Straughan The Energy Method, Stability, and Nonlinear Convection

Erscheinungsjahr 2013
ISBN: 978-1-4757-2194-2
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 91, 243 Seiten, eBook

Reihe: Applied Mathematical Sciences

The writing of this book was begun during the academic year 1984-1985 while I was a visiting Associate Professor at the University of Wyoming. I am extremely grateful to the people there for their help, in particular to Dick Ewing, Jack George and Robert Gunn, and to Ken Gross, who is now at the University of Vermont. A major part of the first draft of this book was written while I was a visiting Professor at the University of South Carolina during the academic year 1988-1989. I am indebted to the people there for their help, in one way or another, particularly to Ron DeVore, Steve Dilworth, Bob Sharpley, Dave Walker, and especially to the chairman of the Mathematics Department at the University of South Carolina, Colin Bennett. I also wish to express my sincere gratitude to Ray Ogden and Profes sor I.N. Sneddon, F.R.S., both of Glasgow University, for their help over a number of years. I also wish to record my thanks to Ron Hills and Paul Roberts, F.R.S., for giving me a copy of their paper on the Boussinesq ap proximation prior to publication and for allowing me to describe their work here. I should like to thank my Ph.D. student Geoff McKay for spotting several errors and misprints in an early draft. Finally, I am very grateful to an anonymous reviewer for several pertinent suggestions regarding the energy-Casimir method.

Zielgruppe

Research

Autoren/Hrsg.

Straughan, Brian

Inhaltsverzeichnis

1. Introduction.- 2. Illustration of the Energy Method on Simple Examples and Discussion of Linear Theory.- 3. The Navier-Stokes Equations, the Boussinesq Approximation, and the Standard Bénard Problem.- 4. Symmetry, Competing Effects, and Coupling Parameters; Multiparameter Eigenvalue Problems; Finite Geometries.- 5. Convection Problems in a Half-Space.- 6. Generalized Energies and the Lyapunov Method.- 7. Geophysical Problems.- 8. Surface Tension Driven Convection.- 9. Convection in Generalized Fluids.- 10. Time Dependent Basic States.- 11. Electrohydrodynamic and Magnetohydrodynamic Convection.- 12. Ferrohydrodynamic Convection.- 13. Convective Instabilities for Reacting Viscous Fluids Far from Equilibrium.- 14. Energy Stability and Other Continuum Theories.- Appendix 1. Some Useful Inequalities in Energy Stability Theory.- Appendix 2. Numerical Solution of the Energy Eigenvalue Problem.- A2.1 The Shooting Method.- A2.2 A System: The Viola Eigenvalue Problem.- A2.3 The Compound Matrix Method.- A2.4 Numerical Solution of (4.65), (4.66) Using Compound Matrices.- References.