Dominique Jault

Fast torsional waves and strong magnetic field within the Earth’s core

The magnetic field inside the Earth’s fluid and electrically conducting outer core cannot be directly probed. The root-mean-squared (r.m.s.) intensity for the resolved part of the radial magnetic field at the core–mantle boundary is 0.3 mT, but further assumptions are needed to infer the strength of the field inside the core. Recent diagnostics obtained from numerical geodynamo models indicate that the magnitude of the dipole field at the surface of a fluid dynamo is about ten times weaker than the r.m.s. field strength in its interior, which would yield an intensity of the order of several millitesla within the Earth’s core. However, a 60-year signal found in the variation in the length of day has long been associated with magneto-hydrodynamic torsional waves carried by a much weaker internal field. According to these studies, the r.m.s. strength of the field in the cylindrical radial direction (calculated for all length scales) is only 0.2 mT, a figure even smaller than the r.m.s. strength of the large-scale (spherical harmonic degree n ≤ 13) field visible at the core–mantle boundary. Here we reconcile numerical geodynamo models with studies of geostrophic motions in the Earth’s core that rely on geomagnetic data. From an ensemble inversion of core flow models, we find a torsional wave recurring every six years, the angular momentum of which accounts well for both the phase and the amplitude of the six-year signal for change in length of day detected over the second half of the twentieth century. It takes about four years for the wave to propagate throughout the fluid outer core, and this travel time translates into a slowness for Alfvén waves that corresponds to a r.m.s. field strength in the cylindrical radial direction of approximately 2 mT. Assuming isotropy, this yields a r.m.s. field strength of 4 mT inside the Earth’s core.

MHD FLOW IN A SLIGHTLY DIFFERENTIALLY ROTATING SPHERICAL SHELL, WITH CONDUCTING INNER CORE, IN A DIPOLAR MAGNETIC FIELD

Motion is generated in a rotating spherical shell, by a slight differential rotation of the inner core. We show how the numerical solution tends, with decreasing Ekman number, to the asymptotic limit of Proudman [J. Fluid Mech. 1 (1956) 505‐516]. Starting from geophysically large values, we show that the main qualitative features of the asymptotic solution show up only when the Ekman number is decreased below 10 6 . Then, we impose a dipolar and force-free magnetic field with internal sources. Both the inner core and the liquid shell are electrically conducting. The first effect of the Lorentz force is to smooth out the change in angular velocity at the tangent cylinder. As the Elsasser number is further increased, the Proudman‐Taylor constraint is violated, Ekman layers are changed into Hartmann type layers, shear at the inner sphere boundary vanishes, and the flow tends to a bulk rotation together with the inner sphere. Unexpectedly, for increasing strength of the field, there is a super-rotation (the angular velocity does not reach a maximum at the inner core boundary but in the interior of the fluid) localized in an equatorial torus. At a given field strength, the amplitude of this phenomenon depends on the Ekman number and tends to vanish in the magnetostrophic limit.

The onset of thermal convection in rotating spherical shells

The correct asymptotic theory for the linear onset of instability of a Boussinesq fluid rotating rapidly in a self-gravitating sphere containing a uniform distribution of heat sources was given recently by Jones et al. (2000). Their analysis confirmed the established picture that instability at small Ekman number

Ensemble inversion of time‐dependent core flow models

E

Axial invariance of rapidly varying diffusionless motions in the Earth's core interior

is characterized by quasi-geostrophic thermal Rossby waves, which vary slowly in the axial direction on the scale of the sphere radius

Numerical study of the motions within a slowly precessing sphere at low Ekman number

r_o

Physical properties at the top of the core and core surface motions

and have short azimuthal length scale

Core-mantle topographic torque: a spherical harmonic approach and implications for the excitation of the Earth's rotation by core motions

O(E^{1/3}r_o)

Planetary gyre, time‐dependent eddies, torsional waves, and equatorial jets at the Earth's core surface

. They also confirmed the localization of the convection about some cylinder radius

Experimental study of super-rotation in a magnetostrophic spherical Couette flow

s\,{=}\,s_M