  We report two simulations that have been carried out at the SX-5 at HLRS
(Stuttgart). One simulation is axisymmetric and purely hydrodynamic, but with a
resolution of 20 points per beam-radius (ppb). The bipolar jet is injected in
the center of a spherically symmetric King profile, initially underdense to its
environment by a factor of 10,000. As expected from our previous work, the jet
starts with producing a spherical bubble around it, bounded by the bow shock.
The bubble slowly elongates, first with roughly elliptical shape, and then
forms narrower extensions in beam direction. The final aspect ratio of the bow
shock is 1.8. We have transformed the results on a 3D-rectangular grid and
integrated the emission properties to compare the results with observed central
cluster radio galaxies. In the particular case of Cygnus A, we come to
convincing consistency, morphologically, regarding the size of the influenced
region by the jet, size, and cylindrical shape of the radio cocoon, and source
age. This strongly supports our earlier hypothesis on the nature of the jet in
Cygnus A, and the derived constraints on other jet parameters like a power of
$8 \times 10^{46}$ erg/s and an age of 27 Myr. But, the simulation also clearly
shows the shortcoming of the model: The jet's beam is very unstable, reaching
the tip of the bow shock only very seldom. Also, the contact discontinuity
between shocked beam plasma and shocked ambient gas is quite disrupted by the
action of the Kelvin-Helmholtz-instability. This is not seen in observations,
and necessitates the presence of dynamically important magnetic fields or an at
least moderately relativistic flow, or both. [abridged]
