Pattern Formation in Viscous Flows

The Taylor-Couette Problem and Rayleigh-Bénard Convection

  • Rita Meyer-Spasche

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

Table of contents

  1. Front Matter
    Pages i-xi
  2. Rita Meyer-Spasche
    Pages 1-28
  3. Rita Meyer-Spasche
    Pages 29-76
  4. Rita Meyer-Spasche
    Pages 77-141
  5. Rita Meyer-Spasche
    Pages 143-189
  6. Back Matter
    Pages 191-212

About this book

Introduction

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 be determined.

Keywords

Navier-Stokes equation Wave convection dynamical systems fluid dynamics modeling numerical methods scientific computing

Authors and affiliations

  • Rita Meyer-Spasche
    • 1
  1. 1.Max-Planck-Institut für PlasmaphysikGarching bei MünchenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0348-8709-0
  • Copyright Information Birkhäuser Verlag 1999
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-0348-9738-9
  • Online ISBN 978-3-0348-8709-0
  • About this book