Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgments
- Chapter I Introduction and Overview of Turbulence
- Chapter II Elements of the Mathematical Theory of the Navier–Stokes Equations
- Chapter III Finite Dimensionality of Flows
- Chapter IV Stationary Statistical Solutions of the Navier–Stokes Equations, Time Averages, and Attractors
- Chapter V Time-Dependent Statistical Solutions of the Navier–Stokes Equations and Fully Developed Turbulence
- References
- Index
Preface
Published online by Cambridge University Press: 14 August 2009
- Frontmatter
- Contents
- Preface
- Acknowledgments
- Chapter I Introduction and Overview of Turbulence
- Chapter II Elements of the Mathematical Theory of the Navier–Stokes Equations
- Chapter III Finite Dimensionality of Flows
- Chapter IV Stationary Statistical Solutions of the Navier–Stokes Equations, Time Averages, and Attractors
- Chapter V Time-Dependent Statistical Solutions of the Navier–Stokes Equations and Fully Developed Turbulence
- References
- Index
Summary
This monograph is an attempt to address the theory of turbulence from the points of view of several disciplines. The authors are fully aware of the limited achievements here as compared with the task of understanding turbulence. Even though necessarily limited, the results in this book benefit from many years of work by the authors and from interdisciplinary exchanges among them and between them and others. We believe that it can be a useful guide on the long road toward understanding turbulence.
One of the objectives of this book is to let physicists and engineers know about the existing mathematical tools from which they might benefit. We would also like to help mathematicians learn what physical turbulence is about so that they can focus their research on problems of interest to physics and engineering as well as mathematics. We have tried to make the mathematical part accessible to the physicist and engineer, and the physical part accessible to the mathematician, without sacrificing rigor in either case. Although the rich intuition of physicists and engineers has served well to advance our still incomplete understanding of the mechanics of fluids, the rigorous mathematics introduced herein will serve to surmount the limitations of pure intuition. The work is predicated on the demonstrable fact that some of the abstract entities emerging from functional analysis of the Navier–Stokes equations represent real, physical observables: energy, enstrophy, and their decay with respect to time.
- Type
- Chapter
- Information
- Navier-Stokes Equations and Turbulence , pp. ix - xiiiPublisher: Cambridge University PressPrint publication year: 2001