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Using $N$-body+SPH simulations of galaxies falling into a cluster, we studythe evolution of their radial density profiles. When evolved in isolation,galaxies develop a type~II (down-bending) profile. In the cluster, theevolution of the profile depends on the minimum cluster-centric radius thegalaxy reaches, which controls the degree of ram pressure stripping. If thegalaxy falls to $\sim 50\%$ of the virial radius, then the profile remainstype~II, but if the galaxy reaches down to $\sim 20\%$ of the virial radius thebreak weakens and the profile becomes more type~I like. The velocitydispersions are only slightly increased in the cluster simulations comparedwith the isolated galaxy; random motion therefore cannot be responsible forredistributing material sufficiently to cause the change in the profile type.Instead we find that the joint action of radial migration driven bytidally-induced spirals and the outside-in quenching of star formation due toram pressure stripping alters the density profile. As a result, this modelpredicts a flattening of the age profiles amongst cluster lenticulars withtype~I profiles, which can be observationally tested. %

The origin of type-I profiles in cluster lenticulars: An interplay between ram pressure stripping and tidally-induced spiral migration