Wave breaking represents one of the most interesting and most challenging problems for both fluid mechanics and physical oceanography. It is an intermittent random process, very fast by comparison with other processes in the wave system. The distribution of wave breaking on the water surface is not continuous, but its role in maintaining the energy balance within the continuous wind–wave field is critical.

The challenges thus outlined make understanding of such wave breaking and even an ability to describe its onset very difficult, and as a result knowledge of the physics of the breaking, and even practical parameterisations of the phenonemon have been hindered for decades. Recently, knowledge of the breaking phenomenon has significantly advanced, and this book is an attempt to summarise the facts into a consistent, even if still incomplete, picture of the phenomenon.

If this picture were to be formulated into a few paragraphs of these conclusions, we would like to say the following. The waves break because the water surface reaches some limiting steepness. Apparently, the fluid interface has to have a limit beyond which it will collapse. In the system of nonlinear water-surface waves subject to a variety of external forcings and internal instabilities, there are a number of physical processes which can lead to such a steepness. They are the modulational instability, linear (dispersive and directional) and nonlinear (amplitude-dispersion) focusing, modulation of steepness of shorter waves by longer waves, direct forcing by the wind (if very strong) or by the current, and wave-bottom interactions, among others.

On many occasions earlier in this book, it has been mentioned and emphasised that knowledge of breaking severity is as important as is understanding the physics driving the breaking occurrence. While the latter, however, has received a lot of attention from the wave-research community lately, our information on breaking strength, its variability, environmental dependences and physics remains limited and fragmental.

If the breaking strength is defined as energy loss in a single breaking event (Section 2.7), then the breaking severity coefficient s can be identified in a number of ways, through measurement of the individual breaking wave (2.24), of the group where the breaking occurred (2.32), of spectra of the respective groups before and after the breaking (2.38) and of short waves modulated by the longer wave only (2.42). The magnitude of such a coefficient varies greatly, from s = 10% (Rapp & Melville, 1990, or even less as seen in Figure 6.3 below) up to 99% (2.31) based on the Black Sea estimates (see also Bonmarin, 1989; Babanin et al., 2010a, 2011a).

Such a range of change of course cannot be disregarded or substituted with some mean value in applications that involve the breaking severity. A typical application is the wave-energy dissipation function Sds employed in wave forecast models (2.21), (2.61) and (5.40).

One of the main roles of wave breaking in the ocean-wave fields is providing the dissipation sink of wave energy (see Chapters 1 and 7). The waves do not grow unlimited in height, and breaking is the main process which restricts this growth even in conditions of continuous wind-energy input over unlimited wave fetches.

Being the loss from the wave system, the breaking dissipation provides a link for the wind-generated waves with other phenomena in the lower atmosphere, upper ocean and on the ocean interface itself. It is a source of energy and momentum for infra-gravity waves, near-surface currents, upper-ocean mixing and the atmospheric boundary layer (e.g. and The WISE Group, 2007).

Some features and physical processes in the air–sea system, related to the breaking, however, are not necessarily of dissipative nature or can be described in terms of the wave-energy dissipation as such, and these are the phenomena to which the current chapter will be dedicated. Some of them have already been mentioned or discussed throughout the book. It was needed and essential to highlight them in order to understand the described features of breaking and whitecapping dissipation.

Others, for example, the spectral-peak downshift which is the topic of the next section, 8.1, have been mentioned as those which contribute to spectral dissipation (see Section 7.3.1). There is no contradiction here.

Following the intuitively familiar concept of wave breaking discussed in Section 1.2, a variety of phenomenological definitions can be formulated. Wikipedia suggests such a definition, applicable across the range of wave processes, including water waves as well as electromagnetic waves, waves in plasmas and in other physical media:

The Glossary of Meteorology of the American Meteorological Society defines the breaking of ocean surface waves more specifically:

As discussed above, a more explicit physical, yet only mathematical definition of the wave-breaking phenomenon is hardly possible.

Wave breaking is a fascinating object to watch and to research. Wind-generated waves are the most prominent feature of the ocean surface, and so are breaking waves manifested by sporadic whitecaps on the wavy surfaces of oceans and lakes. The breaking is so apparent that one does not need to be an oceanographer to have an opinion on what it is and how it works.

Such breaking, however, represents one of the most interesting and most challenging problems for both fluid mechanics and physical oceanography. It is an intermittent random process, very fast by comparison with other processes in the wave system. The distribution of wave breaking on the water surface is not continuous, but its role in maintaining the energy balance within the continuous wind–wave field is critical. Ocean wave breaking also plays the primary role in the air–sea exchange of momentum, mass and heat, and it is of significant importance for practical applications such as ocean remote sensing, coastal and ocean engineering, and navigation among others.

Understanding such wave breaking, predicting its behaviour, the breaking rates and breaking strength, and even an ability to describe its onset have been hindered for decades by the strong nonlinearity of the process, together with its irregular and ferocious nature. Lately, knowledge of the breaking process has significantly advanced, and this book is an attempt to summarise the facts into a consistent, albeit still incomplete, picture of the phenomenon.

Wave breaking, apart from serving as the main dissipation source in the wave field, plays a number of other roles both on the ocean surface, and away from the surface. Chapter 8 was dedicated to such breaking-related other-than-dissipation features in the surface-wave system itself, and this penultimate chapter of the book, prior to Conclusions will extend the topic into a description of the roles wave breaking performs in air–sea interactions in a broader sense.

Section 9.1 and subsections are dedicated to the breaking-related effects in the atmospheric boundary layer. These are not limited to the wind–wave energy/momentum exchanges which have been discussed throughout the book. The breaking alters the sea drag, which then affects the near-surface air flow in general. The breaking is a source of spray, and the presence of the spray has a most essential influence on the boundary layer again. And finally, all these features have their peculiarities or even new behaviours, to a great extent unknown at this stage, in extreme conditions.

