Wave-breaking severity - Breaking and Dissipation of Ocean Surface Waves - page 227

Coming back to the effects of wind on the modulational instability, Waseda & Tulin ( 1999 )
concluded that

“both effects combined will determine whether the modulational instability is enhanced or

suppressed”.

From Figure 6.4 and (6.1) , one can see that on average the severity approaches zero when

≈ . < .

R 2 2, certainly there is no breaking for R 1 8. This makes it possible to conclude

that R 2 represents a lower limit to modulation depth, below which the probability of

breaking in the absence of wind significantly decreases. In the presence of wind, however,
the modulation depth immediately before breaking can be as low as R

≈ 2 .

1-avaluethat
signifies no modulation by definition (5.3) . This result highlights the fact that the actual
role of the wind in wave breaking in general and in regulating breaking severity is not that
unambiguous and in the latter case does not reduce to a mere controlling of the rate of
modulation development.
The modulational depth, in more general terms, if applied to field conditions, is a prop-
erty difficult to measure and hardly possible to employ in spectral applications as there is
no obvious way how information on such a feature can be obtained from a wave spectrum.
In spectral models, perhaps, some combination of characteristic steepness and bandwidth,
which determine the extent of modulation, and some combination of steepness and wind
forcing, which determine the rate of modulation growth, could be used as parameters
for the breaking-severity dependences. The severity of wave breaking in conditions of a
continuous wave spectrum is the subject of the next section.

∼

6.2 Dependence of the breaking severity on wave field spectral properties

As with breaking probability discussed above, the spectral and directional distribution of
the breaking severity bears the principal uncertainty of how this property, which is not a
continuous sequence of instantaneous values, can be converted into the Fourier space. If
the number of individual breaking events is counted and energy loss in each of them is
measured, then the average value of severity at frequency f in direction

θ will depend on

the choice of frequency bin f , particularly in the case of

a function rapidly changing along frequency/direction (see Sections 2.5 and 5.3.3 for more
discussion).
With this uncertainty in mind, we can discuss the spectral distribution of the breaking
severity in the same way as we did with the breaking probability in Section 5.3.2 . In order
to obtain a distribution similar to that for the probability in Figure 5.27 , we need the count
and the strength-measure of individual breaking events in the spectral and directional bins.
The bubble-detection technique described in Section 3.5 can provide both.
This technique employs the sound emitted by individual bubbles when they are created
in the course of breaking. As seen in Figure 3.9 , detected bubbles can be identified with
a period (frequency f ) of the overlying wave. Information on the breaking strength is
carried by the bubble size R 0 , if detected simultaneously. This is illustrated in Figure 3.12

± f and directional bin θ ± θ