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The dynamics of high-latitude jets within Earth's core by computational-fluid-dynamics simulation

Prof Rainer Hollerbach (SoM), Dr Phil Livermore (SEE)

Contact email: rh@maths.leeds.ac.uk

Background

The movement of Earth’s liquid core is responsible for generating our planetary magnetic field, yet we know very little about its structure and dynamics because direct observation is not possible.

Through modelling changes in the magnetic field using recent high-resolution satellite data, we have identified a jet-stream at high-latitude within the core.  This jet is located at about 70 degrees latitude - on the tangent cylinder, the imaginary cylinder tangent to the solid inner core and parallel to Earth’s rotation axis.

Figure 1 Left: the structure of the Earth's interior showing the liquid outer core and the tangent cylinder (image from Lawrence et al. (2009)). Right: a jet on the tangent cylinder as inferred by satellite observations of the geomagnetic field

The tangent cylinder is expected to be the location of important dynamics within the core, being an internal interface between different regimes of core motion. The magnetic field plays a crucial role in this, since unless it satisfies a particular constraint on its structure, it will cause a convergence and therefore a lateral squeezing of fluid: i.e. a jet formation.

The jet may play an important role in the global dynamics of the core (just as the jet-stream does in our atmosphere) and also may (through electromagnetic coupling) act to rotate the solid inner core. This is an important link to establish, as any solid inner core rotation could be detectable using seismology. The dynamics on the tangent cylinder may also cause waves: cylindrical torsional waves and magnetic Rossby waves, both of which have an observational signature.

Most models of the Earth’s core are spherical, and focus on the broad global dynamics. In this project, spanning both geophysics and applied mathematics, we will focus attention at high latitude on how jets and other structures form, and their expected signature within the magnetic field.  The work will involve developing new theory and using numerical high-resolution computational fluid dynamics (CFD) supercomputer models of the core using both the Nek 5000 software package that is based on spectral elements, and OpenFOAM that is based on finite volumes.

The student will learn the theory of fluids within the Earth’s core, but also how to use CFD packages to produce images (and animations) comparable to this engineering application:

(http://inside.hlrs.de/_old/htm/Edition_02_10/article_15.html)

 Project objectives

  1. To model the dynamics within the electrically-conducting fluid of Earth’s core at high-latitude, investigating jet and other flow structures and how they evolve.
  2. To investigate whether a jet can, through electromagnetic coupling, cause the solid inner core to rotate. To identify any waves caused by high-latitude jets.
  3. To compare the magnetic signature of the jet and waves, to the observations from high-resolution satellite measurements of the Earth’s magnetic field.

Project timeline

Year 1: To use the NEK5000 and OpenFOAM CFD packages to model the hydrodynamics (non-magnetic) of a rotating fluid cylinder (as an approximation to the tangent cylinder) containing a horizontal solid disk (modelling the solid inner core). Production of high-quality animations showing, for example, a simulation of the Taylor-Proudman theorem (the movement of the fluid as columnar structures). Investigation of the extension of this model setup to electrically-conducting fluids, and motion with a prescribed background magnetic field whose structure triggers a jet to form.

Year 2: The simulation of dynamics within the northern high-latitude region of Earth’s core, by modelling a cylindrical sub-volume from the spherical core that includes the tangent cylinder. By choosing appropriate background magnetic fields, model the development and evolution of jets and other rapidly evolving structures. Comparison of the jet’s magnetic signature to satellite-observation-derived models of the geomagnetic field.

Year 3: By allowing the solid inner core to freely rotate within the model, investigate whether a jet, through electromagnetic coupling, can cause the inner core to rotate. Identification of any waves (e.g. torsional or magnetic Rossby waves) caused by the jet and their observational signature within the magnetic field.  Comparison of wave motion to satellite observations.

Potential for high impact outcome

The recent discovery of the high-latitude jet was widely publicised in the international media and is one of the most significant deep-Earth discoveries of the Swarm satellites. An explanation of how it arises and how it might change would be of wide interest. A specialised study of the dynamics of the tangent cylinder would complement the many global models being developed (e.g. Schaeffer et al., 2017).

Training

The student will learn both the theory and computational techniques required to model the dynamics of the electrically-conducting fluid of the Earth’s core, and will have access to a broad spectrum of training workshops put on by the Faculty that include an extensive range of workshops in numerical modelling, high-performance computing, through to managing your degree, to preparing for your viva (http://www.emeskillstraining.leeds.ac.uk/).

The student will be a part of the deep Earth research group, a vibrant part of the School of Mathematics and the Institute of Geophysics and Tectonics, comprising staff members, postdocs and PhD students. The deep Earth group has a strong portfolio of international collaborators which the student will benefit from.

Although the project will be based at Leeds, there will be opportunities to attend international conferences (UK, Europe, US and elsewhere), and collaborative visits within Europe.

Requirements

We seek a highly motivated candidate with a strong background in mathematics, physics, computation, geophysics or another highly numerate discipline.

References

Livermore, P. W., Hollerbach, R., & Finlay, C. C. (2017). An accelerating high-latitude jet in Earth’s core. Nature Geoscience, 10(1), 62–68. http://doi.org/10.1038/ngeo2859

Livermore, P. W., & Hollerbach, R. (2012). Successive elimination of shear layers by a hierarchy of constraints in inviscid spherical-shell flows. Journal of Mathematical Physics, 53(7), 073104–19. http://doi.org/10.1063/1.4736990

Schaeffer, N., Jault, D., Nataf, H. C., & Fournier, A. (2017). Turbulent geodynamo simulations: a leap towards Earth’s core. Geophysical Journal International, 211(1), 1–29. http://doi.org/10.1093/gji/ggx265

Hori, K., Jones, C. A., & Teed, R. J. (2015). Slow magnetic Rossby waves in the Earth's core. Geophysical Research Letters, 42(1), 6622–6629. http://doi.org/10.1002/2015GL064733

Codes:

NEK 5000:   https://nek5000.mcs.anl.gov/

OpenFOAM http://www.openfoam.com/

Related undergraduate subjects:

  • Applied mathematics
  • Computing
  • Earth science
  • Geophysical science
  • Geophysics
  • Mathematics
  • Meteorology
  • Physical science
  • Physics