11 - Low-Dimensional Models of the Geodynamo

Summary

Dynamical aspects of dynamo theory are introduced through consideration of a number of low-dimensional models: the segmented disc dynamo, which shows chaotic behaviour with random polarity reversals; the disc dynamo driven by thermal convection (coupling a Bullard disc and a Welander loop) which shows a primary thermal bifurcation, followed by a secondary dynamo bifurcation; and the Rikitake two-disc dynamical system, again showing random polarity reversals. A different mode coupling is introduced between a dipolar and a quadrupolar family. There are similarities with the problem of a particle in a bi-stable potential well in that random excitation can trigger a transition from one minimum to the other. Turbulent fluctuations provide the excitation, whereas the distance from a saddle-node bifurcation accounts for the barrier. Good correspondence is achieved with both VKS and paleomagnetic data.