  We study the dynamics of a Bose-Einstein condensate in a Sinai-oscillator
trap under a monochromatic driving force. Such a trap is formed by a harmonic
potential and a repulsive disk located in the center vicinity corresponding to
the first experiments of condensate formation by Ketterle group in 1995. We
argue that the external driving allows to model the regime of weak wave
turbulence with the Kolmogorov energy flow from low to high energies. We show
that in a certain regime of weak driving and weak nonlinearity such a turbulent
energy flow is defeated by the Anderson localization that leads to localization
of energy on low energy modes. A critical threshold is determined above which
the turbulent flow to high energies becomes possible. We argue that this
phenomenon can be studied with ultra cold atoms in magneto-optical traps.
