Energy dissipation across the wave spectrum - Breaking and Dissipation of Ocean Surface Waves - page 253

belonged. Then, their broader spectral outputs can be interpreted in the context of discus-
sions of Section 7.3.2 . That is, attempts can be made to not only quantify the breaking
outcome, but also to understand, based on the spectral distribution of the dissipation, what
are the physical courses of the breaking in the field.
In this regard, two separate passive acoustic methods were employed (see also Section
3.5 ). The spectrogram method was applied by Young & Babanin ( 2006a ) to determine the
dissipation due to breaking of the dominant waves only. The individual-bubble detection
technique of Manasseh et al. ( 2006 ) allows study of the breaking, and links the dissipation
effects to different narrow frequency bands, starting from below the spectral peak and up
to double the peak frequency 2 f p .
The spectrogram method developed by Babanin et al. ( 2001 ) was used by Young &
Babanin ( 2006a ) to investigate differences between pre-breaking and post-breaking wave
spectra. Such differences, when attributed to the breaking, should clarify the spectral con-
tribution of the breaking, including the directional distribution of this contribution.
For the analysis, a wave record with an approximately 60% dominant-breaking rate was
chosen (record 5 in Table 5.2 ). This was as close as possible to a 50% rate which would
mean that half of the time waves within a single stationary record were breaking and half
of the time waves were recovering from the breaking loss. The 50% division of the record
into breaking/non-breaking parts enabled Young & Babanin ( 2006a ) to estimate spectra of
breaking and non-breaking waves with similar confidence intervals. The waves were sta-
tionary (scatter of 1min standard-deviation surface elevation, relative to the 20min mean,
was less than 10%, with no drift of the mean) under steady U 10 = 19 . 8m / s wind, with

peak frequency f p = 45m. The parameterisa-

tions of Young & Verhagen ( 1996 ) and Young & Babanin ( 2006b ) were used to verify that
the waves were fully developed in the bottom-limited environment with a measured depth
of d

0 . 36 Hz and significant wave height H s = 0 .

= .

1m. The wave record was 20min-long and was segmented into five breaking
parts and four non-breaking parts.
In this strongly forced situation, approximately half of the waves were actively breaking.
It was assumed that those waves not breaking had recently done so, having lost their energy
in the breaking process. This assumption seems reasonable in this highly forced but steady-
in-the-mean environment and the analysis that follows is predicated on this assumption.
Models of wind-waves, both physical and numerical, implicitly accept a double-scale
approach to the wave field (see e.g. Melville , 1994 ; Lavrenov , 2003 ). This implicit assump-
tion is important for correct interpretation and treatment of the wave breaking, and we shall
discuss it here referring to the radiative transfer equation ( Section 2.10 ) that is routinely
employed in the wave spectral modelling.
At long scales of thousands of wavelengths and periods, the waves are assumed to be
evolving. In a general case, at this scale the left-hand side derivative in (2.61) is positive
as the waves grow under wind forcing. If the wave field is stationary and characterised
by constant-depth (or deep) conditions, the evolution along the wave fetch is described by
the advective term on the left-hand side of (2.61) which is small (less than 5% according
to Donelan ( 2001 )) compared to the wind input S in and the dissipation S ds on the right-

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