Fauto Cattaneo, Eun-Jin Kim, Michael Proctor, and Louis Tao
PHYSICAL REVIEW LETTERS 75(8), 1522-1525 (1995)
Abstract.
The ratio R_1 between the average magnetic energy and the square-averaged
flux plays an important role in the study of nonlinear dynamos, as a measure
of the efficiency of a dynamo at generating flux. For large values of
R_m, R_1 displays a scaling behavior of the type R_1~ R_m^n, where R_m is
the magnetic Reynolds number. We show by direct numerical evaluation that
n depends sensitively on the flow complexity for small-scale dynamos.
Furthermore, by relating n to the cancellation exponent and the correlation
dimension of the magnetic field, we argue that n is not likely to be close
to zero in general.
(C) 1995 The American Physical Society
Available as PDF file
Louis Tao,
September 2000,
Applied Mathematics Laboratory,
CNS,
New York, NY 10012