  (Abridged) We report on the properties of radio-selected galaxies within 30
very-rich Abell clusters with z < 0.25. These radio data sample the ultra-faint
(L(1.4) > 2E22 W/Hz) radio galaxy population with M_R < -21 using the
well-known FIR/radio correlation to link the radio with ongoing star formation
within individual cluster galaxies. These radio-selected galaxies reveal the
`active' galaxy population (starburst and active galactic nuclei) within these
rich cluster environments that can be identified regardless of their level of
dust obscuration. For all clusters in our sample, we are sensitive to star
formation rates (M > 5 M_sun) > 5 M_sun/yr. We have found that the excess
number of low-luminosity `starburst' radio-selected galaxies (SBRG) found by
Owen et. al. 1999 in Abell 2125 is not indicative of other rich clusters in our
sample. The average fraction of SBRG is <f(SBRG)> = 0.022+/-0.003. The A2125
fraction is f(SBRG) = 0.09+/-10.03 which is significantly different from the
sample average at a >99.99% confidence level. The bimodal structure of both the
x-ray brightness distribution and optical adaptively smoothed images of A1278
and A2125 suggests that ongoing cluster-cluster mergers may be enhancing this
SBRG population. There is a significant spatial distribution difference between
the low and high-luminosity (HLRG) radio-selected populations. The HLRGs seem
to be a subclass of the cluster's massive red elliptical population, while the
SBRGs have a projected radial distribution more like the blue spiral
population. Our results indicate that most of the SBRGs are probably gas-rich
disk galaxies undergoing > 5 M_sun/yr of star-formation.
