Ohmic dissipation in the Earth's outer core resulting from the free inner core nutation

TL;DR

This study numerically investigates Ohmic dissipation caused by the Earth's free inner core nutation, revealing that magnetic field effects significantly alter dissipation estimates, which are too weak to explain observed damping.

Contribution

It provides new numerical estimates of Ohmic dissipation at very low Ekman numbers, showing dissipation is less influential on FICN damping than previously thought.

Findings

Magnetic field alters perturbation structure and scale.

Ohmic dissipation is insensitive to viscosity and diffusivity at low Ekman numbers.

Dissipation estimates are too weak to explain FICN damping.

Abstract

The diurnal tidal forces can excite a normal mode of the Earth's core, the free inner core nutation (FICN), which is characterized by a tilt of the rotation axis of the inner core with respect to the rotation axis of the outer core. The differential rotation between the inner core and the outer core induces fluid motions in the outer core and gives rise to Ohmic dissipation in the presence of the Earth's internal magnetic field. Nutation measurements can reflect such dissipation if it is sufficiently strong and thus can provide insights into the properties and dynamics of the Earth's core. In this study we perform a set of numerical calculations of the linear perturbations in the outer core induced by the FICN at very low Ekman numbers (as small as $10^{-11}$). Our numerical results show that the back-reaction of the magnetic field notably alters the structure and length scale of the perturbations induced by the FICN, and thus influences the Ohmic dissipation resulting from the perturbations. When the Ekman number is sufficiently small, Ohmic dissipation tends to be insensitive to the fluid viscosity and to the magnetic diffusivity, which allows us to estimate the Ohmic dissipation associated with the FICN without relying on an extrapolation. In contrast to the results of Buffett (2010b), the estimated Ohmic dissipation based on our numerical calculations is too weak to account for the observed damping of the FICN mode. This also implies that nutation measurements cannot provide effective constraints on the strength of the magnetic field inside the Earth's outer core.