Rapid dynamics in the Earth's core

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The problem of how the Earth generates its magnetic field is one of the outstanding scientific challenges of the present time. Observations and models of the geomagnetic field provide a window through which the dynamic processes and structure of the Earth's deep interior can be studied, a technique that complements seismic studies. In the last two decades, a variety of satellite missions have significantly improved our knowledge of the Earth's magnetic field, both in its spatial structure and in its temporal behaviour on decadal time-scales. Because these observations cannot probe deeper than the lower-most mantle, any understanding of the fluid outer core, where the field is generated, along with any insight into its time variability, must be obtained from models. Geodynamo models of the core have traditionally focused on millennial or longer time-scales to understand the long term evolution of the field, for the most part ignoring the shorter time-scales. Our aim is to investigate these rapid dynamics which are of great scientific interest, being the very signal for which we have accurate observations. Such a project complements the vast scientific effort and expense being channelled into the latest generation of satellites. We propose three interlinked yet independent projects which will be split between the Schools of Mathematics and Earth & Environment at the University of Leeds: (i) The construction of numerical Cartesian-box models of the excitation and rapid dynamics in the core; (ii) The development of macrodynamic models of flow instabilities in the core; (iii) The extraction and modelling of flow accelerations in the core from observational satellite data. Convection-driven spherical shell geodynamo simulations, which solve the fundamental equations from first principles, have been remarkably successful in explaining many features of the observed geomagnetic field, but they do suffer from some important limitations. Even with the most powerful computers, the models cannot resolve short length scales and time scales, and so have to be run with parameters many orders of magnitude removed from geophysical estimates of those in the Earth's core. Indeed, the Earth's system is so complicated that there is little prospect of being able to run models which resolve all temporal and spatial scales, at the correct parameter values, for many decades to come. However, we believe that considerable insight can be obtained from running models at the correct parameters but in a simplified geometry. The computational models (i) and (ii) that we propose are targeted at understanding specific aspects of the geodynamo on rapid timescales. Project (i) illustrates well the lack of importance of a realistic geometry, being focussed on excitation mechanisms of the rapid dynamics. These are believed to be driven by turbulent convection which occur independent of any boundary effects, and should be captured in any 3D model run at geophysical parameter values. In particular, the processes will be fully represented in a Cartesian-box model, which is much easier to study computationally at small viscosities than spherical models. By combining knowledge of the excitation mechanisms from project (i) with an understanding of the macrodynamics of core instabilites from (ii), we will significantly improve our understanding of core processes on rapid timescales. Validation and use of these new insights with observational data in (iii) will help explain geomagnetic jerks which are of broad interest. This research will also help us to to investigate the small length-scale behaviour in the core, on scales of 1-100 km, which is too computationally expensive to obtain by spherical simulations. By establishing the important force balance across the whole range of relevant scales in the core, the essential requirements for developing more realistic spherical shell dynamo models will be identified.