The Simple Model of the Evolution of Magnetic and Kinetic Energy of Geodynamo

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Abstract

The induction and momentum equations are simplified to a dynamical system for the kinetic and magnetic energies in the Earth’s core. Stable stationary points of this system give a geomagnetic field of ~ 10 mT and the cosecant of the angle between the magnetic field vector and the fluid velocity vector is on average about 500 at a known speed of ~ 1 mm/sec and a generally accepted dynamo power of ~ 1 TW. With a generally known typical geomagnetic time of the order of a thousand years, harmonic secular variations of the order of several decades and rapid exponential changes of the order of several months, possibly associated with jerks, were obtained. All this is in good agreement with dynamo theory, paleomagnetic reconstructions, numerical modeling and observations. Geomagnetic energy ~ 10 mJ/kg is four orders of magnitude greater than kinetic energy. Under conditions of such dominance of magnetic energy, an analytical solution was obtained, which over time converges to stable stationary points. Apparently unlikely catastrophes with virtually zero magnetic energy near partially stable stationary points are discussed.

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S. V. Starchenko

Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation of the Russian Academy of Sciences

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Email: sstarchenko@mail.ru
Russian Federation, Troitsk

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