The Energy Method, Stability, and Nonlinear Convection

  • Brian Straughan

Part of the Applied Mathematical Sciences book series (AMS, volume 91)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Brian Straughan
    Pages 1-6
  3. Brian Straughan
    Pages 105-111
  4. Brian Straughan
    Pages 112-134
  5. Brian Straughan
    Pages 135-160
  6. Brian Straughan
    Pages 161-179
  7. Brian Straughan
    Pages 180-192
  8. Brian Straughan
    Pages 193-200
  9. Brian Straughan
    Pages 217-224
  10. Brian Straughan
    Pages 238-268
  11. Brian Straughan
    Pages 269-290
  12. Brian Straughan
    Pages 313-353
  13. Brian Straughan
    Pages 354-362
  14. Brian Straughan
    Pages 363-386

About this book

Introduction

This book describes the energy method, a powerful technique for deriving nonlinear stability estimates in thermal convection contexts. It includes a very readable introduction to the subject (Chapters 2-4), which begins at an elementary level and explains the energy method in great detail, and also covers the current topic of convection in porous media, introducing simple models and then showing how useful stability results can be derived. In addition to the basic explanation, many examples from diverse areas of fluid mechanics are described. The book also mentions new areas where the methods are being used, for example, mathematical biology and finance. Several of the results given are published here for the first time.

This volume is a completely revised version of the first edition published in 1992. In addition to an update of material from the first edition, six new chapters have been added, covering topics such as multi-component convection-diffusion, convection flows in a compressible fluid, models of penetrative convection, convection with temperature-dependent viscosity and thermal conductivity, and stability of ocean flows. The final chapter gives details of two very different but highly accurate and efficient methods for numerically solving eigenvalue problems that arise in hydrodynamic stability.

The new methods developed during the last eleven years and presented here will be of use to many readers in applied mathematics, engineering, physics, and other mathematical disciplines.

Keywords

Navier-Stokes equation convection material porous media stability

Authors and affiliations

  • Brian Straughan
    • 1
  1. 1.Department of Mathematical Sciences, Science LaboratoriesUniversity of DurhamDurhamUK

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-21740-6
  • Copyright Information Springer-Verlag New York 2004
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-1824-6
  • Online ISBN 978-0-387-21740-6
  • Series Print ISSN 0066-5452
  • About this book