The Energy Method, Stability, and Nonlinear Convection

by Brian Straughan

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 The Viola Eigenvalue Problem.- A2.3 The Compound Matrix Method.- A2.4 Numerical Solution of (4.65), (4.66) Using Compound Matrices.- References.

256 pages, Paperback

First published January 1, 1992