Do nuclear rings in barred galaxies form at the shear minimum of the
  rotation curve?
  It has been recently suggested that (i) nuclear rings in barred galaxies
(including our own Milky Way) form at the radius where the shear parameter of
the rotation curve reaches a minimum; (ii) the acoustic instability of
Montenegro et al. is responsible for driving the turbulence and angular
momentum transport in the central regions of barred galaxies. Here we test
these suggestions by running simple hydrodynamical simulations in a logarithmic
barred potential. Since the rotation curve of this potential is scale-free, the
shear minimum theory predicts that no ring should form. We find that in
contrast to this prediction, a ring does form in the simulation, with
morphology consistent with that of nuclear rings in real barred galaxies. This
proves that the presence of a shear-minimum is not a necessary condition for
the formation of a ring. We also find that perturbations that are predicted to
be acoustically unstable wind up and eventually propagate off to infinity, so
that the system is actually stable. We conclude that (i) the shear-minimum
theory is an unlikely mechanism for the formation of nuclear rings in barred
galaxies; (ii) the acoustic instability is a spurious result and may not be
able to drive turbulence in the interstellar medium, at least for the case
without self-gravity. The question of the role of turbulent viscosity remains
open.
