Electromagnetically driven westward drift and inner-core superrotation in Earth’s core

Philip W. Livermore; Rainer Hollerbach; Andrew Jackson

doi:10.1073/pnas.1307825110

New Research In

Edited by Gerald Schubert, Institute of Geophysics and Planetary Physics, Los Angeles, CA, and approved August 26, 2013 (received for review April 29, 2013)

Significance

Seismic probing of the earth’s deep interior has shown that the inner core, the solid core of our planet, rotates slightly faster (i.e., eastward) than the rest of the earth. Quite independently, observations of the geomagnetic field provide evidence of westward-drifting features at the edge of the liquid outer core. This paper describes a computer model that suggests that the geomagnetic field itself may provide a link between them: The associated electromagnetic torque currently is westward in the outermost outer core, whereas an equal and opposite torque is applied to the inner core. Decadal changes in the geomagnetic field may cause fluctuations in both these effects, consistent with recent observations of a quasi-oscillatory inner-core rotation rate.

Abstract

A 3D numerical model of the earth’s core with a viscosity two orders of magnitude lower than the state of the art suggests a link between the observed westward drift of the magnetic field and superrotation of the inner core. In our model, the axial electromagnetic torque has a dominant influence only at the surface and in the deepest reaches of the core, where it respectively drives a broad westward flow rising to an axisymmetric equatorial jet and imparts an eastward-directed torque on the solid inner core. Subtle changes in the structure of the internal magnetic field may alter not just the magnitude but the direction of these torques. This not only suggests that the quasi-oscillatory nature of inner-core superrotation [Tkalčić H, Young M, Bodin T, Ngo S, Sambridge M (2013) The shuffling rotation of the earth’s inner core revealed by earthquake doublets. Nat Geosci 6:497–502.] may be driven by decadal changes in the magnetic field, but further that historical periods in which the field exhibited eastward drift were contemporaneous with a westward inner-core rotation. The model further indicates a strong internal shear layer on the tangent cylinder that may be a source of torsional waves inside the core.

Footnotes

↵¹To whom correspondence should be addressed. E-mail: p.w.livermore{at}leeds.ac.uk.

Author contributions: P.W.L., R.H., and A.J. designed research; P.W.L. and R.H. performed research; P.W.L. analyzed data; and P.W.L. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
*Note that the symbol $\text{[math]}$ is not to be confused with the Taylor integral, a closely related quantity that differs by a factor of s from the axial EM torque we consider here.
^†Because viscosity enters into boundary-layer scalings as $\text{[math]}$ rather than E, and further that $\text{[math]}$ , arguably both viscosity and inertia may be equally important in the earth’s core. However, our goal was to explore the magnetostrophic limit, and as such, we chose to focus attention on the Ekman-state balance at very small viscosity.
^‡Although our model provides a consistent description of the dynamics of inner-core rotation over the 10–100-y timescale, different dynamics may be important on millennial timescales (32).