Dynamical Systems Approach to Turbulence

This book treats turbulence from the point of view of deterministic dynamical systems.

Tomas Bohr (Author), Mogens H. Jensen (Author), Giovanni Paladin (Author), Angelo Vulpiani (Author)

9780521017947, Cambridge University Press

Paperback, published 22 August 2005

372 pages, 107 b/w illus. 1 table
24.5 x 17 x 2 cm, 0.908 kg

"...overall this is a useful review of a part of the recent work on dynamical systems and turbulence..." Mathematical Reviews

This book, first published in 1998, treats turbulence from the point of view of dynamical systems. The exposition centres around a number of important simplified models for turbulent behaviour in systems ranging from fluid motion (classical turbulence) to chemical reactions and interfaces in disordered systems.The modern theory of fractals and multifractals now plays a major role in turbulence research, and turbulent states are being studied as important dynamical states of matter occurring also in systems outside the realm of hydrodynamics, i.e. chemical reactions or front propagation. The presentation relies heavily on simplified models of turbulent behaviour, notably shell models, coupled map lattices, amplitude equations and interface models, and the focus is primarily on fundamental concepts such as the differences between large and small systems, the nature of correlations and the origin of fractals and of scaling behaviour. This book will be of interest to graduate students and researchers interested in turbulence, from physics and applied mathematics backgrounds.

Introduction
1. Turbulence and dynamical systems
2. Phenomenology of turbulence
3. Reduced models for hydrodynamic turbulence
4. Turbulence and coupled map lattices
5. Turbulence in the complex Ginzburg-Landau equation
6. Predictability in high-dimensional systems
7. Dynamics of interfaces
8. Lagrangian chaos
9. Chaotic diffusion
Appendix A. Hopf bifurcation
Appendix B. Hamiltonian systems
Appendix C. Characteristic and generalised Lyapunov exponents
Appendix D. Convective instabilities
Appendix E. Generalised fractal dimensions and multifractals
Appendix F. Multiaffine fields
Appendix G. Reduction to a finite-dimensional dynamical system
Appendix H. Directed percolation.

Subject Areas: Fluid mechanics [PHDF]