Modelling Thermal Convection of Earth Mantle with Aspect Code

Document Type : Research Article

Authors

1 Corresponding Author, Department of Physics, Faculty of Science, University of Zanjan, Zanjan, Iran. E-mail: nazilaasaadi@znu.ac.ir

2 Department of Physics, Faculty of Science, University of Zanjan, Zanjan, Iran. E-mail: samane.norouzi7@gmail.com

Abstract

The study of mantle convection is one of the most important topics in geodynamics. Mantle convection causes the transfer of internal heat to the cold parts of the Earth, and the effects of this heat transfer are observed as the motion of tectonic plates on the Earth's surface. Earthquakes, volcanism, and mountain building at the plate margins result from the movement of tectonic plates. Although the mantle occupies a large volume of the Earth, there are many fundamental questions about mantle composition, rheology, dynamics, and history. Many of these questions remain unanswered due to our indirect observations of the mantle. A major tool to study mantle dynamics is numerically analyzing mantle convection equations. In this work, we used Aspect -short for Advanced Solver for Problems in Earth's Convection- code to simulate mantle convection. The geometric model used in the simulation is a box of 4200 km by 3000 km. Using this code, we investigated the effect of different Rayleigh numbers on controlling the mantle convection and creating mantle plumes. Results show that the number of mantle plumes increases with increasing Rayleigh number, and the rising mantle plumes become thinner with the Rayleigh number increasing. Finally, we studied the relationship between the Rayleigh number and the Nusselt number (surface heat flux). We conclude that there is a power-law relation between Rayleigh and Nusselt numbers.

