A coupled low order dynamo/turbulent shell model for geomagnetic field variations and reversals

Abstract

We couple a low order αω dynamo model to a shell model of turbulence, with the dynamo α-effect being identified with the helicity of the shell model. Fluctuations (‘noise’) in this term lead to lognormal-like statistics in the magnetic field, as was noted for inter-reversal duration by Ryan and Sarson (2007). Here we extend the analysis to shorter time-scale field variations (viz. Virtual Axial Dipole Moments, VADMs), and find that a lognormal distribution is also a significant fit for this quantity, both for the output from our model and for the observed paleomagnetic data. This shared lognormality – which Ryan and Sarson (2007) argued arose from a common source in terms of ‘multiplicative noise’ in the underlying dynamo mechanism – makes the synthetic and observed data comparable; we also note some similarities in the patterns of VADM fluctuations (including asymmetric decay and recovery, epitomised in an extreme form by the controversial ‘saw-tooth’ pattern) and in reversal inter-event times (chrons) of widely varying duration. We describe the dynamics behind our coupled model, and discuss the effect of certain model parameters on the synthetic chron durations, including the occurrence of superchrons. Implications for the observed geomagnetic field behaviour are discussed.