Wave-breaking severity - Breaking and Dissipation of Ocean Surface Waves - page 224

( Sections 4.1.3 and 5.1.3 ). Therefore, it appears that the wind does affect the severity in a
most essential way, but it does this indirectly.
As seen in Figure 5.2 , forcing of the nonlinear mechanically generated waves by the
wind in the course of their evolution does not prevent modulational instability, neither
does it change the number of waves in the modulation. It does, however, affect the depth
of the modulation R (5.3) which is reduced significantly. It is therefore this depth that can
perhaps be used as an indicator of breaking severity when modulational-instability physics
is involved.
Since other modulational properties of the wave train appear to be the same, the depth R
most likely simply indicates the change of instability growth, which slows down. Such an
effect was predicted theoretically by Trulsen & Dysthe ( 1992 ) based on numerical exper-
iments on a nonlinear Schrödinger equation with an added linear-growth term to simulate
the wind forcing.
The waves break, however, not because the wave group reaches some limiting value
of R , but because individual waves within this group reach the limiting steepness (2.47) .
Growth of the individual-wave steepness is determined both by the growth of the modula-
tion of the group and by direct energy input from the wind to these individual waves. Thus,
even though the instability development slowed down, the waves still reach the limiting
steepness and break. The severity of the breaking, however, is very different under the cir-
cumstances of lower instability-growth rates. Thus, the wind action alters the modulation
depth and instability growth on a longer time scale, and the hydrodynamics related to the
modulation itself controls the breaking strength at the short scale of the duration of the
breaking process.
If so, the breaking severity, like other wave-breaking features, depends mostly on hydro-
dynamics rather than on air-sea interactions. In order to investigate this dependence in
pure hydrodynamic conditions, Galchenko et al. ( 2010 ) conducted a laboratory experiment
where wind action was removed and different depths of the modulation at the breaking
onset were achieved by imposing various sidebands, both in terms of their steepness and
frequency separation of the primary wave and the sideband.
The experiment was carried out in a wave tank of the Department of Hydraulic and
Ocean Engineering of the National Cheng Kung University, Taiwan. A programmable pis-
ton wavemaker was used to produce the wave trains with primary waves of steepness

1 ,

sideband of steepness 2 , and bandwidth ν such that the number of waves in initial mod-

ulation was N m = 9, close to that typical of ocean waves (see (2.12) ). Surface elevations

were measured and recorded by means of a one-dimensional array of six capacitance-type
wave gauges deployed along the main axis of the tank. Thus, when a breaking happened
within the array, it was possible to estimate the wave energy within the group where the
breaking occurred, before and after the breaking. The severity s g was defined for the wave
groups according to (2.32) .
In Figure 6.4 , s g (denoted as S in the figure) is plotted versus R where the modula-
tion depth is estimated immediately before breaking. The scatter is large, but the positive
trend is robust. As anticipated, the severity appears to be a function of modulation depth:

6 .