  The restoration of symmetries is one of the most fascinating properties of
turbulence. We report a study of the emergence of isotropy in the
Gross-Pitaevskii model with anisotropic forcing. Inspired by recent
experiments, we study the dynamics of a Bose-Einstein condensate in a
cylindrical box driven along the symmetry axis of the trap by a spatially
uniform force. We introduce a measure of anisotropy $A(k,t)$ defined on the
momentum distributions $n(\boldsymbol{k},t)$, and study the evolution of
$A(k,t)$ and $n(\boldsymbol{k},t)$ as turbulence proceeds. As the system
reaches a steady state, the anisotropy, large at low momenta because of the
large-scale forcing, is greatly reduced at high momenta. While
$n(\boldsymbol{k},t)$ exhibits a self-similar cascade front propagation,
$A(k,t)$ decreases without such self-similar dynamics. Finally, our numerical
calculations show that the isotropy of the steady state is robust with respect
to the amplitude of the drive.
