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On the slow steady motion of a viscous fluid due to two rotating tori

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An approximate solution, correct to order three in a small parameter, is established for the velocity field induced in a viscous fluid by the slow rotation of two tori. The tori possess a common axis and have concentric circular sections. The small parameter is the ratio of the radius of the outer circular section to the distance of the section centre from the axis of rotation. The torque acting on each toroidal surface is also obtained.

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References

  1. Schneider, J. C., O'Neill, M. E., Brenner, H.: On the slow viscous rotation of a body straddling the interface between two immiscible semi-infinite fluids. Mathematika20, 175 (1973).

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  3. Murray, J. C.: Coordinate systems associated with a class of boundary value problems. J. Inst. Math. Appl.25, 397 (1980).

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  1. Department of Mathematical Sciences, University of Petroleum and Minerals, Dhahran, Saudi Arabia

    J. C. Murray

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  1. J. C. Murray
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Murray, J.C. On the slow steady motion of a viscous fluid due to two rotating tori. Acta Mechanica 42, 3–10 (1982). https://doi.org/10.1007/BF01176510

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  • DOI: https://doi.org/10.1007/BF01176510

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