Journal of Engineering Mathematics

, Volume 27, Issue 3, pp 245–264 | Cite as

Swirling free surface flow in cylindrical containers

  • A. Siginer
  • R. Knight


Free surface flow in a cylindrical container with steadily rotating bottom cap is investigated. A regular domain perturbation in terms of the angular velocity of the bottom is used. The flow field is made up of the superposition of azimuthal and meridional fields. The meridional field is solved both by biorthogonal series and a numerical algorithm. The free surface on the liquid is determined at the lowest significant order. The aspect ratio of the cylinder may generate a multiple cell structure in the meridional plane which in turn shapes the free surface.


Mathematical Modeling Aspect Ratio Free Surface Flow Field Angular Velocity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    T. Von Kármán, Uber laminare und turbulente Reibung.ZAMM 1 (1921) 233–252.Google Scholar
  2. 2.
    W.G. Cochran, The flow due to a rotating disc.Proceedings of Cambridge Philosophical Society 30 (1934) 365–375.Google Scholar
  3. 3.
    U.T. Bödewadt, Die Drehströmung über festem Grunde.ZAMM 20 (1940), 241–253.Google Scholar
  4. 4.
    G.K. Batchelor, Note on a class of solutions of the Navier-Stokes equations representing steady rotationally-symmetric flow.Quarterly Journal of Mechanics and Applied Mathematics 4 (1951), 29–41.Google Scholar
  5. 5.
    K. Stewartson, On the flow between two rotating coaxial discs.Proceedings of Cambridge Philosophical Society 49 (1953), 333–341.Google Scholar
  6. 6.
    J.F. Brady and L. Durlofsky, On rotating disk flow.Journal of Fluid Mechanics 175 (1987),363–394.Google Scholar
  7. 7.
    P.J. Zandbergen and D. Dijkstra, Von Kármán swirling flows. In: J.L. Lumley, M. Van Dyke and H.L. Reed (eds),Annual Review of Fluid Mechanics 19 (1987), 465–491.Google Scholar
  8. 8.
    F. Schultz-Grunow, Der Reibungswiderstand rotierender Scheiben in Gehausen.ZAMM 14 (1935) 191–204.Google Scholar
  9. 9.
    H.P. Pao, A numerical computation of a confined rotating flow.Journal of Applied Mechanics 37 (1970), 480–487.Google Scholar
  10. 10.
    U. Cederlöf, Free-surface effects on spin-up.Journal of Fluid Mechanics 187 (1988), 395–407.Google Scholar
  11. 11.
    J. O'Donnell and P.F. Linden, Free-surface effects on the spin-up of fluid in a rotating cylinder.Journal of Fluid Mechanics 232 (1991), 439–453.Google Scholar
  12. 12.
    J.M. Hyun, Flow in an open tank with a free surface driven by the spinning bottom.Journal of Fluids Engineering 107 (1985), 495–499.Google Scholar
  13. 13.
    D.D. Joseph and L. Sturges, The free surface on a liquid filling a trench heated from its side.Journal of Fluid Mechanics 69 (1975), 565–589.Google Scholar
  14. 14.
    D.D. Joseph, A new separation of variables theory for problems of Stokes flow and Elasticity. In:Trends in Applications of Pure Mathematics to Mechanics. London: Pitman (1978) pp. 129–162.Google Scholar
  15. 15.
    D.D. Joseph, L.D. Sturges and W.H. Warner, Convergence of biorthogonal series of biharmonic eigenfunctions by the method of Titchmarsh.Archive of Rational Mechanics and Analysis 78 (1982), 223–274.Google Scholar
  16. 16.
    L. Kleiser and U. Schumann, Treatment of incompressibility and boundary conditions in 3-D numerical spectral simulations of plane channel flows. In: E.H. Hirschel (ed.),Proceedings of the Third GAMM-Conference on Numerical Methods in Fluid Mechanics (1980), V. 2, 165–172.Google Scholar
  17. 17.
    B.L. Buzbee, F.W. Dorr, J.A. George and G.H. Golub, The direct solution of the discrete Poisson equation on irregular regions.SIAM Journal of Numerical Analysis 8 (1971), 722–734.Google Scholar

Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • A. Siginer
    • 1
  • R. Knight
    • 1
  1. 1.Department of Mechanical EngineeringAuburn UniversityAuburnUSA

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