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Magnetoelastic interactions in the earth's core Crossley, David John

Abstract

Previous calculations of the interaction of plane elastic waves in a uniform magnetic field in the Earth's liquid core showed negligible damping of such waves. Subsequent extensions of the theory have treated separately the damping of radial oscillations in a uniform field, and the effect of a field gradient on plane waves. It has been speculated that enhanced attenuation would take place for standing waves in a field gradient. An additional effect might also be expected from a proper treatment of the field geometry, as within the Earth both magnetic and free-oscillation fields can be expanded in spherical harmonics. In the present thesis a rigorous evaluation of magnetoelastic interactions in a spherical conductor is given, with a view to clarifying these predictions. The results show that within the Earth's core and at seismic frequencies the interaction is indeed weak. Typical values of the Q of the damping due to magnetic effects are at least 10¹³. Consideration of a wide range of harmonics in the interaction fails to find a significant effect due to field geometry. The role of viscous damping is evaluated using a recent value for the core viscosity and typical viscous Q's were about 10¹⁶. The possibility of gaining useful information from magnetic or viscous damping of the free oscillations is thus remote, but the importance of the results lies in their extension to core oscillations of longer periods. Such oscillations will also be underdamped and their velocity fields may be suitable for the new turbulent dynamo theories of the Earth's main magnetic field.

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