Journal
GEOPHYSICAL AND ASTROPHYSICAL FLUID DYNAMICS
Volume 98, Issue 3, Pages 235-240Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/030919209410001659272
Keywords
kinematic dynamos; toroidal velocity
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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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