Skip to main content
SpringerLink
Log in

Asymmetric stokes flows generated by the motion of a closed torus

  • Original Papers
  • Published:
Zeitschrift für angewandte Mathematik und Physik ZAMP Aims and scope Submit manuscript

Abstract

Exact solutions of the Stokes equations are given for asymmetric flows produced by a closed torus which steadily translates along or rotates about a direction perpendicular to its axis of rotational symmetry in a quiescent viscous fluid. The force and couple acting on the body are calculated and the general motion of a closed torus is considered.

Zusammenfassung

Exakte Lösungen der Stokes'schen Gleichungen werden für eine asymmetrische Strömung angegeben, die von einem geschlossenen Torus in einer ruhenden zähen Flüssigkeit erzeugt wird. Dieser Torus bewegt sich entweder entlang einer Achse oder rotiert um eine Achse, wobei diese Achse jedesmal senkrecht zur Symmetrieaches des Torus steht. Die Kraft und das Moment die am Körper angreifen werden berechnet, und die allgemeine Bewegung eines geschlossenen Torus wird untersucht.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • H. Brenner andM. E. O'Neill, Chem. Engineering Science27, 1421 (1972).

    Google Scholar 

  • J. M. Dorrepaal, S. R. Majumdar, M. E. O'Neill andK. B. Ranger, Quart. J. Mech. Appl. Maths. 29,4, 381 (1976).

    Google Scholar 

  • D. Edwardes, Quart. J. Maths. 26,70, 157 (1909).

    Google Scholar 

  • S. Ghosh, Bull. Calcutta Math. Soc.18, 185 (1927).

    Google Scholar 

  • I. S. Gradshteyn andI. M. Ryzhik,Tables of Integrals, Series and Products, Academic Press, New York (1965).

    Google Scholar 

  • G. B. Jeffery, Proc. Roy. Soc. LondonA 102, 161 (1922).

    Google Scholar 

  • R. P. Kanwal, J. Fluid Mech.10, 17 (1961).

    Google Scholar 

  • H. Lamb,A Treatise on Hydrodynamics, 6th Edition, C.U.P. (1932).

  • S. R. Majumdar andM. E. O'Neill, Z. angew. Math. Phys.28, 541 (1977).

    Google Scholar 

  • H. K. Moffat, J. Fluid Mech.18, 1 (1964).

    Google Scholar 

  • A. Oberbeck, J. Maths.81, 62 (1876).

    Google Scholar 

  • W. M. Pell andL. E. Payne, Mathematika7, 78 (1960).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Mathematics, University of Calgary, Calgary, Alberta, Canada

    S. R. Majumdar

  2. Dept. of Mathematics, University College London, London, England

    M. E. O'Neill

Authors
  1. S. R. Majumdar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. E. O'Neill
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Majumdar, S.R., O'Neill, M.E. Asymmetric stokes flows generated by the motion of a closed torus. Journal of Applied Mathematics and Physics (ZAMP) 30, 967–982 (1979). https://doi.org/10.1007/BF01590494

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01590494

Keywords

Search

Navigation