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Das Taylorsche Stabilitätsproblem mit Modulation

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Summary

The stability of the time-dependent flow between two concentric circular cylinders is considered, whereby the angular velocity of the inner cylinder is modulated sinusoidally. The initial value problem of the corresponding linearized differential equations for the perturbations is solved by means of the Galerkin method. The convergence of this method follows from an earlier investigation [4]. The behavior in time of the perturbations is studied as a function of the modulation frequency. The results agree with experiments ofDonnelly [3].

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Literatur

  1. H. S. Carslaw undJ. C. Jaeger,Conduction of Heat in Solids, Oxford 1960, At the Clarendon Press.

  2. S. Chandrasekhar,The Stability of a Viscous Flow between Rotating Cylinders, Mathematika1, 5 (1954).

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  3. R. J. Donnelly,Experiments on the Stability of Viscous Flow between Rotating Cylinders, III Enhancement of Stability by Modulation, Proc. Roy. Soc. [A]281, 130 (1964).

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  4. B. Meister,Die Anfangswertaufgabe für die Störungsdifferentialgleichungen des Taylorschen Stabilitätsproblems, Arch. Rat. Mech. An.14, 81 (1963).

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  5. G. I. Taylor,Stability of a Viscous Liquid Contained between Two Rotating Cylinders, Phil. Trans. Roy. Soc. London [A]223, 289 (1923).

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Authors and Affiliations

  1. IBM-Forschungslaboratorium Zürich, 8803, Rüschlikon ZH

    Bernd Meister & Willy Münzner

Authors
  1. Bernd Meister
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  2. Willy Münzner
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Meister, B., Münzner, W. Das Taylorsche Stabilitätsproblem mit Modulation. Journal of Applied Mathematics and Physics (ZAMP) 17, 537–540 (1966). https://doi.org/10.1007/BF01595988

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  • DOI: https://doi.org/10.1007/BF01595988

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