Conclusions. What else do we need to know about wave breaking? - Breaking and Dissipation of Ocean Surface Waves - page 422

even a reasonable conclusion on how frequent breaking due to frequency focusing is in a
wave field with a typical background wave steepness and typical wave spectrum.
The amplitude dispersion intuitively seems a less likely event compared to the frequency
focusing because differences in wave phase speeds due to the amplitude variation are
only of the second order of magnitude. This type of focusing, however, can bring together
waves of the same frequency and therefore of close wave heights, and thus can make the
breaking of a primary wave more probable. Again, parameterisation of the breaking rates
due to this type of focusing, or in combination with the other types is not available.
The directional focusing does not rely on the dispersion, but on the contrary on waves
propagating with close phase speeds, at an oblique angle with respect to each other. As
with the amplitude focusing above, the advantage of directional focusing is the fact that
waves of a similar frequency/height are brought together, and therefore fewer waves are
required in order to reach the steepness limit, but the disadvantage is that the steepness of
the waves in the converging trains, if these are two trains, has to be close to half of the
limiting steepness which is too high for typical wave fields. This, again, makes such a type
of focusing a rare event, as shown in Section 5.3.3 .
As a result, none of the focusing mechanisms lends themselves as obvious likely can-
didates to provide the reasonably high breaking rates observed in oceanic wave fields.
Quantitative comparisons of the focusing-breaking probability with the probability due to
modulational instability are impossible because of the lack of respective experimental or
theoretical dependences for the former.
Parameterisations of the wave breaking brought about by the instability of quasi-two-
dimensional wave trains are available and the corresponding breaking rates are quite con-
sistent with those observed in the field ( Section 5.1.4 ). The fact that the modulational
instability is active in the directional fields makes it a likely cause for the majority of the
dominant breaking in the ocean (breaking of the shorter waves is mostly induced, unless
the coherent-wavelet structure is present at those scales, as discussed below).
In this regard, it is worth briefly revisiting a number of features of nonlinear wave
behaviour leading to the modulational-instability breaking, which were revealed both in
the two-dimensional simulations/measurements and in field observations, as mentioned
throughout the topic. The main such feature is the wave-breaking threshold in terms of
the mean background steepness of field waves. This is the typical behaviour of modula-
tional instability, leading to the breaking in two-dimensional wave trains also, and even
the steepness thresholds are consistent in the 2D trains and directional fields as discussed
in Section 5.1.4 . The focusing, whether this is linear or nonlinear, cannot explain such a
threshold feature. If the focusing was the main reason for wave breaking, it should lead
to the gradual vanishing of breaking as the steepness asymptotes zero, rather than to a
cessation of the breaking at some threshold value of steepness.
Other features observed both in the wave flumes and in the field, and characteristic of
the modulational instability, are the upshifting of spectral energy prior to breaking and the
oscillations of the skewness/asymmetry. Loss of energy by the primary breaking compo-
nent is a certain feature of the wave-instability breaking, which in this way is similar to the