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PubMed1999

Up and down cascade in a dynamo model: spontaneous symmetry breaking.

A multiscale turbulent model of dynamo is proposed. A secondary magnetic field is generated from a primary field by a flow made of turbulent helical vortices (cyclones) of different ranges, and amplified by an up and down cascade mechanism. The model displays symmetry breakings of different ranges although the system construction is completely symmetric. Large-scale symmetry breakings for symmetric conditions of the system evolution are investigated for all kinds of cascades: pure direct cascade, pure inverse cascade, and up and down cascade. It is shown that long lived symmetry breakings of high scales can be obtained only in the case of the up and down cascade. The symmetry breakings find expression in intervals of constant polarity of the secondary field (called chrons of the geomagnetic field). Long intervals of constant polarity with quick reversals are obtained in the model; conditions for such a behavior are investigated. Strong variations of the generated magnetic field during intervals of constant polarity are also observed in the model. Possible applications of the model to geodynamo modeling and various directions of future investigation are briefly discussed.

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PubMed1997

Multiple scale dynamo.

A scaling law approach is used to simulate the dynamo process of the Earth's core. The model is made of embedded turbulent domains of increasing dimensions, until the largest whose size is comparable with the site of the core, pervaded by large-scale magnetic fields. Left-handed or right-handed cyclones appear at the lowest scale, the scale of the elementary domains of the hierarchical model, and disappear. These elementary domains then behave like electromotor generators with opposite polarities depending on whether they contain a left-handed or a right-handed cyclone. To transfer the behavior of the elementary domains to larger ones, a dynamic renormalization approach is used. A simple rule is adopted to determine whether a domain of scale l is a generator--and what its polarity is--in function of the state of the (l - 1) domains it is made of. This mechanism is used as the main ingredient of a kinematic dynamo model, which displays polarity intervals, excursions, and reversals of the geomagnetic field.

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