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WT closure relies on the RPA properties of the wave fields, i.e. that
the amplitudes and the phase factors are statistically
independent variables. On the other hand, WT calculation for the
phases shows that these quantities get correlated. In order
to check these properties and predictions numerically, let us
introduce a function that measures the degree of statistical
dependence (or independence) of some Fourier-space variables
and
,
For example, we can examine to what degree amplitudes and independent
of the phase factors by looking at the function
for different values of
and . Independence of the amplitudes at different wavenumbers
can be examined by the auto-correlation function
, and similar for the phase factors
and the phases.
We restrict ourselves with choosing
and
with
.
Figure 15 shows the values of correlators
and
as functions of .
In agreement with WT predictions,
auto-correlations of 's are very small
whereas
the ones of 's are significant (except, of course,
for where by definition these correlators are equal to one).
Correlators
and
are shown in figure 16. Again, we see a good agreement
with the WT prediction: these correlations are very small (except, again,
).
Next: Discussions
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Previous: Nonlinearly active modes and
Dr Yuri V Lvov
2007-01-16