Rapid dynamics in the Earth's core
Lead Research Organisation:
University of Leeds
Department Name: Applied Mathematics
Abstract
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.
Organisations
Publications

Brown W
(2013)
Jerks abound: An analysis of geomagnetic observatory data from 1957 to 2008
in Physics of the Earth and Planetary Interiors

Cox G
(2016)
The observational signature of modelled torsional waves and comparison to geomagnetic jerks
in Physics of the Earth and Planetary Interiors

Cox G
(2014)
Forward models of torsional waves: dispersion and geometric effects
in Geophysical Journal International

Cox G
(2013)
Rapid dynamics of the Earth's core
in Astronomy & Geophysics

Fournier A
(2015)
The impact of geomagnetic spikes on the production rates of cosmogenic 14 C and 10 Be in the Earth's atmosphere
in Geophysical Research Letters

Hori K
(2015)
Slow magnetic Rossby waves in the Earth's core
in Geophysical Research Letters

Li K
(2011)
Variational data assimilation for the initial-value dynamo problem.
in Physical review. E, Statistical, nonlinear, and soft matter physics

Li K
(2014)
Variational data assimilation for a forced, inertia-free magnetohydrodynamic dynamo model
in Geophysical Journal International

Livermore P
(2012)
The Spherical Harmonic Spectrum of a Function with Algebraic Singularities
in Journal of Fourier Analysis and Applications

Livermore P
(2011)
The evolution of a magnetic field subject to Taylor's constraint using a projection operator Evolution subject to Taylor's constraint
in Geophysical Journal International
Description | Torsional waves similar to those found in observations have been found in numerical simulations. This enabled us to show that in Earth's core conditions the torsional waves are excited by the convection occurring in the Earth's core as the planet cools down. By examining the numerical models, we managed to show that in Earth's core conditions the torsional waves are primarily driven by the magnetic Lorentz force rather than by Reynolds stress. We showed also that it is necessary to get to low Ekman numbers, that is low viscosity, before the Lorentz forces dominate. This low viscosity regime is nort easy to reach, which is why previously it was thought that Reynolds stress drove the torsional oscillations. We also developed a magnetoconvection model for the dynamics of the Earth's core. This is a simpler model than the usual full dynamo models used to study the Earth's core. Its advantage is that it enables a low Ekman number regime to be reached, something which is very computationally expensive for a full dynamo code. Using this magnetoconvection model, we showed that the outward propagation of torsional waves from the tangent cylinder can be explained by a near resonance between the torsional oscillation frequency (period approximately six years) and the convective frequency of convective columns near the tangent cylinder. |
Exploitation Route | Further data on torsional waves in the Earth's core is coming in from magnetic satellite data. This will enable further refinement of the ideas that emerged from this project. There is also the exciting possibility that new nonaxisymmetric waves, Rossby waves, may be discovered in the secular variation data. This would enable us to get more information about the state of the Earth's core. |
Sectors | Education Environment |
Description | Our findings have been reported in talks to the general public and to schoolchildren. |
First Year Of Impact | 2012 |
Sector | Education,Environment |
Impact Types | Cultural Societal |
Description | Electromagnetism in the Earth's core |
Form Of Engagement Activity | Participation in an open day or visit at my research institution |
Part Of Official Scheme? | Yes |
Geographic Reach | Local |
Primary Audience | Schools |
Results and Impact | The school children learnt about magnetism and the Earth's magnetic field, taking part in a variety of activities. The session sparked interest for the students in physical sciences. |
Year(s) Of Engagement Activity | 2012,2013,2014 |
Description | SEDI UK |
Form Of Engagement Activity | Participation in an activity, workshop or similar |
Part Of Official Scheme? | Yes |
Geographic Reach | International |
Primary Audience | Public/other audiences |
Results and Impact | After a day of talks, we had an hours general discussion, engaging experienced researchers and students alike. N/A |
Year(s) Of Engagement Activity | 2014 |
URL | http://www.see.leeds.ac.uk/research/igt/deep-earth-research/uksedi-2014/ |
Description | SEDI conference |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | International |
Primary Audience | Public/other audiences |
Results and Impact | We hosted an international conference, Study of the Earth's Deep Interior, at Leeds in 2012. N/A |
Year(s) Of Engagement Activity | 2012 |
URL | http://www.see.leeds.ac.uk/research/igt/deep-earth-research/sedi-2012/ |
Description | Talk at Astronomical Society of Glasgow |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | Regional |
Primary Audience | Public/other audiences |
Results and Impact | ~100 members of the public attended a public lecture on planetary magnetic fields, many questions asked in the following discussion session The society committee produced related material for their monthly newsletter, a recording of the event was made available on the University of Leeds webpages. |
Year(s) Of Engagement Activity | 2013 |
Description | Talk at Cumberland Geological Society |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | Regional |
Primary Audience | Public/other audiences |
Results and Impact | Presentation on the Earth's inner core; what we know and how we know it, plus outstanding questions resulting in lots of questions and discussion afterwards. Asked for more speakers from the group to give future talks. |
Year(s) Of Engagement Activity | 2014 |
Description | Talk at Leeds City Museum (Leeds Cafe Scientifique) |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Geographic Reach | Local |
Primary Audience | Public/other audiences |
Results and Impact | Hour-long discussion of magnetic reversals with lots of questions asked and some public participants relating their relevant experiences (e.g. shielding of electronic components). Appreciation expressed for a stimulating discussion. |
Year(s) Of Engagement Activity | 2014 |
Description | Talk at Manchester Grammar School |
Form Of Engagement Activity | A talk or presentation |
Part Of Official Scheme? | No |
Type Of Presentation | Keynote/Invited Speaker |
Geographic Reach | Local |
Primary Audience | Schools |
Results and Impact | 30 pupils attended and there was discussion about planets for some time afterwards Not really possible to be certain about impact. |
Year(s) Of Engagement Activity | 2013 |