  We present a numerical study of turbulence in Bose-Einstein condensates
within the 3D Gross-Pitaevskii equation. We concentrate on the direct energy
cascade in forced-dissipated systems. We show that behavior of the system is
very sensitive to the properties of the model at the scales greater than the
forcing scale, and we identify three different universal regimes: (1) a
non-stationary regime with condensation and transition from a four-wave to a
three-wave interaction process when the largest scales are not dissipated, (2)
a steady weak wave turbulence regime when largest scales are dissipated with a
friction-type dissipation, (3) a state with a scale-by-scale balance of the
linear and the nonlinear timescales when the large-scale dissipation is a
hypo-viscosity.
