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Figure 7.24 Dependence of kinetic energy dissipation rate
dis
(denoted as
in the figure) versus
wave amplitude
a
0
(denoted as
a
). Dependence
(7.76)
is shown with a solid line. Data points desig-
nated with asterisks and circles were obtained in two separate experiments in the same facility. The
×
-mark on the bottom axis indicates value of
a
0
which corresponds to Re
wave
critical
=
3000, and the
vertical bars show the standard deviations. Figure is reproduced from
Babanin & Haus
(
2009
)
Direct fit (solid line in
Figure 7.24
) provides the dependence
300
a
p
dis
=
0
.
(7.76)
Values of
dis
and
a
0
in this formulae of
Babanin & Haus
(
2009
) are dimensional. There-
fore, the coefficient 300 is dimensional too, and in the form presented in
(7.76)
it is
only suitable for the waves of 1
5 Hz considered in the experiment (see
(7.85)
for a non-
dimensional version of this parameterisation). Statistical uncertainty of this coefficient (the
intercept of dependence
(7.76)
) is large, but for the exponent
p
in
(7.76)
the 95% confi-
dence limit places it between 2 and 4:
p
.
0. This is close to the expectation
(
Babanin
,
2006
) that, since the force due to the turbulent stresses is proportional to
a
0
,the
energy-dissipation rate should be
=
3
.
0
±
1
.
a
0
.
Before applying the results of
(7.76)
and
Figure 7.24
to estimation of possible swell
dissipation in the ocean, which would associate with the wave-induced turbulence, it should
be emphasised again that the
dis
∼
dis
estimates obtained by
Babanin & Haus
(
2009
) are not
sustained dissipation rates. They are instantaneous values incurred intermittently at the
rear-face phase of the wave below the level of the wave trough. Even for the steepest
waves in the experiment, such turbulence occurred (that is occupied the entire 30mm level
of the camera image) not more than once out of the recorded ten phases per wave period.
This is due to the experiment being designed to avoid wave breaking and thus it dealt with
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