  We calculate the local density of states of a vortex in a two-dimensional
s-wave superconductor, in the presence of a uniform applied supercurrent. The
supercurrent induces changes in the electronic structure for the isolated
vortex as well as the vortex lattice, which agree with the recent measurements
in 2H-NbSe2 [Maldonado et al., Phys. Rev. B 88, 064518 (2013)]. We find that
the supercurrent polarizes the core states when the vortices are pinned. This
shows that the transfer of momentum from the supercurrent to the bound states
and the rigidity of the wave functions must be considered for understanding the
various forces acting on collectively pinned Abrikosov vortices.
