Up and down cascade in a dynamo model: Spontaneous symmetry breaking

A multiscale turbulent model of dynamo is proposed. A secondary magnetic fi eld is generated from a primary field by a flow made of turbulent helical v ortices (cyclones) of different ranges? and amplified by an up and down cas cade mechanism. The model displays symmetry breakings of different ranges a lthough the system construction is completely symmetric. Large-scale symmet ry breakings for symmetric conditions of the system evolution are investiga ted for all kinds of cascades: purl direct cascade, pure inverse cascade, a nd up and down cascade. It is shown that long lived symmetry breakings of h igh scales can be obtained only in the cast of the up and down cascade. The symmetry breakings find expression in intervals of constant polarity of th e secondary field (called chrons of the geomagnetic field). Long intervals of constant polarity with quick reversals are obtained in the model; condit ions for such a behavior are investigated. Strong variations of the generat ed magnetic held during intervals of constant polarity are also observed in the model. Possible applications of the model to geodynamo modeling and va rious directions of future investigation are briefly discussed. [S1063-651X (99)10605-6].