Wave-breaking probability - Breaking and Dissipation of Ocean Surface Waves - page 148

IMS 23 are plotted (see the third subplot for comparisons with waves of the same

IMS evolving without wind forcing). Whilst the number of waves in the modulation did
not seem to change, the depth of the modulation R changed dramatically:

= 0 .

H h
H l

R = (5.3)

where R is the height ratio of the highest H h and the lowest H l waves in the group. The
difference in modulation depth is 1.6 times - it changed from R = . = .

3.
The shallower depth of the modulation means that development of the modulation
is slowed down by the applied wind forcing. This effect was predicted theoretically by
Trulsen & Dysthe ( 1992 ). In the experiment, it was observed that this change also led to
a very significant reduction in the breaking severity (see Chapter 6 below). The severity
(energy loss in a breaking event, see Section 2.7 for definitions) is a very important break-
ing property as, along with the frequency of breaking occurrence (breaking rate) discussed
in this chapter, it defines the energy dissipation in a wave field.

2 1downto R 1

5.1.1 Evolution of nonlinear waves to breaking

Nonlinear evolution of two-dimensional laboratory waves to breaking will now be inves-
tigated in a fashion similar to the numerical study of Section 4.1 . We will mainly be
interested in what happens in the physical wave field rather than in Fourier space. Also, we
will deal with individual waves, rather than with average nonlinear properties of the wave
ensemble. The nonlinear characteristics of interest (i.e. individual wave steepness, skew-
ness and asymmetry), will be obtained by means of zero-crossing selection and analysis of
individual waves. In addition to these three characteristics, we will scrutinise the behaviour
of the period (frequency) of individual nonlinear waves. This feature was not examined in
dimensionless numerical simulations, but in the laboratory it appears to be quite variable,
even in the train of waves of initially uniform frequency. The effect of such local-frequency
variation is significant for the breaking-onset study since, when wave-height growth is
accompanied by a synchronous reduction of wave period, this has a combined impact on
the local wave steepness. Like the background-steepness threshold mentioned above, this
modulational-instability feature provides a further hint on this instability as a cause of
wave breaking in the ocean. Multiple indications of such a prior-to-breaking wavelength
decrease are scattered throughout the topic. For example, if the wavelength shrinks, they
have to slow down before breaking which is what the remote-sensing methods observe
(see e.g. Section 3.6 ).
Figure 5.3 shows a wave record with an initial monochromatic frequency IMF

= 1 . 8Hz

and an IMS 30, with no wind forcing. It should be noted that there is a conceptual

change in the frame of reference compared to the numerical-model results. In the case
of the model, a single wave was followed as it approached the point of breaking. Here,
observations are made at a single point as a succession of waves passes. One can move
approximately from the fixed frame of reference in Figure 5.3 to the moving frame by

= 0 .