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An insulating plate drifting over a thermally convecting fluid: the thermal blanket effect on plume motion and the emergence of a unidirectionally moving mode

Published online by Cambridge University Press:  20 May 2022

Yadan Mao Open the ORCID record for Yadan Mao [Opens in a new window]
Yadan Mao*
Affiliation:
Hubei Subsurface Multi-scale Imaging Key Laboratory, Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan 430074, PR China
*
†Email address for correspondence: [email protected]
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Abstract

Floating rather stably above the convective mantle, continents exert a thermal blanket effect on the mantle by locally accumulating heat and altering the flow structure, which in turn affect continent motion. This thermal-mechanic feedback has been captured by a simplified model―a thermally insulating plate floating freely over a bottom-heated convecting fluid. Previous studies have revealed that, as plate size increases, plate motion transitions from long-term stagnancy over cold downwelling to short-term stagnancy over hot upwelling, termed stagnant modes (SMs) I and II, respectively, and eventually to a unidirectionally moving mode (UMM) with no stagnancy. During SM I/II, the adjacent hot/cold plumes are observed to move toward/away from the plate. The present study quantifies these plume motions through analysis on a partially insulated loop model established for SM I and SM II, respectively. The model predictions are well verified by results of numerical simulation. Moreover, the dominant frequency of plate speed is shown to increase linearly with plate size, with an abrupt jump as the coupling mode transitions from SM I to SM II. This suggests that the enhanced thermal blanket effect with plate size enables an increasingly fast feedback between the slowdown of a plate and the strengthening of hot upwelling which boosts plate motion. When plate motion is boosted before it stops, the UMM emerges. The predicted critical plate size for the UMM is well validated by simulation results. Geological implications of the results for continent motion, continent–mantle coupling and particularly the migration of plume and subduction sites are discussed.

JFM classification

Geophysical and Geological Flows: Mantle convection Convection: Plumes/thermals
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 942 , 10 July 2022 , A25
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

