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An Introduction to the Geometry and Topology of Fluid Flows

  • Book
  • © 2001

Overview

Editors:
  1. Renzo L. Ricca

    1. Mathematics Department, University College London, London, UK

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Part of the book series: NATO Science Series II: Mathematics, Physics and Chemistry (NAII, volume 47)

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xi
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  2. Eight Problems For The XXI Century

    1. Front Matter

      Pages 1-1
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    2. Some Remarks on Topological Fluid Mechanics

      • H. Keith Moffatt
      Pages 3-10

  3. Mathematics Background

    1. Front Matter

      Pages 11-11
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    2. Differential Geometry of Curves and Surfaces

      • Rémi Langevin
      Pages 13-33

    3. Topology in Four Days

      • Tadashi Tokieda
      Pages 35-55

    4. Elements of Classical Knot Theory

      • Claude Weber
      Pages 57-75

    5. An Introduction to Knot Theory

      • Louis H. Kauffman
      Pages 77-104

    6. Fluid Mechanics and Mathematical Structures

      • Philip Boyland
      Pages 105-134

  4. Geometry And Topology Of Fluid Flows

    1. Front Matter

      Pages 135-135
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    2. Introduction to a Geometrical Theory of Fluid Flows and Dynamical Systems

      • Tsutomu Kambe
      Pages 137-165

    3. Streamline Patterns and Their Bifurcations Using Methods from Dynamical Systems

      • Morten Brøns
      Pages 167-182

    4. Topological Features Of Inviscid Flows

      • Robert Ghrist, Rafal Komendarczyk
      Pages 183-201

    5. Geometric and Topological Aspects of Vortex Motion

      • Renzo L. Ricca
      Pages 203-228

    6. Topology Bounds the Energy

      • Boris A. Khesin
      Pages 229-238

    7. Measures of Topological Structure in Magnetic Fields

      • Mitchell A. Berger
      Pages 239-252

    8. Diffeomorphisms, Braids and Flows

      • Alexander Shnirelman
      Pages 253-270

    9. Variational Principles, Geometry and Topology of Lagrangian-Averaged Fluid Dynamics

      • Darryl D. Holm
      Pages 271-291

  5. Reconnections and Singularities

    1. Front Matter

      Pages 293-293
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    2. The Geometry of Reconnection

      • Gunnar Hornig
      Pages 295-312
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Keywords

About this book

Leading experts present a unique, invaluable introduction to the study of the geometry and typology of fluid flows. From basic motions on curves and surfaces to the recent developments in knots and links, the reader is gradually led to explore the fascinating world of geometric and topological fluid mechanics.
Geodesics and chaotic orbits, magnetic knots and vortex links, continual flows and singularities become alive with more than 160 figures and examples.
In the opening article, H. K. Moffatt sets the pace, proposing eight outstanding problems for the 21st century. The book goes on to provide concepts and techniques for tackling these and many other interesting open problems.

Editors and Affiliations

  • Mathematics Department, University College London, London, UK

    Renzo L. Ricca

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