The Energy Method, Stability, and Nonlinear Convection

1. Front Matter

   Pages i-xii

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2. Introduction

   • Brian Straughan

   Pages 1-6

3. Illustration of the energy method on simple examples and discussion of linear theory

   • Brian Straughan

   Pages 7-39

4. The Navier-Stokes equations and the Bénard problem

   • Brian Straughan

   Pages 40-58

5. Symmetry, Competing Effects, and Coupling Parameters

   • Brian Straughan

   Pages 59-104

6. Convection problems in a half space

   • Brian Straughan

   Pages 105-111

7. Generalized energies and the Lyapunov method

   • Brian Straughan

   Pages 112-134

8. Geophysical problems

   • Brian Straughan

   Pages 135-160

9. Surface tension driven convection

   • Brian Straughan

   Pages 161-179

10. Convection in generalized fluids

    • Brian Straughan

    Pages 180-192

11. Time dependent basic states

    • Brian Straughan

    Pages 193-200

12. Electrohydrodynamic and magnetohydrodynamic convection

    • Brian Straughan

    Pages 201-216

13. Ferrohydrodynamic convection

    • Brian Straughan

    Pages 217-224

14. Convective instabilities for reacting viscous fluids far from equilibrium

    • Brian Straughan

    Pages 225-237

15. Multi-component convection diffusion

    • Brian Straughan

    Pages 238-268

16. Convection in a compressible fluid

    • Brian Straughan

    Pages 269-290

17. Convection with temperature dependent fluid properties

    • Brian Straughan

    Pages 291-312

18. Penetrative convection

    • Brian Straughan

    Pages 313-353

19. Nonlinear stability in ocean circulation models

    • Brian Straughan

    Pages 354-362

20. Numerical solution of eigenvalue problems

    • Brian Straughan

    Pages 363-386

This book is a revised edition of my earlier book of the same title. The cur­ rent edition adopts the structure of the earlier version but is much changed. The introduction now contains definitions of stability. Chapters 2 to 4 ex­ plain stability and the energy method in more depth and new sections dealing with porous media are provided. Chapters 5 to 13 are revisions of those in the earlier edition. However, chapters 6 to 12 are substantially revised, brought completely up to date, and have much new material in. Throughout the book new results are provided which are not available elsewhere. Six new chapters, 14 - 19, are provided dealing with topics of current interest. These cover the topics of multi-component convection diffusion, convection in a compressible fluid, convection with temperature dependent viscosity and thermal conductivity, the subject of penetrative convection whereby part of the fluid layer can penetrate into another, nonlinear sta­ bility in the oceans, and finally in chapter 19 practical methods for solving numerically the eigenvalue problems which arise are presented. The book presents convection studies in a variety of fluid and porous media contexts. It should be accessible to a wide audience and begins at an elementary level. Many new references are provided.

• Navier-Stokes equation
• convection
• material
• porous media
• stability
• fluid- and aerodynamics

From the reviews of the second edition:

"This application-oriented book is a revised edition … more definitions, new interpretations and new results are included, some chapters are enlarged, 6 chapters are added. … the presentation is very clear, making the book useful to undergraduate and graduate students in applied mathematics too. … The main text and the very rich list of references reflect the interests and results of the author and his collaborators. The book makes a good contribution to the literature on stability of fluid flows … ." (Adelina Georgescu, Mathematical Reviews, 2004i)

• Department of Mathematical Sciences, Science Laboratories, University of Durham, Durham, UK

  Brian Straughan

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