- ... taken.
^{1}
- It is easily to extend the analysis to the infinite Fourier
space,
. In this case, the full joint PDF would
still have to be defined as a
limit of an -mode PDF,
but this limit would have to be taken in such a way that both
and the density of the Fourier modes tend to infinity
simultaneously.
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- ... field.
^{2}
- We keep the same acronym as in
related ``Random Phase Approximation'' but now interpret it differently
because (i) we emphasise the amplitude randomness and (ii) now RPA is a
defined property of the field to be examined and not an approximation.
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- ... scales.
^{3}
- Hereafter we omit superscript
in the -mode objects if it does not lead to a confusion.
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- ...
respectively.
^{4}
- This technique provides a useful
classification method but not a complete mathematical description of
the terms involved.
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- ... means
^{5}
- In the present paper we consider only spatially homogeneous wave
turbulence fields. In spatially homogeneous fields, due to momentum
conservation, there is no coupling to the zero mode because such
coupling would violate momentum conservation. Therefore if one of the
arguments of the interaction matrix element is equal to zero, the
matrix element is identically zero. That is to say that for any
spatially homogeneous wave turbulence system
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