Dynamical Systems Approach to Turbulence

This book 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. In recent decades, turbulence has evolved into a very active field of theoretical physics. The origin of this development is the approach to turbulence from the point of view of deterministic dynamical systems, and in this book it is shown how concepts developed for low dimensional chaotic systems can be applied to turbulent states. Thus, 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.

ISBN 0521017947   Weight (grammes) 590 ISBN13 9780521017947 (What's this?)   Published in Cambridge Publisher Cambridge University Press   Series editor Chirikov, Boris, Cvitanovic, Predrag, Moss, Frank Imprint Cambridge University Press   Series ISSN 8 Format Paperback   Series title Cambridge Nonlinear Science Series Publication date 22 Aug 2005   Height (mm) 247 Library of Congress TA357.5.T87 D88 1998   Width (mm) 174 DEWEY 620.1064   Spine width (mm) 20 DEWEY edition DC21   Academic level Professional / Scholarly Pages 372   Alternative ISBN 9780521475143 Volumes 1

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.

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

 Be the first to write a customer review