Project description
Recent satellite observations have revealed a robust signal in the geomagnetic field at interannual timescales (a few years): the rate at which the field is changing is itself changing, with a characteristic period near seven years and an amplitude that is largest in the equatorial region of the core surface. The leading interpretation is that this signal is the surface manifestation of slow magneto-Coriolis modes in the rotating, magnetised outer core. Therefore, standing-wave oscillations whose frequency and structure are determined jointly by the Coriolis force and a magnetic restoring force. A recent finding is that simple symmetric models of the deep internal magnetic field cannot reproduce the observed set of modes; significant asymmetric structure of the field appears to be required. Since the deep internal field is otherwise inaccessible to direct observation, this is a substantive constraint.
The mathematical work is derivation of the eigenvalue problem (the equation that determines the natural oscillation frequencies and patterns of the system) from MHD by an asymptotic expansion exploiting the smallness of a key dimensionless parameter, the Lehnert number, which compares the magnetic-wave speed to the rotation-driven wave speed. This expansion reduces the three-dimensional MHD system to a two-dimensional problem in the equatorial plane. The numerical work is discretisation of this two-dimensional problem on a spectral grid and its solution as a sparse eigenvalue problem using standard library routines; the first part is spent reproducing two published benchmarks (the analytic Malkus magneto-inertial spectrum and one recent computational test case).
The scientific outcome is a characterisation of which classes of background magnetic field are excluded by observed slow magneto-Coriolis spectra at long-running ground observatories. The realistic expected result is exclusion of broad classes rather than unique recovery of the actual field (the mapping from field to spectrum is many-to-one), but exclusion at this level is itself a meaningful constraint on the deep magnetic field. If time permits, the project extends to non-symmetric background fields taken from existing geomagnetic field models or from numerical simulations of the geodynamo. An optional further extension uses automatic differentiation (a technique from machine learning that computes derivatives of complex calculations efficiently) to study how the mode frequencies depend on the background-field parameters.
The student taking on this project needs to have a bachelor in geophysics or equivalent. An interest in mathematics, computer programming and data analysis would be useful.