Non-unique solutions of the Navier-Stokes equations for the Karman swirling flow

D. Dijkstra; P.J. Zandbergen

doi:10.1007/BF01535696

Non-unique solutions of the Navier-Stokes equations for the Karman swirling flow

D. Dijkstra, P.J. Zandbergen

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Abstract

In this paper it is shown numerically that axially-symmetric solutions of the Navier-Stokes equations, which describe the rotating flow above a disk which is itself rotating, are non-unique. The numerical techniques designed to calculate such solutions with a high power of resolution are given. Especially the behaviour in and around the first branching point is considered. It is found that fors=−0.16054 two branches coincide. The second branch has been almost completely calculated. It ranges back to positive values ofs.

Original language	Undefined
Pages (from-to)	167-188
Journal	Journal of engineering mathematics
Volume	11
Issue number	2
DOIs	https://doi.org/10.1007/BF01535696
Publication status	Published - 1977

Keywords

IR-85516

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10.1007/BF01535696

Dijkstra77non

Cite this

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title = "Non-unique solutions of the Navier-Stokes equations for the Karman swirling flow",

abstract = "In this paper it is shown numerically that axially-symmetric solutions of the Navier-Stokes equations, which describe the rotating flow above a disk which is itself rotating, are non-unique. The numerical techniques designed to calculate such solutions with a high power of resolution are given. Especially the behaviour in and around the first branching point is considered. It is found that fors=−0.16054 two branches coincide. The second branch has been almost completely calculated. It ranges back to positive values ofs.",

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AU - Zandbergen, P.J.

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AB - In this paper it is shown numerically that axially-symmetric solutions of the Navier-Stokes equations, which describe the rotating flow above a disk which is itself rotating, are non-unique. The numerical techniques designed to calculate such solutions with a high power of resolution are given. Especially the behaviour in and around the first branching point is considered. It is found that fors=−0.16054 two branches coincide. The second branch has been almost completely calculated. It ranges back to positive values ofs.

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JO - Journal of engineering mathematics

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