Other
Scientific paper
Mar 1980
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980natur.284..250t&link_type=abstract
Nature, vol. 284, Mar. 20, 1980, p. 250, 251.
Other
6
Compressibility Effects, Compressible Flow, Conducting Fluids, Dynamo Theory, Magnetic Dipoles, Earth Core, Saturn (Planet), Symmetry
Scientific paper
The effects of taking fluid compressibility into account on the validity of various anti-dynamo theorems which depend on incompressible fluid flow and a solenoidal velocity field are examined. It is shown that the original neutral curve argument of Cowling (1933) forbidding stationary axisymmetric dynamos and the radial velocity field anti-dynamo theorem of Namikawa and Matsushita (1970) are unaffected by flow compressibility. On the other hand, the proofs of anti-dynamo theorems forbidding nonstationary axisymmetric dynamos, dynamo action maintained by a toroidal velocity field and dynamos driven by plane two dimensional motion, using global properties of the fields, are shown to fail when a lamellar component is added to the velocity field. It is suggested that, while other proofs of the anti-dynamo theorems considered here not requiring the incompressibility assumption may be found, the real compressibility of electrically conducting fluids in planets may permit the construction of nonstationary axisymmetric dynamos implied by the earth's and Saturn's magnetic fields.
Rochester Michael G.
Todoeschuck John P.
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