The Dynamo Number and Scaling Relations

A schematic estimate of the strength of the dynamo components, and an approximate scaling law, results from the quantitative side of this picture. Differential field stretching causes poloidal to toroidal conversion, which takes place at a rate Su /L. Vorticial motion of rising convective eddies transforms toroidal to locally poloidal field at a rate f, which is a pseudo-scalar quantity whose sign depends on the hemisphere. The dynamo equations simplify by dimensional analysis. For the poloidal field, which is given by a vector potential field. 

The rate at which the poloidal field dissipates by turbulence and diffusion is, in the steady state, balanced by the conversion of toroidal to poloidal flux  

Finally, the poloidal field is wrapped to form the azimuthal field at a rate that depends on the shear 5S2 

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