Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Viscous effects on perturbed spherical flows

Author: Andrea Prosperetti
Journal: Quart. Appl. Math. 34 (1977), 339-352
DOI: https://doi.org/10.1090/qam/99652
MathSciNet review: QAM99652
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Abstract: The problem of two viscous, incompressible fluids separated by a nearly spherical free surface is considered in general terms as an initial-value problem to first order in the perturbation of the spherical symmetry. As an example of the applications of the theory, the free oscillations of a viscous liquid drop and of a bubble in a viscous liquid are studied in some detail. It is shown that the oscillations are initially describable in terms of an irrotational approximation, and that the normal-mode results are recovered as $ t \to \infty $. In between these asymptotic regimes, however, the motion is significantly different from either approximation.

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DOI: https://doi.org/10.1090/qam/99652
Article copyright: © Copyright 1977 American Mathematical Society

American Mathematical Society