Turbulence and Diffusion

Scaling Versus Equations

By: Oleg G. Bakunin

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Hardcover | 26 August 2008

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288 Pages

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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.

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"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)

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Non-Fiction Science Physics Mathematical Physics Engineering & Technology Mechanical Engineering & Materials Materials Science Mechanics of Fluids Classical Mathematics Fluid Mechanics Statistical Physics Applied Physics

Geophysics Nuclear Physics

Turbulent Diffusion Concepts
Introduction	p. 3
Brownian Motion, Random Walks, and Correlation Scales	p. 3
The Fick Transport Equation	p. 7
Diffusion and the Characteristic Velocity Scale	p. 10
Lagrangian Description of Turbulent Diffusion	p. 13
Turbulent Diffusion and Scaling	p. 21
Correlation Functions and Scaling	p. 21
The Richardson Law and Anomalous Transport	p. 23
The Kolmogorov Description of Turbulence	p. 26
Relative Diffusion and Scalings	p. 32
Cascade Phenomenology and Scalar Spectrum	p. 34
Nonlocal Effects and Diffusion Equations	p. 41
The Einstein Functional Equation	p. 41
Nonlocality and Levy-Stable Distributions	p. 44
Fractional Derivatives and Anomalous Diffusion	p. 47
The Monin Nonlocal Equation	p. 51
Correlation Effects and Scalings
Diffusive Renormalization and Correlations	p. 57
The Corrsin Independence Hypothesis	p. 57
The Correlation Function and Anomalous Diffusion	p. 60
Seed Diffusivity and Correlations	p. 62
Effective Diffusivity and the Peclet Number	p. 64
Diffusive Renormalization and the Correlation Function	p. 66
Diffusion Equations and the Quasilinear Approximation	p. 71
The Taylor Dispersion	p. 71
Advection and Scalar Transport	p. 75
Zeldovich Flow and the Kubo Number	p. 77
Quasilinear Equations	p. 81
Short-Range and Long-Range Correlations	p. 83
The Telegraph Equation	p. 84
Return Effects and Random Shear Flows	p. 87
"Returns" and Correlations	p. 87
Superdiffusion and Return Effects	p. 90
Random Shear Flows and Stochastic Equations	p. 93
The "Manhattan-Grid" Flow and Turbulent Transport	p. 95
Turbulence of Magnetic Field Lines	p. 101
Basic Equations of Plasma	p. 101
Magnetic Field Evolution and Magnetic Reynolds Number	p. 104
Magnetic Diffusivity and the Quasilinear Approach	p. 106
Stochastic Magnetic Field and Transport Scalings	p. 110
Diffusive Renormalization and a Braded Magnetic Field	p. 112
Stochastic Instability and Turbulence	p. 117
Stochastic Instability and Correlations	p. 117
Quasilinear Scaling for the Stochastic Instability Increment	p. 119
The Rechester-Rosenbluth Model	p. 122
Collisional Effects and Transport	p. 124
The Quasi-Isotropic Stochastic Magnetic Field	p. 127
Anomalous Transport and Convective Cells	p. 131
Convective Cells and Turbulent Diffusion	p. 131
Complex Structures and the Statistical Topography	p. 135
Fluctuation-Dissipative Relation and Turbulent Mixing	p. 136
Bohm Scaling and Electric Field Fluctuations	p. 138
Diffusive Renormalization and Correlations	p. 141
Fractals and Percolation Transport
Fractal and Percolation Concepts	p. 147
Self-Similarity and the Fractal Dimension	p. 147
Fractality and Anomalous Transport	p. 151
Turbulence Scalings and Fractality	p. 153
Percolation Transition and Correlations	p. 157
Continuum Percolation and Transport	p. 160
Finite Size Renormalization and Scaling	p. 163
Percolation and Turbulent Transport	p. 169
Random Steady Flows and Seed Diffusivity	p. 169
Reorganization of Flow Topology and Percolation Scalings	p. 174
Spatial and Temporal Hierarchy of Scales	p. 178
Percolation in Drift Flows	p. 181
Drift and Low-Frequency Regimes	p. 184
Renormalization and the Stochastic Instability Increment	p. 187
Stochastic Magnetic Field and Percolation	p. 189
Multiscale Approach and Scalings	p. 193
The Nested Hierarchy of Scales and Drift Effects	p. 193
The Brownian Landscape and Percolation	p. 196
Correlations and Transport Scalings	p. 199
Diffusive Approximation and the Multiscale Model	p. 201
Stochastic Instability and the Temporal Hierarchy of Scales	p. 203
Isotropic and Anisotropic Magnetohydrodynamic Turbulence	p. 204
Trapping and the Escape Probability Formalism
Subdiffusion and Trapping	p. 213
Diffusion in the Presence of Traps	p. 213
Trapping and Strong Turbulence	p. 215
Comb Structures and Transport	p. 218
Double Diffusion and Return Effects	p. 220
Continuous Time Random Walks and Transport Scalings	p. 223
The Montroll and Weiss Approach and Memory Effects	p. 223
Fractional Differential Equations	p. 226
Correlation Function and Waiting Time Distribution	p. 228
The Klafter Blumen and Shlesinger Approximation	p. 230
Stochastic Magnetic Field and Balescu Approach	p. 233
Longitudinal Correlations and the Diffusive Approximation	p. 235
Vortex Structures and Trapping	p. 238
Correlation and Phase-Space	p. 243
Kinetics and the Diffusion Equation	p. 243
Phase Space and Transport Scaling	p. 245
The One-Flight Model and Anomalous Diffusion	p. 247
Correlations and Nonlocal Velocity Distribution	p. 249
The Corrsin Conjecture and Phase-Space	p. 252
References	p. 255
Index	p. 263
Table of Contents provided by Ingram. All Rights Reserved.

Turbulence and Diffusion

Scaling Versus Equations

At a Glance

Hardcover

Industry Reviews

Shipping

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Defective items

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