Keywords

References

Ballmer, M.D., Ito, G., Wolfe, C.J., & Solomon, S.C. (2013). Double layering of a thermochemical plume in the upper mantle beneath Hawaii. Earth and Planetary Science Letters, 376, 155–164.
Bangerth, W., Dannberg, J., Gassmoller, R., & Heister, T. (2017). ASPECT: Advanced Solver for Problems in Earth's Convection, CIG.
Baumgardner, J.R. (1985). Three-dimensional treatment of convective flow in the Earth's mantle. J. Statis. Phys., 39, 501-11.
Baumgardner, J.R. (1988). Application of supercomputers to 3-d mantle convection. In: Physics of the Planets, ed. S.K. Runcorn, pp. 199-231, New York: Wiley.
Bercovici, D., Schubert, G., Glatzmaier, G.A., & Zebib, A. (1989a). Three-dimensional thermal convection in a spherical shell. J. Fluid Mech., 206, 75-104.
Bercovici, D., Schubert, G., & Glatzmaier, G.A. (1989b). Three-dimensional, spherical models of convection in the Earth's mantle. Science, 244, 950-55.
Bercovici, D., Schubert, G., & Glatzmaier, G.A. (1989c). Influence of heating mode on three-dimensional mantle convection. Geophys. Res. Lett., 16, 617-20.
Bercovici, D., Schubert, G., & Glatzmaier, G.A. (1991a). Three-dimensional convection of an infinite Prandtl number compressible fluid in a basally heated spherical shell. 1. Fluid Mech. 239, 683-719.
Bercovici, D., Schnbert, G., & Glatzmaier, G.A. (1991b). Modal growth and coupling in three-dimensional spherical convection. Geophys. Astrophys. Fluid Dyn., 61, 149-159.
Christensen, U., & Harder, H. (1991). Three dimensional convection with variable viscosity. Geophys. J. Int., 104, 213-26.
Cserepes, L., Rabinowicz, M. and Rosemberg-Borot, C. (1988), Three-dimensional infinite Prandtl number convection in one and two layers and implications for the Earth’s gravity field. Journal of Geophysical Research, 93, 12009–25.
Cserepes, L., & Christensen, U. (1990), Three dimensional convection under drifting plates. Geophys. Res. Lett., 17, 1497-1500.
d’Acremont, E., Leroy, S., & Burov, E.B. (2003). Numerical modelling of a mantle plume: the plume head–lithosphere interaction in the formation of an oceanic large igneous province. Earth and Planetary Science Letters, 206(3), 379–396.
Davies, G.F. (2004). Dynamic Earth: Plates, Plumes and Mantle Convection. Cambridge Univ. Press, Cambridge.
Farnetani, D.G., & Richards, M.A. (1995). Thermal entrainment and melting in mantle plumes. Earth and Planetary Science Letters, 136(3), 251–267.
Gerya, T. (2010). Introduction to Numerical Geodynamic Modelling. Cambridge Univ. Press, Cambridge.
Glatzmaier, G.A. (1988). Numerical simulations of mantle convection: Time-dependent, three- dimensional, compressible spherical shell. Geophys. Astrophys. Fluid Dyn., 43, 223-64.
Glatzmaier, G.A., Schubert, G., & Bercovici, D. (1990). Chaotic, subduction-like down flows in a spherical model of convection in the Earth's mantle. Nature, 347, 274-77.
Hansen, U.,& Ebel, A. (1984). Experiments with a numerical model related to mantle convection: boundary layer behavior of small and large scale flows. Phys. Earth Planet, 374-390.
Heister, T., Dannberg, J., Gassmöller, R., & Bangerth, W. (2017). High accuracy mantle convection simulation through modern numerical methods II: realistic models and problems. Geophys. J. Int., 210(2), 833–851, doi:10.1093/gji/ggx195.
Holmes, A. (1931). Radioactivity and Earth movements. The Geological Society of Glasgow, 18, 559–606.
Houseman, G. (1988). The dependence of convection planform on mode of heating. Nature, 332, 346–9.
Houston, M.H. Jr., & DeBremacker, J.-Cl. (1975). Numerical models of convection in the upper mantle. J. Geophys. Res., 80, 742-51.
Ismail-Zadeh, A., & Tackley, P.J. (2010). Computational Methods for Geodynamics. Cambridge Univ. Press, Cambridge.
Jarvis, G.T. (1984). Time-dependent convection in the Earth’s mantle. Phys. Earth Planet, 305-327.
Kronbichler, M., Heister, T., & Bangerth, W. (2012). High accuracy mantle convection simulation through modern numerical methods. GJI, 12-29.
Korenaga, J. (2003). Energetics of mantle convection and the fate of fossil heat. Geophys. Res, Lett., 1437.
Lin, S.-C., & van Keken, P.E. (2005). Multiple volcanic episodes of flood basalts caused.
by thermochemical mantle plumes. Nature, 436(7048), 250–252.
Lux, R.A., Davies, G.F., & Thomas, J.H. (1979). Moving lithospheric plates and mantle convection. Geophys. J. R. Astron. Soc., 58, 209-28.
Machetel, P., Rabinowicz, M., & Bernardet, P. (1986). Three-dimensional convection in spherical shells, Geophys. Astrophys. Fluid Dyn., 37, 57-84.
Moore, D.R., & Weiss, N.O. (1973). Two-dimensional Rayleigh-Bimard convection. J. Fluid Mech., 58, 289-312.
Morgan, W.J. (1968). Rises, trenches, great faults, and crustal blocks. J. Geophys. Res., 73, 1959–82.
Ogawa, M., Schubert, G., & Zebib, A., (1991). Numerical simulations of 3-D thermal convection of a strongly temperature dependent viscosity fluid. J. Fluid Mech., In press.
Olsen, P. (1987). A comparison of heat transfer laws for mantle convection at very high Rayleigh numbers. Phys. Earth Planet, 153-160.
Parmentier, E.M., & Turcotte, D.L. (1978). Two-dimensional mantle flow beneath a rigid accreting lithosphere. Phys. Earth Planet. Inter., 17, 281-89.
Richter, F.M. (1973). Dynamical models for seafloor spreading. Rev. Geophys. Space Phys., 11, 223-87.
Schubert, G., & Zebib, A. (1980). Thermal convection of an internally heated infinite Prandtl number fluid in a spherical shell. Geophys. Astrophys. Fluid Dyn., I S: 65-90.
Schubert, G., Bercovici, D., & Glatzmaier, G.A. (1990). Mantle dynamics in Mars and Venus: Influence of an immobile lithosphere on three-dimensional mantle convection. J. Geophys. Res., 95, 14, 105-29.
Schubert, G., Turcotte, D.L., & Olson, P. (2004). Mantle Convection in the Earth and Planets. Cambridge Univ. Press, Cambridge.
Sobolev, S.V., Sobolev, A.V., Kuzmin, D.V., Krivolutskaya, N., Petrunin, A.G., Arndt, N., Radko, V.A., & Vasiliev, Y.R. (2011). Linking mantle plumes, large igneous provinces and environmental Catastrophes Nature, 477(7364), 312–316.
Tackley, P.J. (2008). Modelling compressible mantle convection with large viscosity contrasts in a three-dimensional spherical shell using the yin-yang grid. Phys. Earth Planet. Inter., 171(1–4), 7–18.
Torrance, K.E., & Turcotte, D.L. (1971). Thermal convection with large viscosity Variations. Journal of Fluid Mechanics, 47, 113–25.
Travis, B., Olson, P., & Schubert, G. (1990a). The transition from two-dimensional to three-dimensional planforms in Infinite Prandtl number thermal convection. J. Fluid Mech., 216, 71-91.
Travis, B., Weinstein, S., & Olson, P. (1990b), Three-dimensional convection planforms with internal heat generation. Geophys. Res. Lett., 17, 243-46.
Trompert, R.A., & Hansen, U. (1998a). On the Rayleigh number dependence of convection with a strongly temperature-dependent viscosity. Phys. Fluids, 10, 351–360.
Trompert, R., & Hansen, U. (1998b). Mantle convection simulations with rheologies that generate plate-like behavior. Nature, 686-689.
Trubitsyn, V.P., & Evseev, M.N. (2018). Plume Mode of Thermal Convection in the Earth’s Mantle, Izv. Phys. Solid Earth, 838-848.
Turcotte, D.L., & Oxburgh, E.R. (1967). Finite element calculations of very high Rayleigh number thermal convection. J. Fluid Mech., 29-42.
Wolstencroft, M., Davies, D.H., & Daveis, D.R. (2009). Nusselt–Rayleigh number scaling for spherical shell Earth mantle simulation up to a Rayleigh number of 109. Physics of the Earth and Planetary Interiors, 176, 132–141.
Zhong, S.J., Zuber, M.T., Moresi, L., & Gurnis, M. (2000). Role of temperature-dependent viscosity and surface plates in spherical shell models of mantle convection. J. Geophys. Res., 105(B5), 11,063–11,082.
Zhong, S. (2005). Dynamics of thermal plumes in three-dimensional isoviscous thermal convection. GJI, 289-300.
Zhong, S.J., Yuen, D.A., & Moresi, L.N. (2007). Numerical methods in mantle convection. In Bercovici, D. (ed.) Treatise in Geophysics, Volume 7, (editor-in-chief: Gerard Schubert), Elsevier, 227–52.
Zhong, S., McNamara, A., Tan, E., Moresi, E., & Gurnis, M. (2008). A benchmark study on mantle convection in a 3-D spherical shell using CitcomS. Geochemistry, Geophysics, Geosystems, 9(10), Q10, 017.
Journal of the Earth and Space Physics
Volume 48, Issue 4
online publication date: 5 March 2023
March 2023
Pages 99-106

Files

Share

How to cite

Statistics