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Cylindrical rotating Rayleigh–Taylor instability

Published online by Cambridge University Press:  25 November 2020

M. M. Scase Open the ORCID record for M. M. Scase [Opens in a new window]  and
S. Sengupta
M. M. Scase*
Affiliation:
Geophysical Fluid Dynamics, Woods Hole Oceanographic Institution, Woods Hole, MA02543, USA School of Mathematical Sciences, University of Nottingham, NottinghamNG7 2RD, UK
S. Sengupta
Affiliation:
Geophysical Fluid Dynamics, Woods Hole Oceanographic Institution, Woods Hole, MA02543, USA NERSC, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA94720, USA
*
†Email address for correspondence: [email protected]
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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.

JFM classification

Geophysical and Geological Flows: Rotating flows Multiphase and Particle-laden Flows: Multiphase flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 907 , 25 January 2021 , A33
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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