Effects of interfacial curvature on Rayleigh-Taylor instability

In this work a non-trivial effect of the interfacial curvature on the stability of accelerated interfaces, such as liquid rims, is uncovered. The new stability analysis, based on operator and boundary perturbation theories, reveals and quantifies influence of the interfacial curvature on the growth rate and on the wavenumber selection of the Rayleigh-Taylor instability. The systematic approach developed here also provides a rigorous generalization of the widely used $\mathit{\text{ad}}\mathit{\text{hoc}}$ idea, due to Layzer [Astrophys. J. $\mathbf{\text{122}}$, 1-12 (1955)], of approximating the potential velocity field near the interface.