  We theoretically demonstrate a possibility to observe the macroscopic Zeno
effect in an effectively two-dimensional (pancake-shaped) repulsive
Bose--Einstein condensate subjected to a strong narrow dissipation. We show
that the dissipation can generate stable stationary nonlinear flows which bear
either zero or non-zero topological charge (vorticity). The superfluid flows
towards the dissipative defect compensate the atomic losses. The macroscopic
Zeno effect manifests itself in a nonmonotonous dependence of the inward
current density on the strength of the dissipation.
