Using numerical techniques we study the global stability of cooling flows i
n X-ray luminous giant elliptical galaxies. As an unperturbed equilibrium s
tate we choose the hydrostatic gas recycling model, Non-equilibrium radiati
ve cooling, stellar mass loss, heating by type la supernovae, distributed m
ass deposition and thermal conductivity are included, Although the recyclin
g model reproduces the basic X-ray observables, it appears to be unstable w
ith respect to the development of inflow or outflow, In spherical symmetry
the inflows are subject to a central cooling catastrophe, while the outflow
s saturate in a form of a subsonic galactic wind. Two-dimensional axisymmet
ric random velocity perturbations of the equilibrium model trigger the onse
t of a cooling catastrophe, which develops in an essentially non-spherical
way. The simulations show a patchy pattern of mass deposition and the forma
tion of hollow gas jets, which penetrate through the outflow down to the ga
laxy core, The X-ray observables of such a hybrid gas flow mimic those of t
he equilibrium recycling model, but the gas temperature exhibits a central
depression. The mass deposition rate (M) over dot consists of two contribut
ions of similar size: (i) a hydrostatic one resembling that of the equilibr
ium model, and (ii) a dynamical one which is related to the jets and is mor
e concentrated towards the centre. For a model galaxy, like NGC 4472, our 2
D simulations predict (M) over dot approximate to 2 M. yr(-1) within the co
oling radius for the advanced non-linear stage of the instability. We discu
ss the implications of these results to Her nebulae and star formation in c
ooling flow galaxies and emphasize the need for high-resolution 3D simulati
ons.