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Dynamical Systems Approach to Turbulence

Dynamical Systems Approach to Turbulence

$172.00

Part of Cambridge Nonlinear Science Series

  • Date Published: August 1998
  • availability: Available
  • format: Hardback
  • isbn: 9780521475143

$172.00
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About the Authors
  • 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.

    • Describes new developments in non-linear and chaotic dynamical systems
    • Fills a gap between this new field and more traditional field of turbulence
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    Reviews & endorsements

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

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    Product details

    • Date Published: August 1998
    • format: Hardback
    • isbn: 9780521475143
    • length: 372 pages
    • dimensions: 244 x 170 x 22 mm
    • weight: 0.79kg
    • contains: 107 b/w illus. 1 table
    • availability: Available
  • Table of Contents

    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.

  • Authors

    Tomas Bohr, University of Copenhagen

    Mogens H. Jensen, University of Copenhagen

    Giovanni Paladin

    Angelo Vulpiani, Università degli Studi di Roma 'La Sapienza', Italy

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