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1
1
1
2
0.5
0
0
1.5
0
−1
−1
0
0.5
1
0
0.5
1
0
0.5
1
0
0.5
1
kH
kH
kH
S
k
1
1
1
1
0
0
0
0
−1
−1
−1
−1
0
0.5
1
0
0.5
1
0
0.5
1
0
0.5
1
kH
kH
S
k
S
k
1
1
1
1
0.5
0
0
0
0
−1
−1
−1
0
0.5
1
0
0.5
1
0
0.5
1
−1
0
1
kH
kH
S
k
A
S
1
2
0.5
1.5
0
1.5
2
0
0.5
1
f, Hz
kH
Figure 5.8 Laboratory statistics of the wave following the incipient breaker (20 steepest breakers).
IMF
=
1
.
8Hz
,
IMS
=
0
.
30
,
U
/
c
=
0. (top left panel) Skewness versus steepness. (top line, second
left panel) Asymmetry versus steepness. (top line, second right panel) Frequency (inverse period)
versus steepness. IMF
=
1
.
8 Hz is shown with solid line. (top line, right panel) Asymmetry versus
skewness. (second top line, left panel) Skewness of the wave preceding the breaker versus steep-
ness of the wave following the breaker. (second top line, second left panel) Asymmetry of the wave
preceding the breaker versus steepness of the wave following the breaker. (second top line, second
right panel) Skewness of the wave preceding the breaker versus skewness of the wave following the
breaker. (second top line, right panel) Asymmetry of the wave preceding the breaker versus skewness
of the wave following the breaker. (second bottom line, left panel) Skewness of the breaker versus
steepness of the wave following the breaker. (second bottom line, second left panel) Asymmetry of
the breaker versus steepness of the wave following the breaker. (second bottom line, second right
panel) Asymmetry of the breaker versus skewness of the wave following the breaker. (second bot-
tom line, right panel) Asymmetry of the wave preceding the breaker versus asymmetry of the wave
following breaker. (bottom line, left panel) Frequency of the wave preceding the breaker versus fre-
quency of the wave following the breaker. IMF
=
1
.
8 Hz is shown with solid lines. (bottom line,
right panel) Steepness of the breaker versus steepness of the wave following the breaker
f
=
1
.
7
+
1
.
39
.
(5.9)
If this expression is extrapolated to the ultimate frequency value of
f
=
2
.
08 of the
breaker in the third subplot of
Figure 5.7
, it yields 2
=
0
.
81, which is approximately
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