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On the swirling flow between rotating coaxial disks: a survey

  • Part II: Applications
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Theory and Applications of Singular Perturbations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 942))

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References

  1. R. C. Ackerberg and R. E. O'Malley, Jr., Boundary layer problems exhibiting resonance, Studies in Applied Math. 49, 277–295 (1970).

    Article  MathSciNet  MATH  Google Scholar 

  2. G. K. Batchelor, Note on a class of solutions of the Navier-Stokes equations representing steady rotationally-symmetric flow, Quart. J. Meth. Appl. Math. 4, 29–41 (1951).

    Article  MathSciNet  MATH  Google Scholar 

  3. J. H. Cerutti, Collocation Methods for Systems of Ordinary Differential Equations and Parabolic Partial Differential Equations. Thesis—University of Wisconsin (1975).

    Google Scholar 

  4. W. G. Cochran, The flow due to a rotating disc, Proc. Camb. Phil. Soc. 30, 365 (1934).

    Article  MATH  Google Scholar 

  5. D. Dijkstra and P. J. Zandbergen, Non-unique solutions of the Navier-Stokes equations for the Kármán swirling flow, Jour. Eng. Math. 11 (1977).

    Google Scholar 

  6. A. R. Elcrat, On the swirling flow between rotating coaxial disks, J. Differential Equations 18, 423–430 (1975).

    Article  MathSciNet  MATH  Google Scholar 

  7. D. Greenspan, Numerical studies of flow between rotating coaxial disks, J. Inst. Math. Appl. 9, 370–377 (1972).

    Article  MATH  Google Scholar 

  8. D. M. Hannah, Brit. A.R.C. paper No. 10, 482 (1947).

    Google Scholar 

  9. S. P. Hastings, On existence theorems for some problems from boundary layer theory, Arch. Rational Mech. Anal. 38, 308–316 (1970).

    Article  MathSciNet  MATH  Google Scholar 

  10. G. H. Hoffman, Extension of perturbation series by computer: Viscous flow between two infinite rotating disks, Journal of Comp. Physics 16, 240–258 (1974).

    Article  MATH  Google Scholar 

  11. M. Holodniok, M. Kubicek and V. Hlaváček, Computation of the flow between two rotating coaxial disks, J. Fluid Mech. 81, 689–699 (1977).

    Article  MathSciNet  MATH  Google Scholar 

  12. T. von Kármán, Über laminare und turbulente Reibung, Z. Angew. Nath. Mech. 1, 232–252 (1921).

    Article  MATH  Google Scholar 

  13. H. B. Keller and R.K.-H. Szeto, Calculations of flow between rotating disks, Computing Methods in Applied Sciences and Engineering, R. Glowinski and J. L. Lions, Editors, pp. 51–61, North Holland Publishing Co., (1980).

    Google Scholar 

  14. H.-O. Kreiss and S. V. Parter, On the swirling flow between rotating coaxial disks, Asymptotic behavior I. To appear: Proc. Royal Soc. Edinburgh.

    Google Scholar 

  15. H.-O. Kreiss and S. V. Parter, On the swirling flow between rotating coaxial disks, Asymptotic behavior II. To appear: Proc. Royal Soc. Edinburgh.

    Google Scholar 

  16. H.-O. Kreiss and S. V. Parter, On the swirling flow between rotating coaxial disks: existence and non-uniqueness, to appear.

    Google Scholar 

  17. M. Kubicek, M. Holodniok and V. Hlaváček, Problem of a flow of an incompressible viscous fluid between two rotating disks solved by one-parameter imbedding techniques, Computers in Chemical Engineering, Vysoké Tatry (1977).

    Google Scholar 

  18. M. Kubicek, M. Holodniok, and V. Hlavàček, Calculation of flow between two rotating disks by differentiation with respect to an actual parameter, Computers and Fluids 4, 59–64 (1976).

    Article  MATH  Google Scholar 

  19. H. K. Kuiken, The effect of normal blowing on the flow near a rotating disk of infinite extent, J. Fluid Mech. 47, 789–798 (1971).

    Article  MATH  Google Scholar 

  20. G. N. Lance and M. H. Rogers, The axially symmetric flow of a viscous fluid between two infinite rotating disks, Proc. Roy. Soc. London Ser. A 266, 109–121 (1962).

    Article  MathSciNet  MATH  Google Scholar 

  21. M. Lentini and H. B. Keller, The von Kármán swirling flows, SIAM J. Applied Math. 35, 52–64 (1980).

    Article  MathSciNet  MATH  Google Scholar 

  22. J. H. McLeod, Existence of axially symmetric flow above a rotating disk, Proc. Royal Soc. London A 324, 391–414 (1971).

