Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Slow oscillatory Stokes flow


Author: S. H. Smith
Journal: Quart. Appl. Math. 55 (1997), 1-22
MSC: Primary 76D07
DOI: https://doi.org/10.1090/qam/1433748
MathSciNet review: MR1433748
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Abstract: Two transient problems in slow viscous flow are considered where the corresponding steady-state behaviour leads to the paradoxical results of Stokes and Jeffery. First, the oscillatory flow past a circular cylinder is investigated when the frequency $ \lambda $ tends to zero, where an outer domain of size $ O\left( {\lambda ^{ - 1/2}} \right)$ is required to ensure that the velocity conditions at infinity are satisfied. The flow close to the cylinder is quasi-steady except for a time of length $ O\left( 1 \right)$ about the time of separation; most of the action takes place in the outer domain where the dominant transient behaviour extends over a time that is $ O\left[ {{{\left\{ {ln\left( {\lambda ^{ - 1}} \right)} \right\}}^{ - 1}}} \right]$ of a complete cycle.


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DOI: https://doi.org/10.1090/qam/1433748
Article copyright: © Copyright 1997 American Mathematical Society


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