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We propose a spectral transfer model for the secular variation of the geomagnetic core field to explain the simultaneous decrease in dipole field intensity and the increase in non-dipole field intensity from 1840 to the present in terms of a dynamo cascade process. The main assumption of this model is that magnetic energy is transferred between adjacent spherical harmonic degrees in the Mauersberger–Lowes spectrum of the geomagnetic field. The key parameters are a set of coefficients that indicate the rate and direction of magnetic energy transfer through the spectrum. Applying the spectral transfer model to the historical period, we find that the quadrupole family of the core field can be characterized by a persistent inverse magnetic energy cascade from higher towards lower spherical harmonics. In the dipole family of the core field, we find cascade behaviour generally from lower to higher spherical harmonics, consistent with axial dipole decrease, but with a high level of time variability that correlates with variations in the dipole family intensity. During time intervals when the dipole family intensity rapidly decreases, energy appears to cascade towards higher spherical harmonics, beyond the limit of the observable part of the core field spectrum. During time intervals when the dipole family intensity is nearly constant, a more limited forward cascade appears to trap energy at intermediate spherical harmonics. Similar fluctuations in the rate and direction of spectral transfer are also seen in the Mauersberger–Lowes spectrum of a numerical dynamo model during a dipole decrease event that led to a polarity excursion. We discuss the possibility of this scenario for the current geomagnetic dipole decrease. [ABSTRACT FROM AUTHOR]

The generation of a magnetic field in numerical simulations of the geodynamo is an intrinsically 3-D and time-dependent phenomenon. The concept of magnetic field lines and the frozen-flux approximation can provide insight into such systems, but a suitable visualization method is required. This paper presents results obtained using the Dynamical Magnetic Field line Imaging (DMFI) technique, which is a representation of magnetic field lines accounting for their local magnetic energy, together with an algorithm for the time evolution of their anchor points. The DMFI illustrations are consistent with previously published dynamo mechanisms, and allow further investigation of spatially and temporally complex systems. We highlight three types of magnetic structures: (i) magnetic cyclones and (ii) magnetic anticyclones are expelled by, but corotate with axial flow vortices; (iii) magnetic upwellings are amplified by stretching and advection within flow upwellings, and show structural similarity with helical plumes found in rotating hydrodynamic experiments. While magnetic anticyclones are responsible for the regeneration of a stable axial dipole, here we show that excursions and reversals of the dipole axis are caused by the emergence of magnetic upwellings, which amplify and transport a generally multipolar magnetic field from the inner to the outer boundary of the models. Geomagnetic observations suggest the presence of magnetic structures similar to those found in our models; thus, we discuss how our results may pertain to Earth's core dynamo processes. In order to make DMFI a standard tool for numerical dynamo studies, a public software package is available upon request to the authors (supplementary material is available at: ). [ABSTRACT FROM AUTHOR]