In the previous section, we established that onemode PDF's can deviate from the Rayleigh distributions if the flux of probability in the amplitude space is not equal to zero. However, in the full mode amplitude space, the flux lines cannot originate or terminate, i.e. there the probability ``sources'' and ``sinks'' are impossible, see (69). Even adding forcing or dissipation into the dynamical equations does not change this fact because this can only modify the expression for the flux (see the Appendix) but it cannot change the PDF continuity equation (65). Thus, presence of the finite flux for the onepoint PDF's corresponds to deviation of the flux lines from the straight lines in the mode amplitude space. The global structure of such a solution in the mode space corresponds to a dimensional probability vortex. This probability vortex is illustrated in figure ? which sketches its projection onto a a 2D plane corresponding to one lowwavenumber and one highwavenumber amplitudes. Taking 1D sections of this vortex one observes a positive onemode flux at high and a negative onemode flux at low , in accordance with the numerical observations of figure 2.
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