An extension of the Toroidal Theorem

Details An extension of the Toroidal Theorem An extension of the Toroidal Theorem

Mar 2004

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004gapfd..98..235p&link_type=abstract

Geophysical and Astrophysical Fluid Dynamics, vol. 98, Issue 3, p.235-240

Physics

Fluid Dynamics

4

Scientific paper

The well-known "toroidal theorem" of Elsasser and Bullard and Gellman rules out dynamo action in a conducting sphere when the velocity field has no poloidal part. It is here shown that for a fixed toroidal velocity field any poloidal velocity must attain a finite size if dynamo action is to be possible. The resulting "anti-dynamo" theorem generalises the earlier result of Childress by giving a bound on the product of the suprema of the toroidal and poloidal velocities.

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