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5
4.5
mean(A
WDM
/A
MLM
) = 3.4021
4
3.5
3
2.5
2
1.5
1
0.5
2
4
6
8
10
12
A
WDM
Figure 5.33 Comparison of
A
MLM
and
A
WDM
for the ocean engineering tank records. Circles cor-
respond to modulational instability, diamonds to linear focusing, stars to transitional cases. Figure is
reproduced from
Babanin
et al.
(
2011a
)
WDM indicates much narrower spectra. While the WDM estimates should be more accu-
rate and have other advantages (e.g.
Waseda
et al.
,
2009a
;
Young
,
2010
), here we will use
the MLM estimates in order to be able to compare new results with the field-observed
directional spectra of
Babanin & Soloviev
(
1987
,
1998b
) which were done by means of
MLM.
An important implication of the difference observed in
Figure 5.33
is immediately obvi-
ous if we boldly divide criterion
(5.55)
of
Waseda
et al.
(
2009a
) obtained with the use of
WDM, by three: then the transition from no visible modulational instability to detected
modulational instability happens at
A
3 which, according to
Babanin & Soloviev
(
1987
,
1998b
) falls right into the range of directional spreads typical for dominant waves.
In
Babanin
et al.
(
2011a
), this limit was further investigated on the basis of the direc-
tional data of the experiment. It was shown that, for mean wave steepnesses typical of those
observed in the field, the instability exists at as low values of
A
as
≈
1
.
A
∼
0
.
8
,
(5.56)
which are quite realistic directional widths in field conditions; in fact quite broad by any
standards, certainly at the spectral peak where the modulational instability is expected to
work.
Thus, modulational instability may still be found to be applicable, at least for the domi-
nant waves if they are steep enough. It is not unreasonable to expect a directional condition
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