Turbulence and Diffusion

1. Front Matter

   Pages I-XV

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2. Turbulent Diffusion Concepts

   1. Front Matter

      Pages 1-1

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   2. Introduction

      • Oleg G. Bakunin

      Pages 3-19

   3. Turbulent Diffusion and Scaling

      • Oleg G. Bakunin

      Pages 21-39

   4. Nonlocal Effects and Diffusion Equations

      • Oleg G. Bakunin

      Pages 41-53

3. Correlation Effects and Scalings

   1. Front Matter

      Pages 55-55

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   2. Diffusive Renormalization and Correlations

      • Oleg G. Bakunin

      Pages 57-69

   3. Diffusion Equations and the Quasilinear Approximation

      • Oleg G. Bakunin

      Pages 71-86

   4. Return Effects and Random Shear Flows

      • Oleg G. Bakunin

      Pages 87-99

   5. Turbulence of Magnetic Field Lines

      • Oleg G. Bakunin

      Pages 101-116

   6. Stochastic Instability and Turbulence

      • Oleg G. Bakunin

      Pages 117-130

   7. Anomalous Transport and Convective Cells

      • Oleg G. Bakunin

      Pages 131-144

4. Fractals and Percolation Transport

   1. Front Matter

      Pages 145-145

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   2. Fractal and Percolation Concepts

      • Oleg G. Bakunin

      Pages 147-167

   3. Percolation and Turbulent Transport

      • Oleg G. Bakunin

      Pages 169-192

   4. Multiscale Approach and Scalings

      • Oleg G. Bakunin

      Pages 193-209

5. Trapping and the Escape Probability Formalism

   1. Front Matter

      Pages 211-211

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   2. Subdiffusion and Trapping

      • Oleg G. Bakunin

      Pages 213-222

   3. Continuous Time Random Walks and Transport Scalings

      • Oleg G. Bakunin

      Pages 223-241

   4. Correlation and Phase-Space

      • Oleg G. Bakunin

      Pages 243-254

This book is intended to serve as an introduction to the multidisciplinary ?eld of anomalous diffusion in complex systems such as turbulent plasma, convective rolls, zonal ?ow systems, stochastic magnetic ?elds, etc. In spite of its great importance, turbulent transport has received comparatively little treatment in published mo- graphs. This book attempts a comprehensive description of the scaling approach to turbulent diffusion. From the methodological point of view, the book focuses on the general use of correlation estimates, quasilinear equations, and continuous time random walk - proach. I provide a detailed structure of some derivations when they may be useful for more general purposes. Correlation methods are ?exible tools to obtain tra- port scalings that give priority to the richness of ingredients in a physical pr- lem. The mathematical description developed here is not meant to provide a set of “recipes” for hydrodynamical turbulence or plasma turbulence; rather, it serves to develop the reader’s physical intuition and understanding of the correlation mec- nisms involved.

• Diffusion
• Plasma
• fluid dynamics
• scaling laws
• transport equations
• turbulence

From the reviews:

“The text is organized in four parts. … It provides a terse survey of the recent advances in the field of non-conventional approaches to turbulence modeling. The collection of topics in this book is very broad … . recommended for advanced undergraduate students and graduate students in theoretical physics and geophysical sciences. It can also be used by researcher who are interested in relatively new theoretical concepts, with a strong preference for the scaling and renormalization.” (Andrzej Icha, Pure and Applied Geophysics, Vol. 166, 2009)

• Kurchatov Institute Nuclear Fusion Institute, Russia

  Oleg G. Bakunin

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