### Abstract

Structurally stable heteroclinic cycles (SSHCs) are proposed as the mathematical structures that are responsible for the reversals of dipolar magnetic fields in spherical dynamos. The existence of SSHCs involving dipolar magnetic fields generated by convection in a spherical shell for a non-rotating sphere is rigorously proven. The possibility of SSHCs in a rotating shell is proposed, and their existence in a low-dimensional model of the magnetohydrodynamic equations is numerically confirmed. The resulting magnetic time-series shows a dipolar magnetic field, aligned with the rotation axis that intermittently becomes unstable, changes the polar axis, starts rotating, disappears completely and eventually re-establishes itself in its original or opposite direction, chosen randomly.

Original language | English (US) |
---|---|

Pages (from-to) | 577-596 |

Number of pages | 20 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 459 |

Issue number | 2031 |

DOIs | |

State | Published - Mar 8 2003 |

### Fingerprint

### Keywords

- Heteroclinic cycles
- Reversals
- Spherical dynamos

### ASJC Scopus subject areas

- General

### Cite this

**Dynamics of polar reversals in spherical dynamos.** / Chossat, Pascal; Armbruster, Hans.

Research output: Contribution to journal › Article

*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*, vol. 459, no. 2031, pp. 577-596. https://doi.org/10.1098/rspa.2002.1025

}

TY - JOUR

T1 - Dynamics of polar reversals in spherical dynamos

AU - Chossat, Pascal

AU - Armbruster, Hans

PY - 2003/3/8

Y1 - 2003/3/8

N2 - Structurally stable heteroclinic cycles (SSHCs) are proposed as the mathematical structures that are responsible for the reversals of dipolar magnetic fields in spherical dynamos. The existence of SSHCs involving dipolar magnetic fields generated by convection in a spherical shell for a non-rotating sphere is rigorously proven. The possibility of SSHCs in a rotating shell is proposed, and their existence in a low-dimensional model of the magnetohydrodynamic equations is numerically confirmed. The resulting magnetic time-series shows a dipolar magnetic field, aligned with the rotation axis that intermittently becomes unstable, changes the polar axis, starts rotating, disappears completely and eventually re-establishes itself in its original or opposite direction, chosen randomly.

AB - Structurally stable heteroclinic cycles (SSHCs) are proposed as the mathematical structures that are responsible for the reversals of dipolar magnetic fields in spherical dynamos. The existence of SSHCs involving dipolar magnetic fields generated by convection in a spherical shell for a non-rotating sphere is rigorously proven. The possibility of SSHCs in a rotating shell is proposed, and their existence in a low-dimensional model of the magnetohydrodynamic equations is numerically confirmed. The resulting magnetic time-series shows a dipolar magnetic field, aligned with the rotation axis that intermittently becomes unstable, changes the polar axis, starts rotating, disappears completely and eventually re-establishes itself in its original or opposite direction, chosen randomly.

KW - Heteroclinic cycles

KW - Reversals

KW - Spherical dynamos

UR - http://www.scopus.com/inward/record.url?scp=1542620849&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1542620849&partnerID=8YFLogxK

U2 - 10.1098/rspa.2002.1025

DO - 10.1098/rspa.2002.1025

M3 - Article

AN - SCOPUS:1542620849

VL - 459

SP - 577

EP - 596

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 0962-8444

IS - 2031

ER -