Introduction - Breaking and Dissipation of Ocean Surface Waves - page 7

height 1 6m measured in a natural directional wave field in the Black Sea. The right panel

shows a freely propagating (very small) two-dimensional wave of height 4 cmwithout wind
forcing. This wave was mechanically generated in the Air Sea Interaction Salt water Tank
(ASIST) of the University of Miami.
Once the skewness is non-zero and the amplitude a is not clearly determined, a definition
of the wave steepness in terms of ak becomes ambiguous. Therefore, unless otherwise
specified, the steepness will be expressed in terms of wave height H

.

= a 1 + a 2 rather than

wave amplitude a ,as = Hk / 2. In these terms, steepness = 0 . 335 of the wave shown

in the figure far exceeds the limits of a perturbation analysis.
The dashed line in Figure 1.2 represents a steep sinusoidal wave ( S k

0). Such
a wave will immediately transform itself into a Stokes wave (e.g. Chalikov & Sheinin ,
2005 ). The steep Stokes wave in the figure (dash-dotted line) is highly skewed ( S k

= A s =

=

0 . 39), but remains symmetric (i.e. A s = 0). The incipient breaker in Figure 1.2 ( S k =

1 51) was produced by the CS model, in a simulation which commenced

with a monochromatic wave of

. 15 , A s =− 0 .

25. Such a wave profile looks visually realistic
for a breaker and corresponds to, or even exceeds, experimental values of skewness and
asymmetry for breaking waves previously observed (e.g. up to A s =−

= 0 .

0 . 5 instantaneously

in Caulliez ( 2002 )or A s 2 on average in Young & Babanin ( 2006a )). It is worth

noting that the steepness of the individual wave has grown very significantly at the point
of breaking: from

=− 0 .

335.
When collapsing, the wave shape becomes singular at least at some points along the
wave profile (i.e. space derivatives of the surface profile have discontinuities). This stage
of wave subsistence is called breaking. Breaking of large waves produces a substantial
amount of whitecapping, but smaller waves, the micro-breakers, do not generate whitecaps
or bubbles and lose their energy directly to the turbulence.
Examples of various breaking and non-breaking waves are shown in Figures 1.4 - 1.8 .
Figures 1.4 - 1.5 show deep-water waves. The swell in Figure 1.4 are former wind-waves
which have left the storm region where they were generated. They most closely conform
to our intuitive concept of what the ideal wave should look like: uniform and long-crested,
with crests marching parallel to each other. Their steepness is low and they do not break
until they reach a shore.
Wind-forced waves hardly resemble this ideal picture. They look random and chaotic,
they are multi-scale and directional, and they break. In Figure 1.5 a deep-water breaker is
shown whose height is in excess of 20m.
In Figure 1.6 (see also the cover image), waves approaching finite depths and, ultimately,
the surf zone are pictured. In finite depths, waves break more frequently. Possible reasons
are two-fold. Mainly, the waves break for the same inherent reason as in deep water, but
they do it more often because the bottom-limited waves are steeper on average. Another
fraction of waves break due to direct interaction with the bottom; this fraction grows as the
waters become shallower (see Babanin et al. , 2001 , for more details).
If deep-water waves enter very shallow environments, as shown in Figure 1.7 ,allof
them will break and ultimately lose their entire energy to interaction with the bottom, to

= 0 . 25 initially to = 0 .