Turbulence and Diffusion

This book is an introduction to the multidisciplinary field of anomalous diffusion in complex systems, with emphasis on the scaling approach as opposed to techniques based on the quantitative analysis of underlying transport equations. Typical examples of such systems are turbulent plasmas, convective rolls, zonal flow systems and stochastic magnetic fields.

From the more methodological point of view, the approach relies on the general use of correlations estimates, quasilinear equations and continuous time random walk techniques. Yet, the mathematical descriptions are not meant to become a fixed set of recipes but rather develop and strengthen the reader's physical intuition and understanding on the underlying mechanisms involved.

Most of the material stems from class-tested lectures, where graduate students where assumed to have a working knowledge of classical physics, fluid dynamics and plasma physics but otherwise no prior knowledge of the subject matter is assumed from the side of the reader.

Résumé
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.

Contenu
Turbulent Diffusion Concepts.- Turbulent Diffusion and Scaling.- Nonlocal Effects and Diffusion Equations.- Correlation Effects and Scalings.- Diffusive Renormalization and Correlations.- Diffusion Equations and the Quasilinear Approximation.- Return Effects and Random Shear Flows.- Turbulence of Magnetic Field Lines.- Stochastic Instability and Turbulence.- Anomalous Transport and Convective Cells.- Fractals and Percolation Transport.- Fractal and Percolation Concepts.- Percolation and Turbulent Transport.- Multiscale Approach and Scalings.- Trapping and the Escape Probability Formalism.- Subdiffusion and Trapping.- Continuous Time Random Walks and Transport Scalings.- Correlation and Phase-Space.