Non-dissipative effects of breaking on the wave field - Breaking and Dissipation of Ocean Surface Waves - page 348

interesting to note that the phase-average profile of the breaker does not exhibit a noticeable
asymmetry of the wave with respect to the vertical.
The phase-average profile of the pressure induced by the breaking wave, however, is
very asymmetric ( Figure 8.7 b). While the wave-induced pressure profiles for non-breaking
and non-segregated waves exhibit an evident shift of the pressure maximum towards the
windward wave face, which one should expect for the strongly-forced Lake George waves,
the shift in the asymmetric breaking-induced profile is much greater. The magnitude of the
breaking-induced pressure is also much larger. Together, this leads to the overall breaking-
induced flux enhancement demonstrated in Figure 8.7 c. This is of the order of two when
integrated over the phase-average profile. Again, as in Figure 8.6 , the flux normalisation
was done on the basis of the windward-face steepness.
Thus, in summary, a significant phase shift in the local wind-pressure signal was detected
that was clearly associated with wave-breaking events. These results provide strong field-
observational support for the proposition that local air-flow separation accompanies local
wave-breaking events. Moreover, these strong modifications can result in significant enhan-
cement, of the order of two, to the energy flux from the wind to the wave field.
The parameterisation of the non-breaking wind input was proposed by Donelan et al.
( 2006 ) and applies to a spectrum of wind-waves. In regard to parameterising the input
associated with breaking waves, it is important to note that the findings in Figures 8.6 and
8.7 are based on the observed behaviour of the dominant wind-waves. The results shown
earlier in Figures 8.4 - 8.5 were, however, obtained for any waves that could be determined
by a zero-crossing analysis, which here included waves of up to twice the dominant wave
frequency (see Manasseh et al. , 2006 ).
While the present study has shown clearly that air-flow separation is operative for such
breaking waves, it would be desirable to verify directly that this same effect is also oper-
ative for short breaking waves riding on much longer non-breaking waves, a commonly
observed occurrence at sea. This will require an open-ocean version of a wave-following,
near-surface aerodynamic-pressure measurement system, which is a particularly challeng-
ing measurement to make successfully.
If we adopt the standard mean value of two times the mean flux for the energy-flux
enhancement, then this breaking-induced enhancement of the wind input to the waves can
be parameterised as the product of the non-breaking input with this factor of two. This con-
tribution then needs to be weighted by the breaking probability for these waves. Babanin
et al. ( 2007b ) proposed such parameterisation as

γ( f ) = γ 0 ( f )( 1 + b T ( f )) (8.28)

where γ 0 ( f ) is the spectral wave-growth rate increment in the absence of wave breaking

and b T ( are

spectral functions (see Donelan et al. , 2005 , 2006 ; Babanin et al. , 2001 , for detailed defi-
nitions, respectively). In this regard, see also Section 5.3.2 for discussions of the problem
of wave breaking in the spectrum based on field breaking-wave observations over a range
of spectral scales.

f ) is the associated breaking probability (2.3) . Here, γ( f ), γ 0 ( f ) and b T ( f )