Mean-field effects in the Galloway-Proctor flow - AstrophysicsReport as inadecuate

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Abstract: The coefficients defining the mean electromotive force in a Galloway-Proctorflow are determined. This flow shows a two-dimensional pattern and is helical.The pattern wobbles in its plane. Apart from one exception a circular motion ofthe flow pattern is assumed. This corresponds to one of the cases consideredrecently by Courvoisier, Hughes and Tobias 2006, Phys. Rev. Lett., 96,034503. An analytic theory of the alpha effect and related effects in thisflow is developed within the second-order correlation approximation and acorresponding fourth-order approximation. In the validity range of theseapproximations there is an alpha effect but no gamma effect, or pumping effect.Numerical results obtained with the test-field method, which are independent ofthese approximations, confirm the results for alpha and show that gamma is ingeneral nonzero. Both alpha and gamma show a complex dependency on the magneticReynolds number and other parameters that define the flow, that is, amplitudeand frequency of the wobbling motion. Some results for the magnetic diffusivityeta t and a related quantity are given, too. Finally a result for alpha in thecase of a randomly varying flow without the aforementioned circular motion ispresented. This flow may be a more appropriate model for studying the alphaeffect and related effects in flows that are statistical isotropic in a plane.

Author: Karl-Heinz R├Ądler Potsdam, Axel Brandenburg Nordita



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