Difficulty in understanding turbulence in 2D Gross-Pitaevsky model is
related to the fact that the spectra of both inverse and direct
cascades in weak-turbulence approximation carry fluxes of a wrong sign
and cannot be realized. We derived analytically the exact flux
constancy laws (analogs of Kolmogorov's 4/5-law), expressed via the
fourth-order moment and valid for any nonlinearity. We confirmed the
flux laws in direct numerical simulations. We show that a constant
flux is realized by non-local wave interaction both in direct and
inverse cascades. Wave spectra (second-order moments) are close to
slightly (logarithmically) distorted thermal equilibrium in both
cascades.
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