Geoscience Reference
In-Depth Information
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
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
time, sec
time, sec
Figure 5.4 IMF
=
1
.
8Hz
,
IMS
=
0
.
30
,
U
/
c
=
0. Four steepest incipient breakers (from top left to
bottom right)
Figure 5.5
shows one, five, twenty and fifty steepest breakers in consecutive panels. Note
that no normalisation was applied and the waves are plotted as they appear in physical
space, from the front zero-crossing of the wave preceding the breaking to the rear zero-
crossing of the following wave. Despite this, the pictures are remarkably similar even in
the subplot with 50 waves and this prompts a universality of such incipient-breaker shapes.
The quantitative characteristics of these waves are further scrutinised in
Figures 5.6
-
5.12
.
Figure 5.6
shows data for the five steepest breakers. The analysis is at first limited to
these steepest cases as wave quantities close to the breaking point change rapidly, as shown
in
Figure 5.3
. These steepest cases are considered to be on the point of breaking. Accord-
ing to the numerical simulations, the steepness seems to be the single robust criterion for
breaking. For the 20 steepest breakers (see further
Figure 5.7
), steepness was confined to
the narrow range
Hk
/
2
=
0
.
37 to 0.44, whilst skewness was scattered over the wide range
S
k
4. Considering only those waves at the point
of breaking, however, as in
Figure 5.6
, shows a clearer trend. The steepness appears to
approach an asymptotic limit of
=
0 to 1 and asymmetry
A
s
=
0
.
8to
−
0
.
Hk
2
≈
0
.
44
,
(5.4)
Search WWH ::
Custom Search