  The active galactic nuclei (AGN) lobe radio luminosities modelled in
hydrodynamical simulations and most analytical models do not address the
redistribution of the electron energies due to adiabatic expansion, synchrotron
radiation and inverse-Compton scattering of CMB photons. We present a
synchrotron emissivity model for resolved sources which includes a full
treatment of the loss mechanisms spatially across the lobe, and apply it to a
dynamical radio source model with known pressure and volume expansion rates.
The bulk flow and dispersion of discrete electron packets is represented by
tracer fields in hydrodynamical simulations; we show that the mixing of
different aged electrons strongly effects the spectrum at each point of the
radio map in high-powered FR-II sources. The inclusion of this mixing leads to
a factor of a few discrepancy between the spectral age measured using impulsive
injection models (e.g. JP model) and the dynamical age. The observable
properties of radio sources are predicted to be strongly frequency dependent:
FR-II lobes are expected to appear more elongated at higher frequencies, while
jetted FR-I sources appear less extended. The emerging FR0 class of radio
sources, comprising gigahertz peaked and compact steep spectrum sources, can
potentially be explained by a population of low-powered FR-Is. The extended
emission from such sources is shown to be undetectable for objects within a few
orders of magnitude of the survey detection limit and to not contribute to the
curvature of the radio SED.
