Effects of interfacial curvature on Rayleigh-Taylor instability

TL;DR

This paper investigates how the curvature of an interface affects the stability and growth of Rayleigh-Taylor instability, providing a new analytical framework that extends previous approximations.

Contribution

It introduces a novel stability analysis based on operator and boundary perturbation theories that explicitly accounts for interfacial curvature effects.

Findings

Interfacial curvature influences the growth rate of instability.

The analysis quantifies how curvature affects wavenumber selection.

Provides a rigorous generalization of Layzer's approximation.

Abstract

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 \textit{ad hoc} idea, due to Layzer [Astrophys. J. \textbf{122}, 1-12 (1955)], of approximating the potential velocity field near the interface.