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Pattern Formation in Viscous Flows

The Taylor-Couette Problem and Rayleigh-Bénard Convection

  • Book
  • © 1999

Overview

Authors:
  1. Rita Meyer-Spasche

    1. Max-Planck-Institut für Plasmaphysik, Garching bei München, Germany

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Part of the book series: International Series of Numerical Mathematics (ISNM, volume 128)

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-xi
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  2. The Taylor Experiment

    • Rita Meyer-Spasche
    Pages 1-28

  3. Details of a Numerical Method

    • Rita Meyer-Spasche
    Pages 29-76

  4. Stationary Taylor Vortex Flows

    • Rita Meyer-Spasche
    Pages 77-141

  5. Secondary Bifurcations on Convection Rolls

    • Rita Meyer-Spasche
    Pages 143-189

  6. Back Matter

    Pages 191-212
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About this book

It seems doubtful whether we can expect to understand fully the instability of fluid flow without obtaining a mathematical representa­ tion of the motion of a fluid in some particular case in which instability can actually be ob­ served, so that a detailed comparison can be made between the results of analysis and those of experiment. - G.l. Taylor (1923) Though the equations of fluid dynamics are quite complicated, there are configurations which allow simple flow patterns as stationary solutions (e.g. flows between parallel plates or between rotating cylinders). These flow patterns can be obtained only in certain parameter regimes. For parameter values not in these regimes they cannot be obtained, mainly for two different reasons: • The mathematical existence of the solutions is parameter dependent; or • the solutions exist mathematically, but they are not stable. For finding stable steady states, two steps are required: the steady states have to be found and their stability has to bedetermined.

Authors and Affiliations

  • Max-Planck-Institut für Plasmaphysik, Garching bei München, Germany

    Rita Meyer-Spasche

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