  We have carried out two-dimensional, axisymmetric, hydrodynamic numerical
modelling of the evolution of radio galaxy lobes. The emphasis of our work is
on including realistic hot-gas environments in the simulations and on
establishing what properties of the resulting radio lobes are independent of
the choice of environmental properties and of other features of the models such
as the initial jet Mach number. The simulated jet power we use is chosen so
that we expect the inner parts of the lobes to come into pressure balance with
the external medium on large scales; we show that this leads to the expected
departure from self-similarity and the formation of characteristic central
structures in the hot external medium. The work done by the expanding radio
lobes on the external hot gas is roughly equal to the energy stored in the
lobes for all our simulations once the lobes are well established. We show that
the external pressure at the lobe midpoint is a reasonable estimate of the
internal (lobe) pressure, with only a weak dependence on the environmental
parameters: on the other hand, the predicted radio emission from a source of a
given physical size has a comparatively strong dependence on the environment in
which the lobe resides, introducing an order of magnitude of scatter into the
jet power versus radio luminosity relationship. X-ray surface brightness and
temperature visualizations of our simulations bear a striking resemblance to
observations of some well-studied radio galaxies.
