  We analyse asymptotically and numerically the motion around a single impurity
and a network of impurities inserted in a two-dimensional superfluid. The
criticality for the break down of superfluidity is shown to occur when it
becomes energetically favourable to create a doublet - the limiting case
between a vortex pair and a rarefaction pulse on the surface of the impurity.
Depending on the characteristics of the potential representing the impurity
different excitation scenarios are shown to exist for a single impurity as well
as for a lattice of impurities. Depending on the lattice characteristics it is
shown that several regimes are possible: dissipationless flow, excitations
emitted by the lattice boundary, excitations created in the bulk and the
formation of large scale structures.
