Structural instability of the Rikitake disk dynamo

Details Structural instability of the Rikitake disk dynamo Structural instability of the Rikitake disk dynamo

May 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995georl..22.1057h&link_type=abstract

Geophysical Research Letters (ISSN 0094-8276), vol. 22, no. 9, p. 1057-1059

Mathematics

Logic

15

Disks (Shapes), Dynamo Theory, Friction, Geodynamics, Rotating Generators, Structural Stability, Systems Stability, Analogs, Boundary Layers, Geomagnetism, Moments Of Inertia, Nonlinear Equations, Ohmic Dissipation, Oscillations, Partial Differential Equations

Scientific paper

The Rikitake-type disk dynamo, consisting of two identical single Faraday-disk dynamos of the Bullard type coupled together, has been analyzed intensively for more than thirty years by mathematicians interested in its ability to behave chaotically, and by geophysicists needing low-dimensional electromechanical analogues of the geodynamo in their efforts to elucidate the complex time series of geomagnetic polarity reversals over geological time. Implicit in the theory is what now appears to be an unwarranted assumption, namely that mechanical friction is unimportant both qualitatively and quantitatively as a dissipative agency in comparison with ohmic effects, and can therefore safely be neglected. The assumption is inconsistent findings which show that mechanical friction can render the Rikitake dynamo structurally unstable and consequently incapable of producing chaotic oscillations. Research on low-dimensional analogues of the geodynamo should concentrate attention on structurally stable systems, with properties less dependent on the starting conditions.

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