  The final stage of Bose-Einstein condensation in a large volume occurs
through coarsening--growth of individual correlated patches. We present
analytical arguments and numerical evidence that in the momentum space this
growth corresponds to strong turbulence of the particle number, with a
turbulent cascade towards the infrared and the power law $n(k) \propto
k^{-(d+1)}$ in $d=2,3$ spatial dimensions. As a corollary, we find that the
correlation length grows linearly in time, with the speed of order of the speed
of Bogoliubov's quasiparticles (phonons). We use these results to estimate the
speed of BEC in atomic vapors and in galactic dark matter.
