  We report a numerical study of turbulence and Bose-Einstein condensation
within the two-dimmensional Gross-Pitaevski model with repulsive interaction.
In presence of weak forcing localized around some wave number in the Fourier
space, we observe three qualitatively different evolution stages. At the
initial stage a thermodynamic energy equipartition spectrum forms at both
smaller and larger scales with respect to the forcing scale. This agrees with
predictions of the the four-wave kinetic equation of the Wave Turbulence (WT)
theory. At the second stage, WT breaks down at large scales and the
interactions become strongly nonlinear. Here, we observe formation of a gas of
quantum vortices whose number decreases due to an annihilation process helped
by the acoustic component. This process leads to formation of a coherent-phase
Bose-Einstein condensate. After such a coherent-phase condensate forms,
evolution enters a third stage characterised by three-wave interactions of
acoustic waves that can be described again using the WT theory.
