Spectral methods for analyzing energy balances in geodynamo simulations

The geomagnetic field displays complicated variations over a broad range of frequencies. These variations can be decomposed by frequency and linked to physical processes using frequency domain spectral methods. These spectral methods are well developed but have not previously been applied to study the energy balance of geodynamo simulations. We illustrate their potential by analyzing output from numerical dynamo simulations that have previously been studied for their apparently Earth-like properties. We show that high coherence between variations in axial dipole energy at the outer boundary of the simulation and total magnetic energy within the fluid shell occur at frequencies below similar to 0.1 kyr(-1). This suggests that paleomagnetically-observable signals with periods exceeding 10 kyrs contain information about magnetic energy changes in the bulk core. We then use spectral analysis to investigate differences in the rate of growth and decay of the axial dipole field. This behaviour, characterised by rapid growth and slow decay, is observed when signals with frequencies higher than 0.03 kyr(-1) have been filtered out. The origin of this asymmetric growth and decay is assessed using coherence spectra between rates of change in kinetic and magnetic energy, ohmic and viscous dissipation, and work done by the buoyancy and Lorentz forces. We show that asymmetry is associated with an imbalance between ohmic dissipation and work done by the Lorentz force; when changes in magnetic energy are more coherent with ohmic dissipation the field grows rapidly and decay slowly. Variations in Ohmic dissipation reflect changes in field strength in our models, while changes in viscous dissipation are associated with amplitude fluctuations of the large-scale flow that exists on millennial timescales. Our work shows that spectral analysis coupling observable and global products of the dynamo process can elucidate the physical origin of periodic processes occurring on timescales exceeding 10 kyrs.