Viscous Rayleigh-Taylor instability in spherical geometry

KO Mikaelian - Physical Review E, 2016 - APS
Physical Review E, 2016APS
We consider viscous fluids in spherical geometry, a lighter fluid supporting a heavier one.
Chandrasekhar [QJ Mech. Appl. Math. 8, 1 (1955) 10.1093/qjmam/8.1. 1] 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 …
We consider viscous fluids in spherical geometry, a lighter fluid supporting a heavier one. Chandrasekhar [Q. J. Mech. Appl. Math. 8, 1 (1955)10.1093/qjmam/8.1.1] 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)10.1063/1.4921648].
American Physical Society
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