We report results of sumulation of wave turbulence. Both inverse and direct cascades are observed. The definition of mesoscopic turbulence is given. This is a regime when the number of modes in a system involved in turbulence is high enough to qualitatively simulate most of the processes but significantly smaller then the threshold which gives us quantitative agreement with the statistical description, such as kinetic equation. Such a regime takes place in numerical simulation, in essentially finite systems, etc.
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