An asymptotic model for resistive instability in the Earth's outer core |
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Authors: | S D London |
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Institution: | Department of Computer and Mathematical Sciences , University of Houston-Downtown , One Main Street Houston, Texas, 77002, USA |
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Abstract: | Abstract Numerical work indicates that resistive instability may be the dominant mode of instability in the Earth's outer core for realistic core parameter regimes. In this paper, we assume that the Elsasser number is large in order to obtain an asymptotic analysis of resistive instability in an electrically conducting fluid confined to a rotating cylindrical shell of infinite extent in the axial direction. The dimensionless equations of motion are linearized about an ambient magnetic field which is purely azimuthal and depends only on the cylindrical radial variable. Applying the theory of ordinary differential equations with a large parameter, we obtain an asymptotic approximation to the solution. Relatively simple analytic expressions for the complex frequencies are obtained by applying the boundary conditions for insulating boundaries at the cylindrical sidewalls and then assuming that the ambient magnetic field vanishes at one or both of those sidewalls. The results appear to be consistent with previous numerical work. |
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Keywords: | Asymptotics earth's core hydromagnetic waves magnetic instabilities resistive instability |
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