Lectures on Topological Fluid Mechanics

  • Mitchell A. Berger
  • Louis H. Kauffman
  • Boris Khesin
  • H. Keith Moffatt
  • Renzo L. Ricca
  • De Witt Sumners
  • Renzo L. Ricca

Part of the Lecture Notes in Mathematics book series (LNM, volume 1973)

Also part of the C.I.M.E. Foundation Subseries book sub series (LNMCIME, volume 1973)

Table of contents

  1. Front Matter
    Pages 1-12
  2. Patrick D. Bangert
    Pages 1-73
  3. Louis H. Kauffman, Sofia Lambropoulou
    Pages 99-138
  4. Renzo L. Ricca
    Pages 167-186
  5. Back Matter
    Pages 219-231

About this book


Helmholtz's seminal paper on vortex motion (1858) marks the beginning of what is now called topological fluid mechanics.After 150 years of work, the field has grown considerably. In the last several decades unexpected developments have given topological fluid mechanics new impetus, benefiting from the impressive progress in knot theory and geometric topology on the one hand, and in mathematical and computational fluid dynamics on the other.

This volume contains a wide-ranging collection of up-to-date, valuable research papers written by some of the most eminent experts in the field. Topics range from fundamental aspects of mathematical fluid mechanics, including topological vortex dynamics and magnetohydrodynamics, integrability issues, Hamiltonian structures and singularity formation, to DNA tangles and knotted DNAs in sedimentation. A substantial introductory chapter on knots and links, covering elements of modern braid theory and knot polynomials, as well as more advanced topics in knot classification, provides an invaluable addition to this material.


Braids Fluid flows Knot theory Knots & Links Magnetohydrodynamics Topological Fluid Mechanics computational fluid dynamics fluid dynamics fluid mechanics

Authors and affiliations

  • Mitchell A. Berger
    • 1
  • Louis H. Kauffman
    • 2
  • Boris Khesin
    • 3
  • H. Keith Moffatt
    • 4
  • Renzo L. Ricca
    • 5
  • De Witt Sumners
    • 6
  1. 1.Dept. MathematicsUniversity of ExeterExeterUnited Kingdom
  2. 2.Dept. Mathematics, Statistics &, Computer ScienceUniversity of Illinois, ChicagoChicagoU.S.A.
  3. 3.Dept. MathematicsUniversity of TorontoTorontoCanada
  4. 4.Ctr. Mathematical Sciences, Dept. Applied Mathematics &University CambridgeCambridgeUnited Kingdom
  5. 5.Dipto. Matematica e ApplicazioniUniversità Milano-BicoccaMilanoItaly
  6. 6.Dept. MathematicsFlorida State UniversityTallahasseeUSA

Editors and affiliations

  • Renzo L. Ricca
    • 1
  1. 1.Dipto. Matematica e ApplicazioniUniversità Milano-BicoccaMilanoItaly

Bibliographic information

Industry Sectors
Energy, Utilities & Environment
Oil, Gas & Geosciences