Dynamical Systems Approach to Turbulence

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Cambridge University Press, Aug 22, 2005 - Science - 372 pages
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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.
  

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Contents

Chapter 1 Turbulence and dynamical systems
1
Chapter 2 Phenomenology of hydrodynamic turbulence
21
Chapter 3 Reduced models for hydrodynamic turbulence
48
Chapter 4 Turbulence and coupled map lattices
91
Chapter 5 Turbulence in the complex GinzburgLandau equation
138
Chapter 6 Predictability in highdimensional systems
183
Chapter 7 Dynamics of interfaces
211
Chapter 8 Lagrangian chaos
244
Appendix B Hamiltonian systems
294
Appendix C Characteristic and generalized Lyapunov exponents
301
Appendix D Convective instabilities and linear front propagation
309
Appendix E Generalized fractal dimensions and multifractals
315
Appendix F Multiaffine fields
320
Appendix G Reduction to a finitedimensional dynamical system
325
Appendix H Directed percolation
329
References
332

Chapter 9 Chaotic diffusion
277
Appendix A Hopf bifurcation
292

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About the author (2005)

Angelo Vulpiani is a Professor of Theoretical Physics at the University of Rome Sapienza, and is a Fellow of the Institute of Physics. His research interests are statistical mechanics, dynamical systems, turbulence, transport and reaction-diffusion in fluids.

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