Dissipative Structures and Weak Turbulence

1st Edition

Series Volume Editors: Paul Manneville
Hardcover ISBN: 9780124692602
eBook ISBN: 9780080924458
Imprint: Academic Press
Published Date: 28th June 2014
Page Count: 448
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Dissipative Structure and Weak Turbulence provides an understanding of the emergence and evolution of structures in macroscopic systems. This book discusses the emergence of dissipative structures.

Organized into 10 chapters, this book begins with an overview of the stability of a fluid layer with potentially unstable density stratification in the field of gravity. This text then explains the theoretical description of the dynamics of a given system at a formal level. Other chapters consider several examples of how such simplified models can be derived, complicating the picture progressively to account for other phenomena. This book discusses as well the theory and experiments on plain Rayleigh–Bénard convection by setting first the theoretical frame and deriving the analytical solution of the marginal stability problem. The final chapter deals with building a bridge between chaos as studied in weakly confined systems and more advanced turbulence in the most conventional sense.

This book is a valuable resource for physicists.

Table of Contents


Chapter 1. Outlook

1. Dissipative Structures

2. Transition to Temporal Chaos

3. Spatio-Temporal Chaos and Weak Turbulence

4. Bibliographical Notes

Chapter 2. Evolution and Stability, Basic Concepts

1. General Framework

1.1. Discrete Versus Continuous Systems

1.2. Autonomous Versus Time-Dependent Systems

1.3. Deterministic Evolution

1.4. Perturbations and Stability

2. Global Stability

2.1. General Viewpoint and Definitions

2.2. Energy Method

2.3. Different Concepts of Stability

3· Normal Modes, Linear and Nonlinear Dynamics

3.1. Normal Mode Analysis

3.2. Weakly Nonlinear Dynamics

4. Qualitative Dynamics

4.1. Elements for a Phase Portrait

4.2. Absorbing Zones and Limit Sets

4.3. Limit Sets and Attractors

4.4. Hyperbolicity, Structural Stability, and Bifurcations

4.5. About More General Attractors

5. Bibliographical Notes

Chapter 3. Instability Mechanisms

1. Rayleigh-Bénard Convection

1.1. Qualitative Analysis

1.2. Simplified Model

1.3. Normal Mode Analysis

1.4. Linear Dynamics of Unstable Modes

2. Convection in Binary Mixtures

2.1. Stationary Mode

2.2. Oscillatory Mode

3. Thermal Convection in Nematic Liquid Crystals

4. Electrohydrodynamic Instabilities in Nematics

4.1. Carr-Helfrich Mechanism

4.2. Two Instability Regimes

5. Taylor-Couette instability

5.1. Centrifugal Instabilities

5.2. Ra


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© Academic Press 1990
Academic Press
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About the Series Volume Editor

Paul Manneville