Stability of Fluid Motions II

1. Front Matter

   Pages I-XIV

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2. The Oberbeck-Boussinesq Equations. The Stability of Constant Gradient Solutions of the Oberbeck-Boussinesq Equations

   • Daniel D. Joseph

   Pages 1-33

3. Global Stability of Constant Temperature-Gradient and Concentration-Gradient States of a Motionless Heterogeneous Fluid

   • Daniel D. Joseph

   Pages 34-51

4. Two-Sided Bifurcation into Convection

   • Daniel D. Joseph

   Pages 52-123

5. Stability of Supercritical Convection-Wave Number Selection Through Stability

   • Daniel D. Joseph

   Pages 124-159

6. The Variational Theory of Turbulence Applied to Convection in Porous Materials Heated from below

   • Daniel D. Joseph

   Pages 160-190

7. Stability Problems for Viscoelastic Fluids

   • Daniel D. Joseph

   Pages 191-240

8. Interfacial Stability

   • Daniel D. Joseph

   Pages 241-261

9. Back Matter

   Pages 262-276

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The study of stability aims at understanding the abrupt changes which are observed in fluid motions as the external parameters are varied. It is a demanding study, far from full grown, whose most interesting conclusions are recent. I have written a detailed account of those parts of the recent theory which I regard as established. Acknowledgements I started writing this book in 1967 at the invitation of Clifford Truesdell. It was to be a short work on the energy theory of stability and if I had stuck to that I would have finished the writing many years ago. The theory of stability has developed so rapidly since 1967 that the book I might then have written would now have a much too limited scope. I am grateful to Truesdell, not so much for the invitation to spend endless hours of writing and erasing, but for the generous way he has supported my efforts and encouraged me to higher standards of good work. I have tried to follow Truesdell's advice to write this work in a clear and uncomplicated style. This is not easy advice for a former sociologist to follow; if I have failed it is not due to a lack of urging by him or trying by me. My research during the years 1969-1970 was supported in part by a grant from the Guggenheim foundation to study in London.

• Hydrodynamik
• Mathematica
• calculus
• convection
• dynamics
• energy
• flow
• heat
• hydrodynamics
• material
• mechanics
• oscillation
• stability
• symmetry
• turbulence

• Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, USA

  Daniel D. Joseph