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Figure 1.1 Wind-wave pattern at a moderate wind. Waves of all scales are present simultaneously,
representing a continuous wave spectrum. Only a small fraction of them are breaking at each scale.
Gulf of St Vincent, Indian Ocean, August 2010
So-called whitecapping dissipation is the dissipation due to wave breaking, but it is
not always that waves form whitecaps when they break (i.e. so-called micro-breaking
discussed in Section 2.8 below). Since such a notion contradicts the general intuitive
perception of wave breaking, we first have to answer a question: what do we call wave
breaking?
1.2 Concept of wave breaking
Definitions pertaining to different physical and mathematical aspects of the wave breaking
process will be formulated in Chapter 2 . Here, we would like to discuss a common concept
of breaking - that is what is a wave-breaking event and how is it generally perceived?
In Figure 1.2 , a linear harmonic sinusoidal wave (sometimes called Airy wave), a Stokes
wave, and an incipient breaker of the same height and length, i.e. all waves of the same
average steepness, are compared graphically. This figure tests our ability to describe non-
linear behaviour of waves theoretically. The Stokes wave is a perturbation solution of
hydrodynamic equations, assuming that the steepness of the waves is small. Obviously,
although this traditional approach does produce a nonlinear wave shape, it does not look
like anything close to a breaking wave as we perceive it (dash-dotted line). Needless to say
the steepness of a breaking wave can hardly be expected to be small.
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