### Abstract

Original language | English |
---|---|

Title of host publication | Tubes, sheets and singularities in fluid dynamics |

Subtitle of host publication | proceedings of the NATO ARW, 2-7 September 2001, Zakopane, Poland |

Editors | K. Bajer, H. K. Moffatt |

Publisher | Kluwer Academic Publishers |

Pages | 151-156 |

Number of pages | 6 |

ISBN (Print) | 9781402009808, 1402009801 |

DOIs | |

Publication status | Published - 2002 |

### Publication series

Name | Fluid mechanics and its applications |
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Number | 71(3) |

ISSN (Print) | 0926-5112 |

### Fingerprint

### Cite this

*Tubes, sheets and singularities in fluid dynamics: proceedings of the NATO ARW, 2-7 September 2001, Zakopane, Poland*(pp. 151-156). (Fluid mechanics and its applications; No. 71(3)). Kluwer Academic Publishers. https://doi.org/10.1007/0-306-48420-X_22

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*Tubes, sheets and singularities in fluid dynamics: proceedings of the NATO ARW, 2-7 September 2001, Zakopane, Poland.*Fluid mechanics and its applications, no. 71(3), Kluwer Academic Publishers, pp. 151-156. https://doi.org/10.1007/0-306-48420-X_22

**A third-order topological invariant for three magnetic fields.** / Mayer, Christoph; Hornig, Gunnar.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - A third-order topological invariant for three magnetic fields

AU - Mayer, Christoph

AU - Hornig, Gunnar

N1 - dc.description.sponsorship: Volkswagen Foundation

PY - 2002

Y1 - 2002

N2 - The topology of divergence-free fields is important in many parts of physics, e. g. in magnetohydrodynamics, plasma physics, hydrodynamics, superfluids etc. With the focus on applications in magnetohydrodynamics, our principal aim is the characterisation of magnetic fields by the means of invariants. In this report an introduction to the problem of finding higher order invariants is given. Then a third-order link integral of three magnetic fields is presented, which can be shown to be a topological invariant and therefore an invariant in ideal magnetohydrodynamics. This integral generalises the known third-order link invariant derived from the Massey triple product, which could only be applied to isolated flux tubes. As an example three magnetic fields not confined to flux tubes are given that possess a third-order linkage.

AB - The topology of divergence-free fields is important in many parts of physics, e. g. in magnetohydrodynamics, plasma physics, hydrodynamics, superfluids etc. With the focus on applications in magnetohydrodynamics, our principal aim is the characterisation of magnetic fields by the means of invariants. In this report an introduction to the problem of finding higher order invariants is given. Then a third-order link integral of three magnetic fields is presented, which can be shown to be a topological invariant and therefore an invariant in ideal magnetohydrodynamics. This integral generalises the known third-order link invariant derived from the Massey triple product, which could only be applied to isolated flux tubes. As an example three magnetic fields not confined to flux tubes are given that possess a third-order linkage.

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-84859810332&origin=inward&txGid=58c325934f40b56a4b68804ef1b2743e

U2 - 10.1007/0-306-48420-X_22

DO - 10.1007/0-306-48420-X_22

M3 - Chapter

SN - 9781402009808

SN - 1402009801

T3 - Fluid mechanics and its applications

SP - 151

EP - 156

BT - Tubes, sheets and singularities in fluid dynamics

A2 - Bajer, K.

A2 - Moffatt, H. K.

PB - Kluwer Academic Publishers

ER -