Abstract
Linear magnetoconvection in a model of a non-uniformly stratified horizontal rotating fluid layer with a toroidal magnetic field is investigated for no-slip and finitely electrically conductive boundaries and with very thin stably stratified upper sublayer. The basic parabolic temperature profile is determined by the temperature difference between the boundaries and by the homogeneous heat source distribution in the layer. This results in a density pattern, in which a stably stratified upper sublayer is present. The developed diffusive perturbations (modes) are strongly affected by the complicated coupling of viscous, thermal and magnetic diffusive processes. The calculations were performed for various values of Roberts number (q ≪ 1 and q = O(1)). The mean electromotive force produced by the developed hydromagnetic instabilities is investigated to find the modes, which can be appropriate for creating the α-effect. It was found that the azimuthal part of the EMF is dominant for westward modes when the Elsasser number Λ ≲ O(1).
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References
Bod’a J., 1988. Thermal and magnetically driven instabilities in a non-constantly stratified fluid layer. Geophys. Astrophys. Fluid Dyn., 44, 77–90.
Braginsky S., 1964. Magnetohydrodynamics of the Earth’s Core. Geomagn. Aeron., 4, 898–916 (Engl. Transl. 698-712).
Brestenský J. and Rädler K.-H., 1989. Mean electromotive forces resulting from instabilities in a stratified rapidly rotating fluid layer permeated by a magnetic field. Geophys. Astrophys. Fluid Dynamics, 49, 57–70.
Brestenský J. and Ševčík S., 1994. Mean electromotive force due to magnetoconvection in rotating horizontal layer with rigid boundaries. Geophys. Astrophys. Fluid Dyn., 77, 191–208.
Brestenský J., Ševčík S. and Šimkanin J., 1995. The boundary conditions influence on a magnetoconvection of a rapidly rotating horizontal fluid layer stratified either uniformly or non-uniformly (mathematical approaches). In: I. Tunyi et al. (Eds.), Proceedings of the 1st Conference of Slovak Geophysicists, Geophysical Institute of SAS, Bratislava, 80–85.
Brestenský J., Ševčík S. and Šimkanin J., 1998. Magnetoconvection in dependence on Roberts number. Stud. Geophys. Geod., 42, 280–288.
Brestenský J., Ševčík S. and Šimkanin J., 2001. Rotating magnetoconvection in dependence on stratification, diffusive processes and boundary conditions. In: P. Chossat, D. Armbruster and I. Oprea (Eds.), Dynamo and Dynamics, a Mathematical Challenge, NATO Science Series, Sub-Series II, Vol. 26, Kluwer Academic Publishers, 133–144.
Chandrasekhar S., 1961. Hydrodynamic and Hydromagnetic Stability. Clarendon Press, Oxford.
Fearn D.R. and Loper D.E., 1981. Compositional convection and stratification of the Earth’s core. Nature, 289, 393–394.
Glatzmaier G.A. and Roberts P.H., 1995. A three-dimensional self-consistent computer simulation of geomagnetic field reversal. Nature, 337, 203–209.
Guba P., 2001. On the finite-amplitude steady convection in rotating mushy layers. J. Fluid Mech., 437, 337–365.
Gubbins D., Thomson C.J. and Whaler K.A., 1982. Stable region in the Earth’s liquid core. Geophys. J. R. astr. Soc., 68, 241–251.
Hejda P. and Reshetnyak M., 2003. Control volume method for the dynamo problem in the sphere with free rotating inner core. Stud. Geophys. Geod., 47, 147–159.
Jones C.A., 2000. Convection-driven geodynamo models. Phil. Trans. R. Soc. Lond. A, 358, 873–897.
Kono M. and Roberts P.H., 2002. Recent geodynamo simulations and observations of the geomagnetic field. Rev. Geophys., 40, art. no. 1013.
Krause F., Rädler K.-H., 1980. Mean-Field Magnetohydrodynamics and Dynamo Theory. Akademie-Verlag, Pergamon Press, Berlin, Oxford.
Loper D.E., 2000. A model of the dynamical structure of Earth’s outer core. Phys. Earth Planet. Inter., 117, 179–196.
Rädler K.-H., Kleeorin N. and Rogachevskii I., 2003. The mean electromotive force for MHD turbulence: The case of a weak magnetic field and slow rotation. Geophys. Astrophys. Fluid Dyn., 97, 249–274.
Roberts P.H. and Glatzmaier G.A., 2000. Geodynamo theory and simulations. Rev. Mod. Phys., 72, 1081–1123.
Soward A.M., 1979. Thermal and magnetically driven convection in a rapidly rotating fluid layer. J. Fluid Mech., 90, 669–684.
Ševčík, S., 1989. Thermal and magnetically driven instabilities in a non-constantly stratified rapidly rotating fluid layer with azimuthal magnetic field. Geophys. Astrophys. Fluid Dyn., 49, 195–211.
Ševčík S., Brestenský J. and Šimkanin J., 2000. MAC waves and related instabilities influenced by viscosity in dependence on boundary conditions. Phys. Earth Planet. Inter., 122, 161–174.
Šimkanin J., Brestenský J. and Ševčík S., 1997. Dependence of rotating magnetoconvection in horizontal layer on boundary conditions and stratification. In: J. Brestenský and S. Ševčík (Eds.), Stellar and Planetary Magnetoconvection, Acta Astron. et Geophys. Univ. Comenianae, XIX, 195–220.
Šimkanin J., Brestenský J. and Ševčík S., 2003. Problem of the rotating magnetoconvection in variously stratified fluid layer revisited. Stud. Geophys. Geod., 47, 827–845.
Tilgner A. and Busse F., 2001. Fluid flows in precessing spherical shells. J. Fluid Mech., 426, 387–396.
Velímský J. and Matyska C., 2000. The influence of adiabatic heating/cooling on magnetohydrodynamic systems. Phys. Earth Planet. Inter., 117, 197–207.
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Šimkanin, J., Brestenský, J. & Ševčík, S. On hydromagnetic instabilities and the mean electromotive force in a non-uniformly stratified Earth’s core affected by viscosity. Stud Geophys Geod 50, 645–661 (2006). https://doi.org/10.1007/s11200-006-0041-9
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DOI: https://doi.org/10.1007/s11200-006-0041-9