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基本説明
Presents convection studies in a variety of fluid and porous media contexts.
Full Description
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.
Contents
1 Introduction.- 2 Illustration of the energy method.- 3 The Navier-Stokes equations and the Bénard problem.- 4 Symmetry, competing effects, and coupling parameters.- 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 Reacting viscous fluids.- 14 Multi-component convection diffusion.- 15 Convection in a compressible fluid.- 16 Temperature dependent fluid properties.- 17 Penetrative convection.- 18 Nonlinear stability in ocean circulation models.- 19 Numerical solution of eigenvalue problems.- A Useful inequalities.- A.1 The Poincaré inequality.- A.2 The Wirtinger inequality.- A.3 The Sobolev inequality.- A.4 An inequality for the supremum of a function.- A.7 A two-dimensional surface inequality.- A.8 Inequality (A.20) is false in three-dimensions.- References.
