  We present three dimensional simulations of the interaction of a light
hypersonic jet with an inhomogeneous thermal and turbulently supported disk in
an elliptical galaxy. We model the jet as a light, supersonic non-relativistic
flow with parameters selected to be consistent with a relativistic jet with
kinetic power just above the FR1/FR2 break.
  We identify four generic phases in the evolution of such a jet with the
inhomogeneous interstellar medium: 1) an initial ``flood and channel'' phase,
where progress is characterized by high pressure gas finding changing weak
points in the ISM, flowing through channels that form and re-form over time, 2)
a spherical, energy-driven bubble phase, were the bubble is larger than the
disk scale, but the jet remains fully disrupted close to the nucleus, 3) a
rapid, jet break--out phase the where jet breaks free of the last dense clouds,
becomes collimated and pierces the spherical bubble, and 4) a classical phase,
the jet propagates in a momentum-dominated fashion leading to the classical jet
+ cocoon + bow-shock structure.
  Mass transport in the simulations is investigated, and we propose a model for
the morphology and component proper motions in the well-studied Compact
Symmetric Object 4C31.04.
