cumulative dissipation tends to dominate at high frequencies
( Babanin & Young , 2005 ; Babanin et al. , 2007c ). Therefore, even if the proportionality
coefficient in (3.27) could be adequately quantified, the dissipation formulation of this
kind, strictly speaking, is only applicable at the spectral peak region, where the cumulative
effect is negligible. The cumulative effect is also absent below the peak, but clearly the
dissipation (3.27) is not suitable there as it would have to keep growing towards longer
waves, which contradicts common sense.
Generation of deterministic unsteady breaking in the laboratory has been most fre-
quently attempted through focusing the wave energy by using wave frequency dispersion.
The waves are generated mechanically with frequency being linearly decreased and thus
the group velocity increased (2.19) . As a result, linear superposition of waves in a pre-
determined location is achieved (although at the later stages, because of the increasing
average steepness in the converging wave packet, some essential nonlinear interactions take
place ( Brown & Jensen , 2001 )). The technique was originally suggested in ship design test-
ing ( Cummins , 1962 ; Davis & Zarnik , 1964 ) and was introduced into the broad research of
wave breaking by Longuet-Higgins ( 1974 ), since when it has been employed in numerous
laboratory experiments.
The most comprehensive study of this kind is that by Rapp & Melville ( 1990 ). Laser
Doppler velocimetry was used to obtain two components of the velocity in the breaking
region, but the main wave-measuring probes were simple surface-piercing resistance wires.
Since the method allows positioning of the breaking location quite precisely, energy losses
and other relevant information concerning the breaking can be obtained with only two wave

10 5 -4 0 . 1-0 . 3 Hz, then the range of dissipation rates at the spectral peak S ds ≈ 9 · ·