### Abstract

The mean tangential stresses at a corrugated interface between a solid, electrically insulating mantle and a liquid core of magnetic diffusivity λ are calculated for uniform rotation of both mantle and core at an angular velocity Ω in the presence of a corotating magnetic field B. The core and mantle are assumed to extend indefinitely in the horizontal plane. The interface has the form z = η(x, y), where z is the upward vertical distance and x, y are the zonal and latitudinal distances respectively. The function η(x, y) has a planetary horizontal length scale (i.e. of the order of the radius of the Earth) and small amplitude and vertical gradient. The liquid core flows with uniform mean zonal velocity U_{0} relative to the mantle. Ω and B possess vertical and horizontal components. The vertical (poloidal) component B_{p} is uniform and has a value of 5 G while the horizontal (toroidal) field B_{T} = B_{p}αz, where α is a constant. When |α| ≪ 1, the mean horizontal stresses are found to have the same order of magnitude (10^{-2} N m^{-2}) as those inferred from variations in the decade fluctuations in the length of the day, although the exact numerical values depend on the orientation of Ω as well as on the wavenumbers in the zonal and latitudinal directions. The influence of the steepness (as measured by α) of the toroidal field on the stresses is investigated to examine whether the constraint that the mean horizontal stresses at the core-mantle interface be of the order of 10^{-2} N m^{-2} might provide a selection mechanism for the behaviour of the toroidal field in the upper reaches of the outer core of the Earth. The results indicate that the restriction imposed on α is related to the value assigned to the toroidal field deep into the core. For example, if |α| ≫ 1 then the tangential stresses are of the right order of magnitude only if the toroidal field is comparable with the poloidal field deep in the core.

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

Pages (from-to) | 14-26 |

Number of pages | 13 |

Journal | Physics of the Earth and Planetary Interiors |

Volume | 28 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1982 |

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### ASJC Scopus subject areas

- Geophysics
- Space and Planetary Science
- Physics and Astronomy (miscellaneous)
- Astronomy and Astrophysics

### Cite this

*Physics of the Earth and Planetary Interiors*,

*28*(1), 14-26. https://doi.org/10.1016/0031-9201(82)90116-9

**On the topographic coupling at the core-mantle interface.** / Hassan, M. H A; Eltayeb, I. A.

Research output: Contribution to journal › Article

*Physics of the Earth and Planetary Interiors*, vol. 28, no. 1, pp. 14-26. https://doi.org/10.1016/0031-9201(82)90116-9

}

TY - JOUR

T1 - On the topographic coupling at the core-mantle interface

AU - Hassan, M. H A

AU - Eltayeb, I. A.

PY - 1982

Y1 - 1982

N2 - The mean tangential stresses at a corrugated interface between a solid, electrically insulating mantle and a liquid core of magnetic diffusivity λ are calculated for uniform rotation of both mantle and core at an angular velocity Ω in the presence of a corotating magnetic field B. The core and mantle are assumed to extend indefinitely in the horizontal plane. The interface has the form z = η(x, y), where z is the upward vertical distance and x, y are the zonal and latitudinal distances respectively. The function η(x, y) has a planetary horizontal length scale (i.e. of the order of the radius of the Earth) and small amplitude and vertical gradient. The liquid core flows with uniform mean zonal velocity U0 relative to the mantle. Ω and B possess vertical and horizontal components. The vertical (poloidal) component Bp is uniform and has a value of 5 G while the horizontal (toroidal) field BT = Bpαz, where α is a constant. When |α| ≪ 1, the mean horizontal stresses are found to have the same order of magnitude (10-2 N m-2) as those inferred from variations in the decade fluctuations in the length of the day, although the exact numerical values depend on the orientation of Ω as well as on the wavenumbers in the zonal and latitudinal directions. The influence of the steepness (as measured by α) of the toroidal field on the stresses is investigated to examine whether the constraint that the mean horizontal stresses at the core-mantle interface be of the order of 10-2 N m-2 might provide a selection mechanism for the behaviour of the toroidal field in the upper reaches of the outer core of the Earth. The results indicate that the restriction imposed on α is related to the value assigned to the toroidal field deep into the core. For example, if |α| ≫ 1 then the tangential stresses are of the right order of magnitude only if the toroidal field is comparable with the poloidal field deep in the core.

AB - The mean tangential stresses at a corrugated interface between a solid, electrically insulating mantle and a liquid core of magnetic diffusivity λ are calculated for uniform rotation of both mantle and core at an angular velocity Ω in the presence of a corotating magnetic field B. The core and mantle are assumed to extend indefinitely in the horizontal plane. The interface has the form z = η(x, y), where z is the upward vertical distance and x, y are the zonal and latitudinal distances respectively. The function η(x, y) has a planetary horizontal length scale (i.e. of the order of the radius of the Earth) and small amplitude and vertical gradient. The liquid core flows with uniform mean zonal velocity U0 relative to the mantle. Ω and B possess vertical and horizontal components. The vertical (poloidal) component Bp is uniform and has a value of 5 G while the horizontal (toroidal) field BT = Bpαz, where α is a constant. When |α| ≪ 1, the mean horizontal stresses are found to have the same order of magnitude (10-2 N m-2) as those inferred from variations in the decade fluctuations in the length of the day, although the exact numerical values depend on the orientation of Ω as well as on the wavenumbers in the zonal and latitudinal directions. The influence of the steepness (as measured by α) of the toroidal field on the stresses is investigated to examine whether the constraint that the mean horizontal stresses at the core-mantle interface be of the order of 10-2 N m-2 might provide a selection mechanism for the behaviour of the toroidal field in the upper reaches of the outer core of the Earth. The results indicate that the restriction imposed on α is related to the value assigned to the toroidal field deep into the core. For example, if |α| ≫ 1 then the tangential stresses are of the right order of magnitude only if the toroidal field is comparable with the poloidal field deep in the core.

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U2 - 10.1016/0031-9201(82)90116-9

DO - 10.1016/0031-9201(82)90116-9

M3 - Article

VL - 28

SP - 14

EP - 26

JO - Physics of the Earth and Planetary Interiors

JF - Physics of the Earth and Planetary Interiors

SN - 0031-9201

IS - 1

ER -