    Article  MathSciNet  MATH  Google Scholar 

  23. J. B. McLeod and S. V. Parter, On the flow between two counterrotating infinite plane disks, Arch. Rational Mech. Anal. 54, 301–327 (1974).

    Article  MathSciNet  MATH  Google Scholar 

  24. J. B. McLeod and S. V. Parter, The non-monotonicity of solutions in swirling flow, Proc. Royal Soc. Edinburgh 761, 161–182 (1977).

    Article  MATH  Google Scholar 

  25. B. J. Matkowsky and W. L. Siegmann, The flow between counterrotating disks at high Reynolds numbers, SIAM J. Appl. Math. 30, 720–727 (1976).

    Article  MathSciNet  MATH  Google Scholar 

  26. G. L. Mellor, P. J. Chapple and V. K. Stokes, On the flow between a rotating and a stationary disk, J. Fluid Mech. 31, 95–112 (1968).

    Article  MATH  Google Scholar 

  27. N. D. Nguyen, J. P. Ribault and P. Florent, Multiple solutions for flow between coaxial disks, J. Fluid Mech. 68, 369–388 (1975).

    Article  MATH  Google Scholar 

  28. H. Ockendon, An asymptotic solution for steady flow above an infinite rotating disk with suction, Quart. J. Mech. Appl. Math. 25, 291 (1972).

    Article  MATH  Google Scholar 

  29. F. W. J. Olver, Asymptotics and Special Functions, Academic Press, New York, (1974).

    MATH  Google Scholar 

  30. C. E. Pearson, Numerical solutions for the time-dependent viscous flow between two rotating coaxial disks, J. Fluid Mech. 21, 623–633 (1965).

    Article  MATH  Google Scholar 

  31. H. J. Pesch and P. Rentrop, Numerical solution of the flow between two-counter-rotating infinite plane disks by multiple shooting, ZAMM 58, 23–28 (1978).

    Article  MathSciNet  MATH  Google Scholar 

  32. M. H. Protter and H. F. Weinberger, Maximum Principles in Differential Equations, Prentice Hall, Englewood Cliffs, N. J., (1967).

    MATH  Google Scholar 

  33. H. Rasmussen, High Reynolds number flow between two infinite rotating disks, J. Austral. Math. Soc. 12, 483–501 (1971).

    Article  MathSciNet  MATH  Google Scholar 

  34. S. M. Roberts and J. S. Shipman, Computation of the flow between a rotating and a stationary disk, J. Fluid Mech. 73, 53–63 (1976).

    Article  MATH  Google Scholar 

  35. M. H. Rogers and G. N. Lance, The rotationally symmetric flow of a viscous fluid in the presence of an infinite rotating disc, J. Fluid Mech. 7, 617–631 (1960).

    Article  MathSciNet  MATH  Google Scholar 

  36. D. Schultz and D. Greenspan, Simplification and improvement of a numerical method for Navier-Stokes problems, Proc. of the Colloquium on Differential Equations, Kesthaly, Hungary, Sept. 2–6, 1974, pp. 201–222.

    Google Scholar 

  37. J. Serrin, Existence theorems for some compressible boundary layer problems, Studies in Applied Math. 5 (SIAM), Symposium held at Madison, Wisconsin, summer 1969, edited by J. Nohel (1969).

    Google Scholar 

  38. K. Stewartson, On the flow between two rotating coaxial disks, Proc. Cambridge Philos. Soc. 49, 333–341 (1953).

    Article  MathSciNet  MATH  Google Scholar 

  39. K. K. Tam, A note on the asymptotic solution of the flow between two oppositely rotating infinite plane disks, SIAM J. Appl. Math. 17 (1969), 1305–1310.

    Article  MATH  Google Scholar 

  40. A. M. Watts, On the von Kármán equations for axi-symmetric flow, Appl. Math. Preprint No. 74, (1974), University of Queensland.

    Google Scholar 

  41. W. Wasow, Asymptotic Expansions for Ordinary Differential Equations, Wiley (Interscience), New York (1965).

    MATH  Google Scholar 

  42. L. O. Wilson and N. L. Schryer, Flow between a stationary and a rotating disk with suction, J. Fluid Mech. 85, 789–496 (1978).

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Mathematics Research Center, University of Wisconsin-Madison, 53706, Madison, WI

    Seymour V. Parter

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  1. Seymour V. Parter
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W. Eckhaus E. M. de Jager

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© 1982 Springer-Verlag

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Parter, S.V. (1982). On the swirling flow between rotating coaxial disks: a survey. In: Eckhaus, W., de Jager, E.M. (eds) Theory and Applications of Singular Perturbations. Lecture Notes in Mathematics, vol 942. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0094752

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  • DOI: https://doi.org/10.1007/BFb0094752

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  • Print ISBN: 978-3-540-11584-7

  • Online ISBN: 978-3-540-39332-0

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