Dynamical Systems Approach to Turbulence

ISBN-13: 9780521475143 / Angielski / Twarda / 1998 / 372 str.

Tomas Bohr; Thomas Bohr; Mogens H. Jensen

Opis

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 this book shows how concepts developed for low dimensional chaotic systems are applied to turbulent states. This book centers around a number of important simplified models for turbulent behavior in systems ranging from fluid motion (classical turbulence) to chemical reactions and interfaces in disordered systems. The 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. The book contains simplified models of turbulent behavior, notably shell models, coupled map lattices, amplitude equations and interface models.

Recenzje

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

Spis treści

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.