Magnetic energy transfer at the top of the Earth's core

We introduce a formalism to track magnetic energy transfer between spherical harmonic degrees due to the interaction of fluid flow and radial magnetic field at the top of the Earths core. Large-scale synthetic single harmonic flows are characterized by a fixed difference between harmonics participating in the transfer. Large-scale toroidal flows result in more local energy transfer than small-scale poloidal flows. Axisymmetric poloidal flows are most efficient in producing energy transfer and dipole changes. The azimuthal phase relation between the field and the flow may play a major role in the energy transfer. Geomagnetic energy transfer induced by core flow models exhibit a striking transfer spectrum pattern of alternating extrema suggestive of energy cascade, but the detailed transfer spectrum matrix reveals rich behaviour with both local Kolmogorov-like transfer and non-local transfer, the latter about twice larger. The transfer spectrum reverses from even maxima and odd minima between 1840 and 1910 to odd maxima and even minima between 1955 and 1990. The transfer spectrum matrix shows geomagnetic energy cascade from low to high degrees as well as non-local transfer from the dipole directly to higher degrees, explaining the simultaneous dipole decrease and non-dipole increase during the historical period.