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.

References [Enhancements On Off] (What's this?)

  • [1] G. G. Stokes, On the effect of the internal friction of fluids on the motion of pendulums, Trans. Camb. Phil. Soc. 9, 9-106 (1851)
  • [2] S. Kaplun and P. A. Lagerstrom, Asymptotic expansions of Navier-Stokes solutions for small Reynolds numbers, J. Math. Mech. 6, 585-593 (1957) MR 0091693
  • [3] I. Proudman and J. R. A. Pearson, Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder, J. Fluid Mech. 2, 237-262 (1957) MR 0086545
  • [4] A. Erdelyi, et al., Tables of Integral Transforms, Vol. 1, McGraw-Hill, New York, 1954
  • [5] Y. Y. Shi, Low Reynolds number flow past an ellipsoid of revolution of large aspect ratio, J. Fluid Mech. 23, 657-671 (1965) MR 0189369
  • [6] S. H. Smith, The Jeffery paradox as the limit of a three dimensional Stokes flow, Phys. Fluids A. 2, 661-665 (1990) MR 1050009

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

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