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0.04
0.04
0.02
0.02
0
0
−0.02
−0.02
0
0.5
1
1.5
0
0.5
1
1.5
a)
b)
0.04
0.04
0.02
0.02
0
0
−0.02
−0.02
0
0.5
1
1.5
0
0.5
1
1.5
c)
time, sec
d)
time, sec
Figure 5.5 IMF
=
1
.
8Hz
,
IMS
=
0
.
30
,
U
/
c
=
0. (top left panel) The steepest incipient breaker. (top
right panel) Five steepest incipient breakers. (bottom left panel) Twenty steepest incipient breakers.
(bottom right panel) Fifty steepest incipient breakers
which may represent an absolute steepness limit for two-dimensional or quasi-two-
dimensional waves (see also
Toffol i
et al.
,
2010a
). We should point out that this limit
is remarkably close to the theoretical steady limiting steepness of
ak
=
0
.
443
(2.47)
, i.e.
the Stokes limit
H
7
(2.46)
. It is also in excellent agreement with the dedicated
fully nonlinear simulations of the breaking onset (see
Section 4.1
). The skewness at the
breaking point asymptotes the value of
/λ
=
1
/
S
k
≈
1
(5.5)
which means that the crest is twice as high as the trough
(1.2)
. Values of asymmetry
(1.3)
in the imminent breaker are transitional rather than definite.
Such an observation is very important because it signifies that the waves break once
they achieve the well-established state beyond which the water surface cannot sustain its
stability. It may be postulated that the other geometric, kinematic and dynamic criteria of
breaking, explored in the literature (see
Section 2.9
), are indicative of a wave approaching
this state, but are not a reason or a cause for the breaking. As this limit is approached, the
skewness increases very rapidly and immediately after the limit is reached the asymmetry
becomes negative (i.e. the wave starts tilting forward at the point of breaking).
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