Wave-breaking probability - Breaking and Dissipation of Ocean Surface Waves - page 142

5
Wave-breaking probability
As already mentioned in Chapter 2 dedicated to definitions of wave properties and phe-
nomena related to wave breaking, the breaking probability, or as it is also often called
breaking rate or frequency of breaking occurrence is one of the most important statistical
characteristics of wave fields that contain the breaking events. Technical definitions for the
breaking probability are given in Section 2.5 .
Together with the breaking severity ( Section 2.7 , Chapter 6 ), the probability defines the
wave-energy dissipation due to wave breaking. Knowledge of such dissipation is required
across a broad range of wave-related applications, with the wave forecast being the most
frequent and obvious, and therefore the breaking occurrence has enjoyed key attention
within wave-breaking studies.
Experimental and statistical techniques of breaking-probability studies have been dis-
cussed in detail in Chapter 3 , and theoretical approaches in Chapter 4 . As described in
these chapters, in the past parameterisations of the breaking rates in terms of environmen-
tal characteristics have usually relied on wind speed or its derivatives. In this topic, we
have argued that, although the wind is of course essentially responsible for the formation
of fields of wind-generated waves, its capacity to directly trigger or even affect a break-
ing event is only marginal, except perhaps for very strong wind forcing. Breaking mainly
happens due to hydrodynamic phenomena, that is due to processes in the wave train itself.
Therefore, as far as the wave-breaking probability is concerned, the wind influence is indi-
rect and parameterisations have to be done in terms of the properties of wave fields. In this
chapter, we will concentrate on the latter approach and will describe the hydrodynamics
which controls wave-breaking occurrence and rates.
In Section 5.1 , we start from breaking events that develop within trains of initially
monochromatic waves due to the modulational instability of such wave trains. While the
frequency of breaking occurrence depends on the initial monochromatic steepness, there is
a steepness threshold below which the breaking does not happen. Such a threshold is of key
importance, both for monochromatic wave trains and directional wave fields, and points to
the course of breaking in real oceanic conditions. It will be scrutinised in Section 5.2 .
Breaking in wave fields with a continuous spectral distribution of wave scales will be dis-
cussed in Section 5.3 , which is subdivided into further subsections. The wave spectrum
usually has a narrow and sharp peak, and the physics of breaking of the dominant waves,
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