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Now we consider the PDF of amplitudes for which predictions where made
recently within the WT approach. To measure the PDF of amplitudes
, we set two radial regions in
space
and
. These
regions were inside the inertial range and had well mixed phases and
amplitudes since the experiment was done after performing 2000
rotations of the peak mode. We looked at the timespan of
approximately 855 rotations of modes or 1230 rotations of modes
and collected amplitudes of all modes from these three
regions. The number of amplitudes collected was over 1.1 million in
region and over 2.1 million in region .
Figure 4:
Probability density function for
the amplitude with
.
Same notations as in Figure 3.
[width=10cm]akpdf35.eps

Figure 3 shows a logplot of the PDF the amplitude
in and an exponential fit of its lowamplitude part. One can
see intermittency, i.e., an anomalously large probability of strong
waves. We can also see that this discrepancy from Gaussianity happens
in the tail, i.e. well below the mean amplitude value . While
the PDF tail in not long enough for drawing decisive conclusions about
realization of the theoretically predicted scaling, it certainly
gives a conclusive evidence that the probabilities of large amplitudes
are orders of magnitude higher than in Gaussian turbulence. Figure
4 shows the PDF of in . We can see some
nonGaussianity in as well, although much less than in
. Similar conclusion that the gravity wave turbulence is more
intermittent at low rather than high wavenumbers was reached on the
basis of numerical simulations in [3].
Deviations from Gaussianity can be also seen in figure 5
which shows ratio of the moments
to their values in Gaussian turbulence, . Again, we can see
that such deviations are greater at the small part of the inertial
range.
Next: Frequency properties.
Up: Results
Previous: Spectrum
Dr Yuri V Lvov
20070116