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upper parts of the ink patterns. At
a
0
=
04m, the motion was obviously turbulent, with
the ink being completely dissolved within seconds after injection. When the amplitude was
reduced down to
a
0
=
0
.
02m again, the laminar behaviour of the traces was immediately
restored as the source of turbulence was apparently removed. Note that the time interval
between the measurements is minutes, that is wave turbulence completely dissipates at
this time scale, and certainly cannot persist for hours and tens of hours as it is implicitly
assumed in ocean-mixing schemes which rely on wave-breaking turbulence. The wave-
breaking turbulence is directly injected down to the depths of the order of wave height (e.g.
Agrawal
et al.
,
1992
;
Babanin
et al.
,
2005
;
Gemmrich
,
2010
), and to mix the ocean at the
scale of MLD
0
.
50m, as, for example, if the wave-breaking turbulence scheme of
Craig &
Banner
(
1994
) is employed, would have to be diffused down and survive for hours and tens
of hours (e.g.
Martin
,
1985
). Back to our experiment, on the return back to
a
0
=
∼
04m, the
onset of turbulence was observed at approximately the same wave amplitude as previously.
Now, let us apply Re
wave
critical
0
.
3000 to find
z
cr
(7.74)
in the ocean. This will only be
an approximate value as, for the ocean wave conditions it is just mean (rather than mean
extreme) magnitudes of wave height and peak period that are available to us (wave atlas of
Young & Holland
,
1996
). Mean extremes would need a designated definition for this kind
of estimate anyway, even if the raw wave data of interest were available, because those
would have to be not only high waves, but also waves persisting long enough (normally
tens of hours within the month - e.g.
Martin
(
1985
) for MLD to settle. Besides, read-
ings of mean waves and mean MLDs used here, even though taken for the same month of
April, were done in different years and may be out of synch to some degree due to inter-
annual variability. Also, the thermal, advective and other effects, although assumed to be
relatively small, may not be negligible. And importantly, sea surface temperature (SST)
is used here to estimate kinematic viscosity which is further applied in
(7.73)
and
(7.74)
.
The temperature and therefore the viscosity are different belowMLD (temperature is lower
and viscosity is greater), and thus Re
wave
will be slightly smaller down there. This fact can
lead us to some overestimation of MLD in the current exercise. Such precision details are
beyond our scope, and what we would like to see in this section is an approximate quantita-
tive and reasonable qualitative agreement of our predictions, based on
(7.73)
-
(7.74)
, with
ocean observations.
For the ocean estimations, we will begin from well-documented directly measured April
values of MLD and SST in the Pacific at the ocean stations
No
=
ember
(140
◦
W
30
◦
N)
v
,
and
Papa
(145
◦
W
50
◦
N). Values of
z
critical
75m were read for
the stations
N
and
P
respectively from Figs. 5 and 6 of
Martin
(
1985
). Corresponding
surface temperatures were 19
,
≈
104m and
z
critical
≈
6
◦
C and 5
3
◦
C, which lead us to
10
−
6
m
2
.
.
ν
≈
1
.
07
·
/
s
10
−
6
m
2
and
s, respectively. The mean significant wave height and mean peak
period, provided by the atlas of
Young & Holland
(
1996
) for April, were
H
s
=
ν
=
1
.
58
·
/
2
.
33m and
f
p
=
0
.
084 Hz at
N
, and
H
s
=
3
.
44m and
f
p
=
0
.
097 Hz at
P
.
Estimates, obtained for Re
wave
critical
=
3000 using
(7.74)
,are
z
critical
≈
95m for
N
and
z
critical
≈
78m for
P
. Given the uncertainties mentioned above, they are in excellent
quantitative (9% and 4% deviations, respectively) and very good qualitative agreement
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