A comprehensive study of the effect of the cluster environment on the far-i
nfrared (FIR)-radio correlation in nearby Abell clusters is presented. Usin
g a cluster radio galaxy database, optical spectroscopy, and high-resolutio
n radio images to remove active galactic nuclei (AGNs), we assess the FIR-r
adio correlation of cluster galaxies from the centers of the clusters out w
ell past the classical Abell radius. The FIR-radio correlation is shown to
hold quite well for star-forming galaxies, and the FIR and radio fluxes for
cluster AGNs are also well correlated. In the case of AGNs, the relative r
adio-to-FIR fluxes are greater and the scatter in the correlation is larger
than those seen for star-forming galaxies. We also find that there is a ra
re but statistically significant excess of star-forming galaxies with enhan
ced radio emission in the centers of the clusters and that the degree of th
is enhancement is typically a factor of 2 or 3. The FIR-radio correlation f
or cluster star-forming galaxies is also tested against the line-of-sight v
elocity relative to the cluster systemic velocities, but no significant cor
relation is found. While the radial dependence of the FIR-radio correlation
is consistent with the model wherein ram pressure increases the magnetic f
ield strengths of the cluster galaxies through compression, the velocity da
ta do not confirm this model. Although a contribution from ram pressure can
not be ruled out, the thermal pressure due to the ICM alone is an equally v
iable alternative. The high-resolution radio images largely reject the hypo
thesis that the increased radio emission arises from an AGN component, stre
ngthening the claim that the change in the correlation is caused by a chang
e in the environment of the galaxies.