On Vainshtein's dynamo conjecture.

Details On Vainshtein's dynamo conjecture. On Vainshtein's dynamo conjecture.

Aug 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999rspsa.455.3139k&link_type=abstract

Proc. R. Soc. London, Ser. A, Vol. 455, No. 1988, p. 3139 - 3162

Computer Science

Dynamo Theory: Models, Dynamo Theory: Sun

Scientific paper

Vainshtein's conjecture in dynamo theory states that all fluid motions that are not precluded from dynamo action by known anti-dynamo theorems act as dynamos at least in some part of the parameter space. The authors disprove this conjecture by analysing in detail two dynamo models with very simple flow fields. In both models, fluid motion is represented by a rigidly rotating cylinder of infinite length. In the first model, this cylinder is surrounded by an infinite expanse of fluid at rest with a different conductivity than the moving fluid. In the second model, the cylinder is enclosed in a cylindrical gap of an identical fluid at rest, which itself is surrounded by a vacuum region extending to infinity. The models are sufficiently complicated so that none of the known anti-dynamo theorems excludes dynamo action. In fact, the latter model has been claimed to be a working dynamo. It is shown in this paper, by a combination of analytical and numerical methods, that neither of these models operates as a dynamo. This result is valid in the entire parameter space, in particular for arbitrarily large Reynolds numbers.

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