Viscous Rayleigh-Taylor instability in spherical geometry

Karnig O. Mikaelian
Phys. Rev. E 93, 023104 – Published 8 February 2016

Abstract

We consider viscous fluids in spherical geometry, a lighter fluid supporting a heavier one. Chandrasekhar [Q. J. Mech. Appl. Math. 8, 1 (1955)] analyzed this unstable configuration providing the equations needed to find, numerically, the exact growth rates for the ensuing Rayleigh-Taylor instability. He also derived an analytic but approximate solution. We point out a weakness in his approximate dispersion relation (DR) and offer a somewhat improved one. A third DR, based on transforming a planar DR into a spherical one, suffers no unphysical predictions and compares reasonably well with the exact work of Chandrasekhar and a more recent numerical analysis of the problem [Terrones and Carrara, Phys. Fluids 27, 054105 (2015)].

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  • Received 11 September 2015

DOI:https://doi.org/10.1103/PhysRevE.93.023104

©2016 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Karnig O. Mikaelian

  • Lawrence Livermore National Laboratory, Livermore, California 94551, USA

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Issue

Vol. 93, Iss. 2 — February 2016

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