Cylindrical rotating Rayleigh-Taylor instability

Scase, M. M.; Sengupta, S.

Abstract

We consider a spun-up system of an inner cylinder of fluid surrounded by an outer fluid layer within a rotating cylindrical container, in the absence of gravity. The outer layer may be of differing density and viscosity to the inner layer. If the inner layer is denser than the outer layer then the effect of rotation, in the presence of a perturbation to the interface between the two layers, is to force the inner fluid outwards and the outer fluid inwards, subject to possible surface tension stabilisation. The relative importance of viscosity to rotation is described by an Ekman number. We investigate the behaviour of perturbations to the interface in the inviscid limit and low and high viscosity limits. In the low viscosity limit perturbations grow as an O(Ek 1/2) correction to the inviscid growth rate. In the high viscosity limit perturbations grow as O(Ek −1). In the absence of surface tension the preferred mode of growth is independent of the layer density difference and depends only upon the domain aspect ratio, initial position of the interface, and viscosity contrast. Numerical simulations of the flow are carried out using a volume-of-fluid formulation. The growth rates from these simulations are compared with the theoretical predictions in both low and high viscosity limits and the agreement is seen to be good. Finally, we examine the special case of a single-layer rotating viscous column and describe the preferred-mode boundary between a varicose mode and a spiral mode in the high viscosity, high surface tension limit.

Citation

Scase, M. M., & Sengupta, S. (2021). Cylindrical rotating Rayleigh-Taylor instability. Journal of Fluid Mechanics, 907, Article A33. https://doi.org/10.1017/jfm.2020.842

• Journal Article Type: Article
• Acceptance Date: Sep 30, 2020
• Online Publication Date: Nov 25, 2020
• Publication Date: Jan 25, 2021
• Deposit Date: Sep 25, 2020
• Publicly Available Date: May 26, 2021
• Journal: Journal of Fluid Mechanics
• Print ISSN: 0022-1120
• Electronic ISSN: 1469-7645
• Publisher: Cambridge University Press
• Peer Reviewed: Peer Reviewed
• Volume: 907
• Article Number: A33
• DOI: https://doi.org/10.1017/jfm.2020.842
• Keywords: Mechanical Engineering; Mechanics of Materials; Condensed Matter Physics
• Public URL: https://nottingham-repository.worktribe.com/output/4924995
• Publisher URL: http://journals.cambridge.org/action/displayJournal?jid=FLM