Geoscience Reference
In-Depth Information
Hk
2
≈
0
.
69
,
(5.6)
(
Penney & Price
,
1952
;
Schwartz & Fenton
,
1982
)or
Hk
2
≈
0
.
61
,
(5.7)
(
Okamura
,
1986
). The dynamics of the standing waves will not be further discussed in
this topic.
Various quantitative characteristics of waves propagating to their breaking are analysed
in
Figures 5.7
-
5.12
.
Figure 5.7
shows a comprehensive set of statistics of the properties of
the 20 highest incipient breakers and their relationship with the preceding and following
wave. The first (top left) subplot is similar to the statistical plot of numerically simulated
skewness versus steepness in
Figure 4.9
. Remarkably, values of limiting local steepness,
the property which was revealed by the model as the likely indicator of breaking, is in the
same range as was predicted in numerical simulations: 2
8. For a real wave, even
if two-dimensional, such steepness is extremely high. Noting that the mean steepness is
≈
≈
0
.
4 and that near the crest the wave is even steeper, it is not surprising that the wave is
on the point of collapse.
The skewness of the 20 highest waves in the first subplot scatters from almost 0 to
almost 1. As indicated in the simulational
Section 4.1
, we would expect the skewness to
also have a limiting value. Clearly, however, such a limit is not a very robust breaking
characteristic, although for the five waves closest to the breaking point in
Figure 5.6
the
skewness does exhibit the limiting value. Also in the top row of the subplots, asymmetry
is scattered from
A
s
=−
0
.
75 (second panel), with a possible dependence of
S
k
on
A
s
in the fourth panel, consistent with the numerical simulations (
Figure 4.9
).
A robust property of the breaking, in the third panel, is the wave frequency. The scatter
of this property is small, with all the values falling into a range
f
0
.
33 to
A
s
=
0
.
=
2
−
2
.
08 Hz, that is the
ratio is
f
IMF
=
1
.
11-1
.
16
.
(5.8)
It should be pointed out that, for
ak
44, a frequency increase of about 10% is simply
expected from the second-order term of the basic dispersion relationship
(2.14)
. Thus, the
wave clearly reduces in length prior to collapse. We should mention that the measured
steepness
≈
0
.
2 in the figure is the physical rear-face steepness, and therefore the
effect of period contraction has already been accounted for.
In the second row of plots, the skewness of the wave following the incipient breaker (first
panel) and its asymmetry (second panel) are much less scattered than the skewness and
asymmetry of the breaker itself:
S
k
=
=
kH
/
29
to 0.33. We have already discussed the double-breaking in observational
Chapter 3
, which
means that this following wave will break soon after the incipient breaker. Thus, its
0
.
32-0
.
70, asymmetry changes from
A
s
=−
0
.
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