Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



The time-dependent Stokes paradox

Author: S. H. Smith
Journal: Quart. Appl. Math. 49 (1991), 427-435
MSC: Primary 76D07
DOI: https://doi.org/10.1090/qam/1121675
MathSciNet review: MR1121675
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Abstract: When a uniform stream starts to flow impulsively at time $ t = 0$ past a two-dimensional body, the solution of the Stokes equation indicates that the velocity grows without bound as $ t \to \infty $. It is seen that this is a natural extension of the Stokes paradox to unsteady flows. Two resolutions of this result are presented: firstly, through an analysis of the Oseen equation on the basis of singular perturbation theory and, secondly, through considering the two-dimensional body as the limit of a three-dimensional body when the length increases without bound.

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DOI: https://doi.org/10.1090/qam/1121675
Article copyright: © Copyright 1991 American Mathematical Society

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