https://doi.org/10.1140/epjp/s13360-023-04804-6
Regular Article
New insights on the Stokes paradox for flow in unbounded domains
1
Simula Research Laboratory, Oslo, Norway
2
University of Chicago, Chicago, IL, USA
Received:
18
July
2023
Accepted:
17
December
2023
Published online:
6
January
2024
Stokes flow equations, used to model creeping flow, are a commonly used simplification of the Navier–Stokes equations. In infinite domains, they admit a fundamental paradox. In this work we review this paradox and present new insights related to recent research. We approach the paradox from three different points of view: modern functional analysis, numerical simulations, and classical analytic techniques. The first approach yields a novel, rigorous derivation of the paradox. We also show that relaxing the Stokes no-slip condition (by introducing a Navier friction condition) in one case resolves the Stokes paradox but gives rise to d’Alembert’s paradox. The Stokes paradox has previously been resolved by Oseen, who showed that it is caused by a limited validity of Stokes’ approximation. We show that the paradox still holds for the Reynolds–Orr equations describing kinetic energy flow instability, meaning that flow instability steadily increases with domain size. We refer to this as an instability paradox.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
