Overview

The intimate relationship between three-dimensional vortex dynamics and topology was recognized as early as 1869 by Lord Kelvin, whose discoveries in fluid dynamics led to the development of knot theory as a well-defined branch of topology. It is only in the last 25 years, however, with the parallel stimulus of the development of magnetohydrodynamics in astrophysical and geophysical contexts, that the great potential of topological techniques in fluid and plasma has been fully recognized. This volume provides a comprehensive survey of this interdisciplinary field. The relevant background in knot theory, flow kinematics, dynamo theory, and relaxation under topological constraints, is provided by the introductory chapters of Part I. These themes are developed in the subsequent papers which are grouped under the following headings: Part II: Relaxation and Minimum Energy States; Part III: Helicity, Linkage, and Flow Topology; Part IV: The Euler Equations: Extremal Properties and Finite-Time Singularities; Part V: Vortex Interactions and the Structure of Turbulence; Part VI: Chaos, Instability, and Dynamo Theory.

Full Product Details

Author:   H.K. Moffatt ,  G.M. Zaslavsky ,  P. Comte ,  M. Tabor
Publisher:   Springer
Imprint:   Springer
Edition:   Softcover reprint of the original 1st ed. 1992
Volume:   218
Dimensions:   Width: 15.50cm , Height: 3.10cm , Length: 23.50cm
Weight:   0.943kg
ISBN:  

9789048141876

ISBN 10:   9048141877
Pages:   606
Publication Date:   04 December 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
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Table of Contents

I. Introductory Lectures.- Relaxation under Topological Constraints.- Knot Theory, Jones’ Polynomials, Invariants of 3-Manifolds, and the Topological Theory of Fluid Dynamics.- Topology of Knots.- Stretching and Alignment in General Flow Fields: Classical Trajectories from Reynolds Number Zero to Infinity.- Fast Dynamo Theory.- II. Relaxation and Minimum Energy States.- Relaxation and Topology in Plasma Experiments.- Taylor’s Relaxation in an Unbounded Domain of Space.- Force-Free Magnetic Fields with Constant Alpha.- Minimum Energy Magnetic Fields with Toroidal Topology.- Research Announcement on the “Energy” of Knots.- III. Helicity, Linkage, and Flow Topology.- The Helicity of a Knotted Vortex Filament.- A Heirarchy of Linking Integrals.- Borromeanism and Bordism.- Topology of Steady Fluid Flows.- IV. The Euler Equations: Extremal Properties and Finite Time Singularities.- Extremal Properties and Hamiltonian Structure of the Euler Equations.- Blow Up in Axisymmetric Euler Flows.- Is There a Finite-Time Singularity in Axisymmetric Euler Flows?.- Evidence for a Singularity of the Three-Dimensional Incompressible Euler Equations.- Singularity Formation on Vortex Sheets: The Raleigh-Taylor Problem.- V. Vortex Interactions and the Structure of Turbulence.- 2D Turbulence: New Results for Re ? ?.- On Vortex Reconnection and Turbulence.- New Aspects of Vortex Dynamics: Helical Waves, Core Dynamics, Viscous Helicity Generation, and Interaction with Turbulence.- Intermittency Growth in 3D Turbulence.- Dynamical Mechanisms for Intermittency Effects in Fully Developed Turbulence.- The Multispiral Model of Turbulence and Intermittency.- Measurements of Local Scaling of Turbulent Velocity Fields at High Reynolds Numbers.- On the Determination of Universal MultifractalParameters in Turbulence.- VI. Chaos, Instability and Dynamo Theory.- Anomolous Transport and Fractal Kinectics.- Kinematical Instability and Line-Stretching in Relation to the Geodesics of Fluid Motion.- The Behavior of Active and Passive Particles in a Chaotic Flow.- Chaos Associated with Fluid Inertia.- Instability Criteria in Fluid Dynamics.- Localized Instabilities in Fluids.- Kinematic Fast Dynamo Action in a Time-Periodic Chaotic Flow.- An Exact Turbulent Closure for the Hydromagnetic Dynamo.- Author Index.

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