Acton, G.D. 1999 Apparent polar wander of India since the Cretaceous with implications for regional tectonics and true polar wander. Mem. Geol. Soc. India 44, 129–175.Google Scholar
Ahlers, G., Grossmann, S. & Lohse, D. 2009 Heat transfer and large scale dynamics in turbulent Rayleigh–Bénard convection. Rev. Mod. Phys. 81, 503–537.CrossRefGoogle Scholar
Argus, D.F., Gordon, R.G. & DeMets, C. 2011 Geologically current motion of 56 plates relative to the no-net-rotation reference frame. Geochem. Geophys. Geosyst. 12, Q11001.CrossRefGoogle Scholar
Bunge, H.-P. & Richards, M.A. 1996 The origin of large scale structure in mantle convection:effects of plate motions and viscosity stratification. Geophys. Res. Lett. 23, 2987–2990.CrossRefGoogle Scholar
Bunge, H.-P., Richards, M.A. & Baumgardner, J.-R. 1996 Effect of depth-dependent viscosity on the planform of mantle convection. Nature 379, 436–438.CrossRefGoogle Scholar
Bunge, H.-P., Richards, M.A. & Baumgardner, J.R. 1997 A sensitivity study of threedimensional spherical mantle convection at 108 Rayleigh number: effects of depth-dependent viscosity, heating mode, and an endothermic phase change. J. Geophys. Res. 102, 11991–12007.CrossRefGoogle Scholar
Burk, K. & Torsvik, T.H. 2004 Derivation of large Igneous provinces of the past 200 million years from long-term heterogeneities in the deep mantle. Earth Planet. Sci. Lett. 227, 531–538.CrossRefGoogle Scholar
Cande, S.C. & Stock, J.M. 2004 Pacific-Antarctic-Australia motion and the formation of the Macquarie plate. Geophys. J. Intl 157, 399–414.CrossRefGoogle Scholar
Chu, T.Y. & Goldstein, R.J. 1973 Turbulent convection in a horizontal layer of water. J. Fluid Mech. 60, 141–159.CrossRefGoogle Scholar
Coltice, N., Bertrand, H., Rey, P., Jourdan, F., Phillips, B.R. & Ricard, Y. 2009 Global warming of the mantle beneath continents back to the Archaean. Gondwana Res. 15, 254–266.CrossRefGoogle Scholar
Coltice, N., Phillips, B.R., Bertrand, H., Ricard, Y. & Rey, P. 2007 Global warming of the mantle at the origin of flood basalts over supercontinents. Geology 35, 391–394.CrossRefGoogle Scholar
Cooper, C.M., Moresi, L.-N. & Lenardic, A. 2013 Effects of continental configuration on mantle heat loss. Geophys. Res. Lett. 40, 2647–2651.CrossRefGoogle Scholar
DeMets, C., Gordon, R.G., Argus, D.F. & Stein, S. 1990 Current plate motions. Geophys. J. Intl 21, 2191–2194.Google Scholar
Ebinger, C.J. & Sleep, N.H. 1998 Cenozoic magmatism throughout east Africa resulting from impact of a single plume. Nature 395, 788–791.CrossRefGoogle Scholar
Elder, J. 1967 Convective self-propulsion of continents. Nature 214, 657–750.CrossRefGoogle Scholar
Gable, C.W., O'Connell, R.J. & Travis, B.J. 1991 Convection in three dimensions with surface plates: generation of toroidal flow. J. Geophys. Res. 96, 8391–8405.CrossRefGoogle Scholar
Gait, A.D. & Lowman, J.P. 2007 Time-dependence in mantle convection models featuring dynamically evolving plates. Geophys. J. Intl 171, 463–477.CrossRefGoogle Scholar
Griffiths, R.W. 1986 Thermals in extremely viscous fluids, including the effects of temperature-dependent viscosity. J. Fluid Mech. 166, 115–138.CrossRefGoogle Scholar
Grigné, C., Labrosse, S. & Tackley, P.J. 2005 Convective heat transfer as a function of wavelength: implications for the cooling of the Earth. J. Geophys. Res. 110, B03409.Google Scholar
Grigné, C., Labrosse, S. & Tackley, P.J. 2007 a Convection under a lid of finite conductivity in wide aspect ratio models: effect of continents on the wavelength of mantle flow. J. Geophysic. Res. 112, B08403.Google Scholar
Grigné, C., Labrosse, S. & Tackley, P.J. 2007 b Convection under a lid of finite conductivity: heatflux scaling and application to continents. J. Geophysic. Res. 112, B08402.Google Scholar
Guillou, L. & Jaupart, S. 1995 On the effect of continents on mantle convection. J. Geophys. Res. 100 (24), 217–24.Google Scholar
Gurnis, M. 1988 Large-scale mantle convection and aggregation and dispersal of supercontinents. Nature 313, 541–546.Google Scholar
Gurnis, M. & Zhong, S. 1991 Generation of long wavelength heterogeneity in the mantle by the dynamic interaction between plates and convection. Geophys. Res. Lett. 18, 581–584.CrossRefGoogle Scholar
