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.
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)
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- Ian 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 (1957), 237–262. MR 86545, DOI https://doi.org/10.1017/S0022112057000105
A. Erdelyi, et al., Tables of Integral Transforms, Vol. 1, McGraw-Hill, New York, 1954
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- S. H. Smith, The Jeffery paradox as the limit of a three-dimensional Stokes flow, Phys. Fluids A 2 (1990), no. 5, 661–665. MR 1050009, DOI https://doi.org/10.1063/1.857718
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)
S. Kaplun and P. A. Lagerstrom, Asymptotic expansions of Navier-Stokes solutions for small Reynolds numbers, J. Math. Mech. 6, 585–593 (1957)
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)
A. Erdelyi, et al., Tables of Integral Transforms, Vol. 1, McGraw-Hill, New York, 1954
Y. Y. Shi, Low Reynolds number flow past an ellipsoid of revolution of large aspect ratio, J. Fluid Mech. 23, 657–671 (1965)
S. H. Smith, The Jeffery paradox as the limit of a three dimensional Stokes flow, Phys. Fluids A. 2, 661–665 (1990)
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Article copyright:
© Copyright 1991
American Mathematical Society
