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Abstract
Parker's analytic Cartesian interface dynamo is generalized to the case of a shear layer of finite thickness and low resistivity (“tachocline”), bounded by a perfect conductor (“radiative zone”) on the one side, and by a highly diffusive medium (“convective zone”) supporting an α-effect on the other side. In the limit of high diffusivity contrast between the shear layer and the diffusive medium, thought to be relevant for the Sun, a pair of exact dispersion relations for the growth rate and frequency of dynamo modes is analytically derived. Graphic solution of the dispersion relations displays a somewhat unexpected, non-monotonic behavior, the mathematical origin of which is elucidated. The dependence of the results on the parameter values (dynamo number and shear layer thickness) is investigated. The implications of this result for the solar dynamo problem are discussed.
Acknowledgments
This research was supported by the Hungarian Science Research Fund (OTKA) under grant no. K67746; by the European Commission through the SOLAIRE Network (MTRN-CT-2006-035484); by the European Union and European Social Fund (grant no. TÁMOP-4.2.1/B-09/1/KMR); by the Theoretical Institute for Advanced Research in Astrophysics (TIARA) operated under Academia Sinica and the National Science Council Excellence Projects program in Taiwan administered through grant number NSC95-2752-M-007-006-PAE; as well as by the Science and Technology Facilities Council (STFC), UK and the Mathematics and Statistics Research Centre (MSRC) of the University of Sheffield. K. Petrovay acknowledges the warm hospitality received at the Department of Applied Mathematics, University of Sheffield during his visit. R. Erdélyi acknowledges M. Kéray for his patient encouragement.