  The observed super-massive black hole (SMBH) mass -- galaxy velocity
dispersion ($M_{\rm bh} - \sigma$) correlation may be established when
winds/outflows from the SMBH drive gas out of the potential wells of classical
bulges. Here we present numerical simulations of this process in a static
isothermal potential. Simple spherically symmetric models of SMBH feedback at
the Eddington luminosity can successfully explain the $M_{\rm bh} - \sigma$ and
nuclear cluster mass $M_{\rm NC}-\sigma$ correlations, as well as why larger
bulges host SMBHs while smaller ones host nuclear star clusters. However these
models do not specify how SMBHs feed on infalling gas whilst simultaneously
producing feedback that drives gas out of the galaxy.
  More complex models with rotation and/or anisotropic feedback allow SMBHs to
feed via a disc or regions not exposed to SMBH winds, but in these more
realistic cases it is not clear why a robust $M_{\rm bh} - \sigma$ relation
should be established. In fact, some of the model predictions contradict
observations. For example, an isotropic SMBH wind impacting on a disc (rather
than a shell) of aspect ratio $H/R \ll 1$ requires the SMBH mass to be larger
by a factor $\sim R/H$, which is opposite to what is observed. We conclude that
understanding how a SMBH feeds is as important a piece of the puzzle as
understanding how its feedback affects its host galaxy.
  Finally, we note that in aspherical cases the SMBH outflows induce
differential motions in the bulge. This may pump turbulence that is known to
hinder star formation in star forming regions. SMBH feedback thus may not only
drive gas out of the bulge but also reduce the fraction of gas turned into
stars.
