Nonlinear Rayleigh–Taylor instability of a finite-thickness fluid shell in cylindrical geometry

A theoretical model is developed for the nonlinear evolution of single-mode Rayleigh–Taylor instability (RTI) in a finite-thickness, incompressible cylindrical shell within the (r, z) plane. This model is employed to investigate the individual and combined effects of cylindrical geometry and finite thickness on the RTI evolution. Results reveal that in cylindrical geometry, the perturbation velocity in divergent configurations is suppressed compared to that in planar geometry and decreases at late times. Conversely, in convergent configurations, the perturbation velocity is initially enhanced but eventually approaches the asymptotic velocity observed in planar geometry. Unlike the semi-infinite case, finite shell thickness results in continuous bubble acceleration, which increases as growing perturbations drive the bubble region further from hydrostatic equilibrium. Notably, in divergent configurations, cylindrical geometry mitigates the effects of finite thickness. Furthermore, parameter space analysis reveals the competition between the effects of finite thickness and cylindrical geometry.