Three-dimensional elastic Rayleigh-Taylor instability at the cylindrical interface

This paper presents a linear analysis of elastic Rayleigh-Taylor instability at both cylindrical column and cylindrical shell interfaces. By considering the rotational part of the disturbance flow field, an exact solution is derived, revealing that the most unstable mode is two-dimensional in the cross section. As the column radius decreases, the maximum growth rate increases, while the corresponding azimuthal wave number decreases incrementally until it reaches 1. Thinning the cylindrical shell is found to be a destabilizing effect, leading to an increase in both the cutoff wave number and the most unstable azimuthal wave number. The maximum growth rate usually increases as the shell becomes thinner, except in cases with small radii where feedthrough effects occur. For thin shells with small radii, the cutoff axial wave number is determined by the radius rather than the shell thickness. Comparisons between the growth rates derived from the potential flow theory and the exact solution show significant discrepancies in cylindrical shells, mainly due to substantial deviations in the cutoff wave number.