Fluid mechanics.

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Abstract

The geomagnetic field is generated by a dynamo process acting in Earth’s outer core that is thermally coupled to the lower mantle. This thesis investigates thermal core-mantle coupling using numerical simulations. The numerically accessible parameter regime is investigated and simulations incorporating thermal variations at the outer spherical boundary are used to investigate the paleomagnetic signature of core-mantle coupling and the effects of this coupling on convection and magnetic field generation. Current dynamo simulations cannot reach the very rapid rotation rates and low viscosities of Earth due to limitations in available computing power. Using a pseudospectral method, the most widely-used method for simulating the geodynamo, computational requirements needed to run simulations in an ‘Earth-like’ parameter regime are explored theoretically by approximating operation counts, memory requirements, and communication costs in the asymptotic limit of large problem size. Theoretical scalings are tested using numerical calculations. The limiting aspect of the method for asymptotically large problems is shown to be the spherical transform, which also places an upper bound on the number of processors that the method can use for a given resolution. Extrapolating numerical results, based upon the code analysis, shows that simulating a problem characterising the Earth would require approximately 160 days per magnetic diffusion time when 18000 processors are available. The paleomagnetic signature of thermal core-mantle coupling is investigated by comparing three dynamo solutions incorporating laterally varying boundary heat flux, derived from seismic tomography, with paleomagnetic data. The three solutions use modest parameters and differ only in the amplitude of the boundary anomalies; each exhibit fields dominated by two pairs of intense flux patches that ‘lock’ to the boundary anomalies to differing degrees. All models are dominated by non-axisymmetric components. The solution with the largest amplitude of boundary heating displays encouraging similarities with the non-axisymmetric time-averaged field, paleosecular variation data, and observed inclination difference between Hawai’i and Réunion Island. This comparative study prompts two further studies on inhomogeneous thermal coupling. First, convection in a rotating spherical shell subject to inhomogeneous outer boundary heating is investigated as a function of the rotation rate and amplitude of boundary anomalies. The analysis explores conditions under which steady flows can be obtained, and the stability of these solutions, for different boundary heating modes. When the boundary heating has a larger scale than the most unstable mode of the convection, as in the locked solutions, stable steady solutions are always possible, and unstable solutions show convection rolls that cluster into nests and remain trapped for many thermal diffusion times. Secondly, the Rayleigh number-dependence of inhomogeneous dynamo simulations is investigated for tomographic and single Y 2 2 harmonic boundary conditions. Solutions with both boundary conditions exhibit rich time-dependent be-