Section 9.2 also includes a number of subsections on important roles which the breaking plays in the upper-ocean dynamics and mixing. These cover descriptions of interface momentum and gas transfer, of which the breaking is part. In particular, two subsections are dedicated to the physical phenomena by means of which breaking facilitates such air–sea exchanges and mixing, i.e. the wave-induced turbulence and injection of the air bubbles under the water surface.

Measurements and even detection of wave breaking are challenging tasks, particularly if carried out by unattended devices in the open ocean. As a result, there are vast amounts of wave records accumulated, and most of them contain breaking waves, but information about the breaking cannot be extracted. There is an obvious need for methods and instrumentation to directly detect breaking events and measure their properties, and for the analytical means and criteria to identify the breaking waves in existing time series of surface elevations.

Until recently, visual observations were arguably the only reliable means of breaking detection. These are based on viewing and quantifying information on whitecaps produced by breaking waves and are obviously biased towards large breakers (see Section 2.8). Over the past two decades, more technological methods have become available, both contact type and by remote sensing of the ocean surface or subsurface. These utilise acoustic (passive and active), optical (both visible and infrared range), reflective and other properties of breakers which distinguish them from the more homogeneous background wave field.

Without giving a comprehensive review, we will mention here passive acoustic techniques based on air bubbles ringing while being created during air entrainment (e.g. Lowen & Melville, 1991a; Ding & Farmer, 1994; Babanin et al., 2001; Manasseh et al., 2006), sonar observations of bubble clouds produced by breaking wind-waves (e.g. Thorpe, 1992), aerial imaging (e.g. Melville & Matusov, 2002; Kleiss & Melville, 2011, 2010), infrared remote sensing of breaking waves (e.g. Jessup et al., 1997a), radar observations of microwave backscatter from breakers (e.g. Jessup et al., 1990; Lowen & Melville, 1991a; Smith et al., 1996; Phillips et al., 2001), and conductivity measurements of the void fraction produced by breakers (e.g. Lammarre & Melville, 1992; Gemmrich & Farmer, 1999),amongst others.

As already mentioned in Chapter 2 dedicated to definitions of wave properties and phenomena 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 discussed 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 environmental characteristics have usually relied on wind speed or its derivatives. In this book, 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 breaking 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.

The previous chapter was dedicated to experimental methods of detecting wave breaking, quantifying the breaking probability and severity, and measuring effects related to the breaking, including the wave energy dissipation. In the next chapter, it is logical to describe theoretical methods of describing wave-breaking physics or phenomena leading to the breaking.

While experimental oceanography has produced an abundant variety of techniques and approaches to detect and measure breaking, the theories capable of dealing with wave breaking are few. These should not be confused with analytical methods intended to detect the breaking events in surface-wave records (Section 3.7) or with the statistical methods of quantifying the breaking probability and strength (Section 3.8). Both such groups of analytical techniques are placed into experimental Chapter 3 for a good reason – they principally rely on empirical criteria.

Another significant group of analytical approaches, dealing with the dissipation due to breaking, rather than with the breaking as such is also not included in this chapter. Some of these models are based on assumptions intended to interpret pre-breaking or post-breaking properties of the waves, rather than on working with the physics leading to breaking or driving the breaking and its consequences. Others attempt to deduce the dissipation from differences between wave-evolution predictions done by means of kinetic and dynamic equations. In any case, these are indirect techniques that do not depict the wave-breaking event explicitly. They will be described in Section 7.1.

In previous chapters, we have considered in some detail dissipation of wave energy in the course of individual wave-breaking events. This makes clear physical sense as breaking is an intermittent rather than continuous process, and the breaking rates in realistic circumstances are of the order of a few percent. That is, only a few waves out of a hundred break at any given spot or any given time, and that is sufficient to keep the energy balance in a wave system that experiences a consistent and uninterrupted energy input from the wind.

As discussed in Chapter 6 and throughout the book, it is often the case that more than one wave is affected in a single breaking occurrence. The dynamics of these waves is locked and coupled in many ways, and as far as the wave-energy dissipation is concerned, these energy losses are impossible to separate. Therefore, it usually makes sense to look at the properties of the wave group where the breaking took place rather than investigate the dynamics of some individual wave.

One way or another, there are no theoretical or even experimental approaches that would allow us to describe the breaking-dissipation process as such, in terms of some decay rate, as, for example, gradual energy decline due to the action of viscosity in fluid flows. First of all, unlike most if not all other dissipation causes, breaking dissipation has a start and an end.

Wind-generated waves are the most prominent feature of the ocean surface. As much as the oceans cover a major part of our planet, the waves cover all of the oceans. If there is any object in oceanography that does not need too much of a general introduction, it is the surface waves generated by the wind.

Being such a conspicuous entity, these waves, however, represent one of the most complex physical phenomena of nature. Three major processes are responsible for wave evolution in general, with many more whose significance varies depending on conditions (such as wave-bottom interaction which is only noticeable in shallow areas). The first process is energy and momentum input from the wind. The waves are generated by turbulent wind, and the turbulence is most important both for their initial creation and for subsequent growth (e.g. Miles', 1957; Miles, 1959, 1960; Phillips', 1957; Janssen, 1994, 2004; Belcher & Hunt, 1993; Belcher & Hunt, 1998; Kudryavtsev et al., 2001, among many others). There is, however, no fixed theory of turbulence to begin with. Experimentalists have to deal with tiny turbulent fluctuations of air which are of the order of 10-5-10-6 of the mean atmospheric pressure and which must be measured very close to the water surface, typically below the wave crests (e.g. Donelan et al., 2005).