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The satellite-measured SST for April were taken from US NOAA site http://www.osdpd.
noaa.gov/PSB/EPS/SST/al_climo_mon.html. Because variations were small, we assumed
an approximately constant value of 25
◦
C which thus gives
10
−
6
m
2
ν
≈
0
.
96
·
/
sat
30
◦
N.
The results are shown in
Figure 7.22
. Along the transect, significant wave height varies
four times, from 0
.
65m to 2
.
7m, and so does the peak frequency which varies from 0
.
08 Hz
to 0
3Hz (
Figures 7.22
b and c, respectively). Comparison of the NRL results with the
present Reynolds-number-based estimate of MLD is shown in
Figure 7.22
d. The Re-based
estimate reproduces the trend very well, and given the fact that both methods are results
of modelling rather than direct
in situ
measurements, the quantitative agreement is also
very good. It should be pointed out that possible rates of development of the mixed layer
cannot be addressed on the basis of this hypothesis: the predicted MLD will be achieved
if the duration of the wave-carrying storms, or duration of a combined succession of such
storms, is long enough for the turbulent diffusion to take its course.
Obviously, prediction of MLD is not the only potential outcome of the introduction of
wave-induced turbulence. It is therefore interesting to check our results across a range of
oceanographic applications, including swell propagation discussed above in this section.
The two records described by
Yefimov & Khristoforov
(
1971
) (assuming the water tem-
peratures being between 5
◦
C and 20
◦
C) produce Re
wave
between 120000 and 180000 and
between 50000 and 70000, respectively, and therefore should have induced the turbulence
as they did. The swell, propagating across the Pacific from New Zealand to Alaska without
much attenuation in the observation by
Snodgrass
et al.
(
1966
), had Re
wave
of 310, 260,
140 and 50 at stations Tutuila, Palmyra, Honolulu and Yakutat, respectively, and therefore
could not have spent any energy on producing the turbulence which would be accompanied
by a more rapid damping (compare, for example, with swell-attenuation rates in Fig. 1 of
Ardhuin
et al.
,
2009a
). Here, our estimates are done for the case described in Fig. 30 of
Snodgrass
et al.
(
1966
) and the water temperature is taken to be 20
◦
C along the entire swell
path which makes the Reynolds numbers upper-limit values).
More material for verifications are the results of
Cavaleri & Zecchetto
(
1987
) where mul-
tiple unexpected features were measured which could not have been explained: (1) wave-
induced turbulence existed, even in the case of non-breaking swell; (2) momentum fluxes
below the water surface did not match (exceeded) the wind stress; (3) in the case of wind-
forcing, the wave orbits were tilted. Consequences (1) and (2) appear to be directly related
to expectations due to the influence of wave-induced turbulence.
.
(1) The observed swell was quite steep, with peak steepness of 0.054 just below the breaking thresh-
old of 0.055
(5.19)
. Corresponding Re
wave
∼
200000 clearly indicates a value well-above the
onset of turbulence and therefore non-zero vertical momentum fluxes from such a source of
turbulence are to be expected.
(2) Turbulent stresses in the water and in the air do not have to match in a general case, as the
wave turbulence can be generated even in the absence of the wind if the swells are steep
enough. Obviously, the two-order magnitude difference observed in the paper under conditions
of active generation is mostly due to the phase shift between the horizontal-vertical components
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