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Dynamical Systems Approach to Turbulence : Cambridge Nonlinear Science Series - Tomas Bohr

Dynamical Systems Approach to Turbulence

Cambridge Nonlinear Science Series

Hardcover Published: 11th June 2014
ISBN: 9780521475143
Number Of Pages: 372

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This book 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. 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 in this book it is shown how concepts developed for low dimensional chaotic systems can be applied to turbulent states. Thus, 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.

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

Introduction
Turbulence and dynamical systems
Phenomenology of turbulence
Reduced models for hydrodynamic turbulence
Turbulence and coupled map lattices
Turbulence in the complex Ginzburg-Landau equation
Predictability in high-dimensional systems
Dynamics of interfaces
Lagrangian chaos
Chaotic diffusion
Hopf bifurcation
Hamiltonian systems
Characteristic and generalised Lyapunov exponents
Convective instabilities
Generalised fractal dimensions and multifractals
Multiaffine fields
Reduction to a finite-dimensional dynamical system
Directed percolation.
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521475143
ISBN-10: 0521475147
Series: Cambridge Nonlinear Science Series
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 372
Published: 11th June 2014
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 24.7 x 17.4  x 2.2
Weight (kg): 0.91