Definitions for wave breaking - Breaking and Dissipation of Ocean Surface Waves - page 19

The residual-breaking process should be important for upper-ocean mixing (see
Section 9.2.1 ). As far as the wave field and boundary-layer interactions are concerned,
however, the dynamic impact of the breaking event by this stage is already spent: the wave
has already lost the associated momentum and energy to turbulence and mean currents, the
air bubbles have been injected under the surface and the droplets suspended into the air, and
flow-separation and other impacts on the atmospheric boundary layer are exhausted. The
wave as such has already left the point of the underwater turbulent front and even if there
is interaction of surface waves with this enhanced sub-surface turbulence, it is subsequent
waves in the wave train that are now involved.

2.4 Classification of wave-breaking phases

Thus, following Liu & Babanin ( 2004 ) we classify the wave-breaking process into four
stages: incipient breaking, developing breaking, subsiding breaking and residual breaking.
As discussed in Section 2.2 , we expect both whitecapping-based breaking measurements
and analytical approaches based on limiting breaking-onset criteria to detect the same
breaking events only at the developing stage of breaking phases. The incipient breakers, for
example, will be detected by the wavelet method and will not be detected by measurements,
and the subsiding breakers, on the other hand, will be detected by measurements whereas
the wavelet method will fail to pick them up ( Liu & Babanin , 2004 ).
The relative durations of the different breaking phases are not immediately clear, espe-
cially those of incipient and subsiding phases, as these are the least investigated. If the latter
two phases are comparable in terms of duration, then the breaking count, i.e. total num-
ber of breakers detected on the basis of measurements and those obtained by the wavelet
approach will be the same, even though there will be no 100% match of waves indicated
as breakers. This is checked in Figure 2.4 .
Two kinds of counts are shown here: total breaking counts are designated with open
triangles and counts of perfect matchings are designated by triangles with a circle inscribed
inside. The Lake George finite-depth cases are shown by triangles with vertex points up,
and the Black Sea deep-water cases are shown with triangular vertex points down.
The straight line through points of total breaking counts in the figure is the one-to-one
correlation line. The points follow the line with a 0.94 correlation coefficient and a 0.19
deviation index ( DI ) defined as

M |

1 N wavelet − N measured |

N measured

DI = (2.2)

where M is the total number of records available and N measured and N wavelet are the break-
ing cases detected by measurements and by the wavelet method respectively.
Thus, the wavelet method effectively predicts the same breaking statistics as the mea-
surements, based on single-point observations of whitecaps or related acoustic noise. This
implies that the incipient and the subsiding phases of wave breaking have approximately
the same relative duration.