Introduction - Breaking and Dissipation of Ocean Surface Waves - page 3

the breaking-in-progress process of wave collapse, is a highly nonlinear mechanism of
very rapid transfer of wave energy and momentum to other motions. So far, there are no
adequate mathematical and physical descriptions of such a process.
Conceptually, however, the physics of wave collapse is completely different from the
physics leading to breaking onset. While collapse is driven, to a greater extent, by grav-
ity and inertia of the moving water mass and, to a lesser extent, by hydrodynamic forces,
breaking onset occurs mostly due to the dynamics of wave motion in the water. Approach-
ing breaking onset by a background wave is also very rapid, and also happens in the space
of one wave period (e.g. Bonmarin , 1989 ; Babanin et al. , 2007a , 2009a , 2010a ), but it
should be considered separately from the following wave collapse. Essentially, the break-
ing process consists of two different sets of physics - one leading to breaking and another
driving the wave breaking once it has started. These are not entirely disconnected, however,
and the outcome of breaking collapse appears to 'remember' the 'input' that made a wave
break. This will be discussed in more detail in Section 7.3.2.
The distinct difference between whitecapping dissipation and other processes involved
in wave evolution is also determined by the fact that not every wave breaks whereas every
wave experiences continuous energy input from the wind and continuous nonlinear energy
exchange with other components of a continuous wave spectrum. A typical picture of a
wavy surface under moderately strong wind conditions is shown in Figure 1.1 .Waves
of all scales, forming a continuous spectrum in terms of wave periods and lengths, exist
simultaneously and run concurrently with different phase speeds, riding on top of each
other or intercepting momentarily in different directions. All of these waves are subject to
wind input and nonlinear exchange, but as is seen in Figure 1.1 just a small fraction of them
break. Only under very strong winds does the rate of breaking crests reach 50% or more,
but normally it is well below 10% ( Babanin et al. , 2001 ). This means that, on average, it
is every 20th or even every 50th wave that breaks, and this is sufficient to hold the energy
balance in the wave system where every single wave gains energy one way or another.
In the continuous time-space environment of a continuous wave spectrum and continuous
physical processes, random breaking, which is intermittent in time and does not cover the
surface uniformly, appears to control the equilibrium and ultimately wave growth. There
is evidence that coverage of the ocean surface with breaking has a fractal dimension rather
than being a two-dimensional surface ( Zaslavskii & Sharkov , 1987 ), and this fact provides
further mathematical complications if a description of this phenomenon is attempted by
means of hydrodynamics or statistics.
It is important to mention at this stage that the three major processes, wind energy input,
energy redistribution due to nonlinear interactions and energy dissipation, are closely cou-
pled, affect each other and are equally important in wave evolution. Obviously, there would
be no waves if they were not generated by the wind, but the wind input mechanism alone
cannot explain evolution to any extent. As soon as the waves grow beyond the infinitesimal
stage, nonlinear interactions begin to play an important role, and soon after, once individ-
ual steeper waves start to break, whitecapping dissipation assumes its responsibility as the
balance holder.