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Dynamics of mantle convection with realistic material properties

Dr Chris Davies (SEE), Dr Andrew Walker (SEE)

Contact email: c.davies@leeds.ac.uk

Convection in rocky or icy planetary mantles controls the long-term evolution of the terrestrial planets and many of the moons in the solar system. The style of mantle convection is intimately linked to planetary habitability: it determines whether surface material participates in the global-scale dynamics (as on Earth) or remains isolated (as on Venus) and also determines the viability of magnetic field generation in the liquid core. The rich and complex dynamics exhibited by the terrestrial planets arise since the physical properties that characterise mantle material are enormously sensitive to small changes in temperature, pressure and composition. The nonlinear feedbacks between transport properties (e.g. thermal conductivity and viscosity) and flow dynamics are most prevalent in the upper and lower regions of the mantle, the so-called boundary layers, and it is the behaviour in these regions that is largely responsible for the diversity of planetary behaviour and evolution. The overall aim of this project is to quantitatively analyse the boundary layer dynamics of mantle convection using computer simulations that couple fluid dynamics with state-of-the-art transport properties obtained from mineral physics.

Boundary layers are thin regions at the top and bottom of a convecting system where temperature, composition and flow change dramatically in order to meet externally-imposed conditions (Figure 1). These regions are thought to control the efficiency of heat transfer into and out of the mantle and therefore dictate the long-term thermal evolution of terrestrial planets [1]–[3]. There have been extensive efforts to build physical models of heat transfer in mantle boundary layers using results from numerical simulations of varying complexity [4]–[6], but the results are extremely varied and lead to dramatically different predictions when applied to planets.  The discrepancy centres on the treatment of material properties, specifically thermal conductivity and viscosity. Most studies that focus on boundary layer dynamics assume that these properties vary with depth and/or with temperature [6]–[9]. However, the reality is that mantle properties will depend strongly on chemical composition as well as the stable mineral phase at a given location (Figure 2). These dependencies are now being revealed by mineral physics calculations constrained by seismic observations of deep Earth structure. The time is ripe to use this information in fluid dynamical models to elucidate the role of realistic material properties in determining the dynamics and evolution of mantle convection.

Figure 1. Time evolution of temperature (top) and composition (bottom) in an example mantle convection model [10]. Note the remarkable spatial and temporal variations that occur near the lower boundary.

Figure 2. Cartoon illustrating the complex nature of the lowermost mantle [11]. Two large low shear velocity provinces (LLSVP’s) encompass ~30% of the core-mantle boundary (CMB) at the present-day. These regions are thought to be hotter (shown by background colour), chemically distinct from surrounding mantle material and contain small-scale heterogeneity of their own, including the ultra-low velocity zones (ULVZ’s).

The project

You will undertake numerical simulations of mantle convection with spatially-varying thermal conductivity and viscosity. You will use these models to quantify heat transfer and flow dynamics with a view to developing simplified models of the fundamental physics. The first stage is to begin with 2D models and simple parameterizations of the material properties since this is the configuration used by most previous studies. Using the 2D model you will systematically add more complex dependencies between material and thermodynamic properties, approaching the predictions made by mineral physics calculations. This understanding will permit a numerical study of the 3D case where statistical measures of boundary layer behaviour can be compared with observations of the Earth, and boundary layer heat-flux can be used to explore the long-term evolution of the terrestrial planets.

Training environment

You will receive training in skills tailored to the project but also useful to help secure a future career as a research scientist in academia or elsewhere. To allow you to complete the project you will learn the principles and practice of computational fluid dynamics with focus on the specifics pertaining to mantle convection. You will need to understand the physics of convection and become skilled in some of the mathematical and computational techniques needed to analyse the simulation results. These advanced methods have obvious utility in a wide range of academic and industrial settings such as the automotive and aerospace industries, climate and ocean simulation, and finance. You will also learn how to confidently develop software for the analysis of results and to use large-scale high performance computing resources such as those available at the University of Leeds and the ARCHER national capability computing facility. Alongside the transferable skills in communication and management this can open a wide range of career pathways. These skills will be developed by a mixture of hands on experience, attending external training courses, and by participating in the Leeds – York NERC doctoral training partnership programme

Student profile

You will have a good first degree in the physical or mathematical sciences (e.g. physics, geophysics, chemistry, mathematics or computer science) that included modules on fluid dynamics or Earth dynamics. The ideal candidate will also have experience of basic scientific programming and computation possibly derived from the completion of an undergraduate research project.

References and further reading

[1]      J. Korenaga, “Urey ratio and the structure and evolution of Earth’s mantle,” Rev. Geophys., vol. 46, p. 2007RG000241, 2008.

[2]      C. Jaupart, S. Labrosse, and J. C. Mareschal, “Temperatures, Heat and Energy in the Mantle of the Earth,” Treatise Geophys., vol. 7, no. February, pp. 253–303, 2007.

[3]      P. Driscoll and D. Bercovici, “On the thermal and magnetic histories of Earth and Venus: Influences of melting, radioactivity, and conductivity,” Phys. Earth Planet. Int., vol. 236, pp. 36–51, 2014.

[4]      C. Grigne and S. Labrosse, “Convective heat transfer as a function of wavelength : Implications for the cooling of the Earth,” J. Geophys. Res., vol. 110, pp. 1–16, 2005.

[5]      G. F. Davies, “Mantle regulation of core cooling: A geodynamo without core radioactivity?,” Phys. Earth Planet. Int., vol. 160, pp. 215–229, 2007.

[6]      J. Korenaga, “Scaling of stagnant-lid convection with Arrhenius rheology and the effects of mantle melting,” Geophys. J. Int., pp. 154–170, 2009.

[7]      L. Moresi and V. Solomatov, “Mantle convection with a brittle lithosphere : thoughts on the global tectonic styles of the Earth and Venus,” J. Geophys. Res., pp. 669–682, 1998.

[8]      S. A. Hunt, D. R. Davies, A. M. Walker, R. J. Mccormack, A. S. Wills, D. P. Dobson, and L. Li, “On the increase in thermal diffusivity caused by the perovskite to post-perovskite phase transition and its implications for mantle dynamics,” vol. 320, pp. 96–103, 2012.

[9]      N. Tosi, D. A. Yuen, N. De Koker, and R. M. Wentzcovitch, “Mantle dynamics with pressure- and temperature-dependent thermal expansivity and conductivity,” Phys. Earth Planet. Inter., vol. 217, pp. 48–58, 2013.

[10]    T. Nakagawa and P. J. Tackley, “Implications of high core thermal conductivity on {E}arth’s coupled mantle and core evolution,” Geophys. Res. Lett., vol. 40, pp. 1–5, 2013.

[11]    E. J. Garnero, A. K. McNamara, and S.-H. Shim, “Continent-sized anomalous zones with low seismic velocity at the base of Earth’s mantle,” Nat. Geosci., vol. 9, no. June, p. 481, 2016.

 

Related undergraduate subjects:

  • Chemistry
  • Computer science
  • Mathematics
  • Physics