  Using numerical techniques we studied the global stability of cooling flows
in giant elliptical galaxies. As an initial equilibrium state we choose the
hydrostatic gas recycling model (Kritsuk 1996). Non-equilibrium radiative
cooling, stellar mass loss, heating by type Ia supernovae, distributed mass
deposition, and thermal conductivity are included. Although the recycling model
reproduces the basic X-ray observables, it appears to be unstable with respect
to the development of inflow or outflow. In spherically symmetry the inflows
are subject to a central cooling catastrophe, while the outflows saturate in a
form of a subsonic galactic wind. Two-dimensional axisymmetric random velocity
perturbations of the equilibrium model trigger the onset of a cooling
catastrophe, which develops in an essentially non-spherical way. The
simulations show a patchy pattern of mass deposition and the formation of
hollow gas jets, which penetrate through the outflow down to the galaxy core.
The X-ray observables of such a hybrid gas flow mimic those of the equilibrium
recycling model, but the gas temperature exhibits a central depression. The
mass deposition rate M_dot consists of two contributions of similar size: (i) a
hydrostatic one resembling that of the equilibrium model, and (ii) a dynamical
one which is related to the jets and is more concentrated to the centre. For a
model galaxy, like NGC 4472, our 2D simulations predict M_dot = 2 M_sun/yr
within the cooling radius for the advanced non-linear stage of the instability.
We discuss the implications of these results to H_alpha nebulae and star
formation in cooling flow galaxies and emphasize the need for high-resolution
3D simulations.
