If spiral galaxies form due to perturbations, why aren't there more spiral galaxies in galaxy clusters, where interaction/perturbation is likely? I read the other article with an excellent explanation of simulation results and the mathematics behind spiral arm formation yet was left baffled by the point that the principal influence that would lead to arm formation was perturbation. That's because separately I read that spiral galaxies in galaxy clusters were exceedingly rare. Seems counterintuitive.
 A: I don't think this is an entirely settled issue, but it is clear that spiral galaxies were more common in the past in higher redshift clusters. The fact that the number of gas-poor S0 (lenticular) galaxies also increases with decreasing redshift suggests that there is some transformation going on as the universe ages, associated with some sort of interaction. This idea is supported by the observation that spiral galaxies are rarer in denser clusters (e.g. Dressler 1980).
There are at least two proposed mechanisms for these transformations:
Galaxy clusters have a relatively dense intracluster medium and ram-pressure stripping when a galaxy is in the central parts of the cluster can remove gas and dust from a spiral galaxy, quenching star formation and transforming it into an S0 (e.g. D'Onofrio et al. 2015).
Another idea, originating I think with Moore et al. (1996), is that spiral galaxies transform thanks to tidal interactions and stripping, both with the cluster potential in the central regions and due to close encounters with other large galaxies - so-called "galaxy harassment".
But you are right to be somewhat confused. Spiral galaxies (or rather disk galaxies) are thought to be built up by a sequence of mergers, which might be thought to be enhanced within a cluster. The spiral structure is then brought about by density waves triggering star formation. But for a visible spiral structure to be maintained, there needs to be a supply of gas in the disk and ongoing star formation. The processes described in the previous paragraphs must remove the gas and quench the star formation effectively.
