Introduction - Breaking and Dissipation of Ocean Surface Waves - page 6

respectively (see Figure 1.2 and its caption). Here, a is wave amplitude, H is wave height
( a

is wavelength, a 1 and
a 2 are the wave crest height and trough depth, and b 1 and b 2 are horizontal distances
from the breaker crests to the zero-upcrossing and -downcrossing, respectively. Thus, the
steepness

= H / 2 in the linear case), k = 2 π/λ is wavenumber and λ

is an average steepness over the wave length, and obviously, local steepness
is much higher near the crest and is less than average at the trough. Positive skewness
S k > 0 represents a wave with a crest height greater than the trough depth (a typical surface

wave outside the capillary range), and negative asymmetry A s

0 corresponds to a wave
tilted forward in the direction of propagation. Importantly here, experimentally observed
negative asymmetry A s has been broadly associated with wave breaking (e.g. Caulliez ,
2002 ; Young & Babanin , 2006a ).
Intrinsically, both the asymmetry and the skewness are natural features of steep deep-
water waves regardless of their size, crest length, forcing or generation source (see e.g.
Soares et al. , 2004 ). In Figure 1.3 , examples of real waves are demonstrated which exhibit
both these properties. The left panel shows a wind-generated and wind-forced wave of

<

1 0.04

0.8

0.03

0.6

0.02

0.4

0.01

0.2

0 0

−0.2

−0.01

−0.4

−0.02

−0.6

b)

a)

−0.03

−0.8

−1 −0.04

452 453 454 455 7.2 7.4 7.6 7.8

time, sec time, sec

Figure 1.3 Real waves exhibiting both skewness and asymmetry. The waves propagate from right
to left. a) Field wave measured in the Black Sea; b) laboratory (two-dimensional) wave measured in
ASIST