The Energy Method, Stability, and Nonlinear Convection by Brian StraughanThe Energy Method, Stability, and Nonlinear Convection by Brian Straughan

The Energy Method, Stability, and Nonlinear Convection

byBrian Straughan

Paperback | November 29, 2010

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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.
Title:The Energy Method, Stability, and Nonlinear ConvectionFormat:PaperbackDimensions:450 pagesPublished:November 29, 2010Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:1441918248

ISBN - 13:9781441918246


Table of Contents

Introduction*Illustration of the energy method*The Navier-Stokes equations and the Benard problem*Symmetry, Competing Effects, and Coupling Parameters*Convection problems in a half space*Generalized energies and the Lyapunov method*Geophysical problems*Surface tension driven convection*Convection in generalized fluids*Time dependent basic states*Electrohydrodynamic and magnetohydrodynamic convection* Ferrohydrodynamic convection*Reacting viscous fluids*Multi-component convection diffusion*Convection in a compressible fluid*Temperature dependent fluid properties* Penetrative convection*Nonlinear stability in ocean circulation models*Numerical solution of eigenvalue problems*Useful Inequalities*References*Index.

Editorial Reviews

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)