THE MAGNETIC TAYLOR-PROUDMAN CONSTRAINT ON CONVECTION IN PLANETARY CORES

Planets cools, spin-down and sustain magnetic fields through the interplay between buoyancy, the Coriolis and the Lorentz forces within their liquid core. This combination of forces in extreme regimes make the resulting convection challenging to elucidate. Planetary rotation opposes any flow across an imaginary cylindrical surface called the Tangent Cylinder (TC), extruded along the rotation axis from the solid core to the mantle. Magnetic fields act similarly but the questions of which topological constraint is imposed by the combination of both and how it affects convection there are unanswered. To address them, we show theoretically that they impose a constraint on the compound current of mass and charge. In axisymmetric domains, this translates into a kinematic link between radial and azimuthal velocities near the TC, suggesting the existence of a radial flow across the Earth's TC.

This theory is tested on the Little Earth Experiment (LEE), a device where optical measurements are performed in a transparent but electrically conducting liquid subject to rotation, magnetic field and buoyancy in a TC geometry. Magneto-Convective patterns are visualised for the first time and we show that the time- and azimuthally- averaged radial flow near the TC boundary follows the theory.