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Dynamical Systems Approach to Turbulence
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Book description

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.

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Contents

  • Frontmatter
    pp i-vi
  • Contents
    pp vii-xii
  • To the memory of Giovanni
    pp xiii-xiv
  • Preface
    pp xv-xvi
  • Introduction
    pp xvii-xx
  • Chapter 1 - Turbulence and dynamical systems
    pp 1-20
  • Chapter 2 - Phenomenology of hydrodynamic turbulence
    pp 21-47
  • Chapter 3 - Reduced models for hydrodynamic turbulence
    pp 48-90
  • Chapter 4 - Turbulence and coupled map lattices
    pp 91-137
  • Chapter 5 - Turbulence in the complex Ginzburg–Landau equation
    pp 138-182
  • Chapter 6 - Predictability in high-dimensional systems
    pp 183-210
  • Chapter 7 - Dynamics of interfaces
    pp 211-243
  • Chapter 8 - Lagrangian chaos
    pp 244-276
  • Chapter 9 - Chaotic diffusion
    pp 277-291
  • Appendix A - Hopf bifurcation
    pp 292-293
  • Appendix B - Hamiltonian systems
    pp 294-300
  • Appendix C - Characteristic and generalized Lyapunov exponents
    pp 301-308
  • Appendix D - Convective instabilities and linear front propagation
    pp 309-314
  • Appendix E - Generalized fractal dimensions and multifractals
    pp 315-319
  • Appendix F - Multiaffine fields
    pp 320-324
  • Appendix G - Reduction to a finite-dimensional dynamical system
    pp 325-328
  • Appendix H - Directed percolation
    pp 329-331
  • References
    pp 332-346
  • Index
    pp 347-350

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