Dynamical Systems Approach to Turbulence

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More About This Textbook

Overview

This book treats turbulence from the point of view of dynamical systems. In recent decades, turbulence has evolved into a very active field of theoretical physics. 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, in a much broader context than hydrodynamics. 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.
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Product Details

  • ISBN-13: 9780521017947
  • Publisher: Cambridge University Press
  • Publication date: 7/31/2005
  • Series: Cambridge Nonlinear Science Series , #8
  • Pages: 372
  • Product dimensions: 6.70 (w) x 9.60 (h) x 1.00 (d)

Table of Contents

To the memory of Giovanni
Preface
Introduction
Ch. 1 Turbulence and dynamical systems 1
Ch. 2 Phenomenology of hydrodynamic turbulence 21
Ch. 3 Reduced models for hydrodynamic turbulence 48
Ch. 4 Turbulence and coupled map lattices 91
Ch. 5 Turbulence in the complex Ginzburg-Landau equation 138
Ch. 6 Predictability in high-dimensional systems 183
Ch. 7 Dynamics of interfaces 211
Ch. 8 Lagrangian chaos 244
Ch. 9 Chaotic diffusion 277
App. A Hopf bifurcation 292
App. B Hamiltonian systems 294
App. C Characteristic and generalized Lyapunov exponents 301
App. D Convective instabilities and linear front propagation 309
App. E Generalized fractal dimensions and multifractals 315
App. F Multiaffine fields 320
App. G Reduction to a finite-dimensional dynamical system 325
App. H Directed percolation 329
References 332
Index 347
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