Introduction - Breaking and Dissipation of Ocean Surface Waves - page 2

(high-frequency) and slowly moving waves which then transfer this energy across the con-
tinuous spectrum of waves of all scales towards longer (lower-frequency) components thus
allowing those to grow - by means of nonlinear interactions. So, this small nonlinearity
plays a large role in developing wind-waves as we know them. Analytically, to account
for this sort of interaction the theoreticians have to solve relevant equations of hydro-
dynamics with accuracy down to expansion terms of the third order (e.g. Hasselmann ,
1962 ; Zakharov , 1968 ; Hasselmann et al. , 1994 ; Badulin et al. , 2005 ). Experimentally,
such interactions could not have been studied directly because of a great number of tech-
nical difficulties, one of which is the slowness of the process, thousands of wave peri-
ods being its time scale. Here, we would also like to mention that there are alternative
approaches to explaining the evolution of long wind-generated waves.
The third most important process that drives wave evolution is the wave energy dissi-
pation. Common experience tells us that wind-generated waves, no matter how strong the
wind and how long its duration and wave fetch, do not grow beyond a certain limit. In
the absence of mainland in the Southern Ocean, high continuous westerly winds are free
to run the waves around the globe and thus provide conditions of unlimited wind-wave
forcing and growth. Yet, the significant wave height (height of one third of the highest
waves) rarely goes beyond 10m. Individual waves of some 30m are occasionally reported
(e.g. Liu et al. , 2007 ), but these are very seldom and would certainly be the ultimate limit
for wind-generated waves on the planet. Therefore, there is a process that controls the wave
growth from above, and that is wave dissipation.
1.1 Wave breaking: the process that controls wave energy dissipation
There are a number of physical mechanisms in the oceanic and atmospheric boundary
layers, other than breaking, that contribute to wave energy dissipation (e.g. Babanin , 2006 ;
Ardhuin et al. , 2009a ), but once wave breaking occurs it is the most significant sink
for energy. In well-developed deep-water wind-forced waves, it is believed that breaking
accounts for more than 80% of dissipation. Wave energy is proportional to the wave height
squared, and therefore a sudden reduction of wave height during breaking by, for exam-
ple, two times, signifies a four-times' reduction in energy. Obviously, provided there is a
sufficient number of waves breaking, such a dissipation mechanism is much more efficient
compared to viscosity, to the interaction of waves with winds, currents, background turbu-
lence and to other ways of gradual decline. The energy lost to breaking is spent on injecting
turbulence and bubbles under the ocean interface, emitting spray into the air, and thus wave
breaking, and wind-generated waves in general, play a very significant role in negotiating
the exchange of momentum, heat and gases between the atmosphere and the ocean.
Breaking happens very rapidly, it only lasts a fraction of the wave period ( Bonmarin ,
1989 ; Rapp & Melville , 1990 ; Babanin et al. , 2010a ), but the wave may indeed lose
more than half of its height ( Liu & Babanin , 2004 ). Thus, the wave energy slowly accu-
mulated under wind action and through nonlinear transfer over thousands of wave peri-
ods is suddenly released in the space of less than one period. Obviously, this process,