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In-Depth Information
1
1
2
1
0.5
0
1.5
0
0
−1
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
0.5
0
0.5
0
0
−1
0
−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
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
2
2
0
0
1.5
1.5
−1
−1
1
1
−1
0
1
−1
0
1
1
1.5
2
1
1.5
2
A
s
A
s
f, Hz
f, Hz
Figure 5.16 As in
Figure 5.10
, with wind forcing. IMF
=
1
.
5Hz,IMS
=
0
.
30,
U
/
c
=
3
.
9. Laboratory
statistics for the five steepest incipient breakers
As mentioned earlier in this section, distance to breaking in a train of steep initially
monochromatic waves can be controlled by varying IMS and therefore can be predicted.
Based on the laboratory measurements, such predictions are summarised in
Figure 5.17
(top), which shows the non-dimensional distance to breaking
N
as a function of
IMS, where
x
b
is the dimensional distance to breaking. A range of values of IMS are
shown, along with cases with and without wind forcing. As expected, the addition of wind
forcing reduces the non-dimensional distance to breaking. However, this reduction is not so
great that the data points would deviate markedly from the functional relationship between
N
and IMS, and the nonlinear effect obviously dominates over the wind forcing.
In accordance with the numerical simulations, for each wave length an increase of its ini-
tial steepness resulted in the breaking occurring closer to the wavemaker. In dimensionless
terms, this dependence was parameterised as follows:
=
x
b
/λ
N
=−
11 atanh
(
5
.
5
(
−
0
.
26
))
+
23
,
for 0
.
08
≤
≤
0
.
44
.
(5.10)
Consistent with the model results, the formula imposes two threshold values of IMS.
For
>
0
.
44, the wave breaks immediately (compared to
=
0
.
3 for the two-dimensional
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