Heron, P. & Lowman, J.P. 2011 The effects of supercontinent size and thermal insulation on the formation of mantle plumes. Tectonophysics 510, 28–38.CrossRefGoogle Scholar
Hess, H.H. 1962 History of ocean basin. In Petrologic Studies: A Volume to Honor A.F. Buddington (ed. A.E.J. Engel, H.L. James & B.F. Leonard), pp. 599–620. Geological Society of America.CrossRefGoogle Scholar
Höink, T. & Lenardic, A. 2008 Three-dimensional mantle convection simulations with a low-viscosity asthenosphere and the relationship between heat flow and the horizontal length scale of convection. Geophys. Res. Lett. 35, L10304.CrossRefGoogle Scholar
Holmes, A. 1931 Radioactivity and earth movements. Trans. Geol. Soc. Glasg. 18, 559–606.CrossRefGoogle Scholar
Honda, S., Yoshida, M., Ootorii, S. & Iwase, Y. 2000 The timescales of plume generation caused by continental aggregation. Earth Planet. Sci. Lett. 176, 31–43.CrossRefGoogle Scholar
Howard, L.N. 1966 Convection at high Rayleigh number. In Proceedings of the 11th International Congress of Applied Mechanics (ed. H. Görtler). Springer.CrossRefGoogle Scholar
Howard, L.N., Malkus, W.V.R. & Whitehead, J.A. 1970 Self-convection of floating heat sources: a model for continental drift. Geophys. Fluid Dyn. 1, 123–142.CrossRefGoogle Scholar
Huang, J.M., Zhong, J.-Q., Zhang, J. & Laurent, M. 2018 Stochastic dynamics of fluid-structure interaction in turbulent thermal convection. J. Fluid Mech. 854, R5.CrossRefGoogle Scholar
Kao, H. & Rau, R.-J. 1999 Detailed structures of the subducted Philippine Sea plate beneath northeast Taiwan: a new type of double seismic zone. J. Geophys. Res. 104, 1015–1033.CrossRefGoogle Scholar
Lenardic, A. & Moresi, L. 2001 Heat flow scaling for mantle convection below a conducting lid: resolving seemingly inconsistent modeling results regarding continental heat flow. Geophys. Res. Lett. 28, 1311–1314.CrossRefGoogle Scholar
Lenardic, A., Moresi, L., Jellinek, A.M. & Manga, M. 2005 Continental insulation, mantle cooling, and the surface area of oceans and continents. Earth Planet. Sci. Lett. 234, 317–333.CrossRefGoogle Scholar
Lenardic, A., Richards, M.A. & Busse, F.H. 2006 Depth-dependent rheology and the horizontal length scale of mantle convection. J. Geophys. Res. 111, B07404.Google Scholar
Leonard, B.P. 1979 A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comput. Meth. Appl. Mech. Engng 19, 59–98.CrossRefGoogle Scholar
Lithgow-Bertelloni, C. & Silver, P.G. 1998 Dynamic topography, plate driving forces and the African superswell. Nature 395, 296–272.CrossRefGoogle Scholar
Lowman, J.P. & Gable, C.W. 1999 Thermal evolution of the mantle following continental aggregation in 3D convection models. Geophys. Res. Lett. 26, 2649–2652.CrossRefGoogle Scholar
Lowman, J.P. & Jarvis, G.T. 1993 Mantle convection flow reversals due to continental collisions. Geophys. Res. Lett. 20, 2087–2090.CrossRefGoogle Scholar
Lowman, J.P. & Jarvis, G.T. 1995 Mantle convection models of continental collision and breakup incorporating finite thickness plates. Phys. Earth Planet. Inter. 88, 53–68.CrossRefGoogle Scholar
Lowman, J.P., King, S.D. & Gable, C.W. 2001 The influence of tectonic plates on mantle convection patterns, temperature and heat flow. Geophys. J. Intl 146, 619–636.CrossRefGoogle Scholar
Mao, Y. 2021 An insulating plate drifting over a thermally convecting fluid: the effect of plate size on plate motion, coupling modes and flow structure. J. Fluid Mech. 916, A18.CrossRefGoogle Scholar
Mao, Y., Lei, C. & Patterson, J.C. 2009 Unsteady natural convection in a triangular enclosure induced by absorption of radiation - a revisit by improved scaling analysis. J. Fluid Mech. 622, 75–102.CrossRefGoogle Scholar
Mao, Y., Lei, C. & Patterson, J.C. 2010 Unsteady near-shore natural convection induced by surface cooling. J. Fluid Mech. 642, 213–233.CrossRefGoogle Scholar
Mao, Y., Zhong, J.-Q. & Zhang, J. 2019 The dynamics of an insulating plate over a thermally convecting fluid and its implication for continent movement over convective mantle. J. Fluid Mech. 868, 286–315.CrossRefGoogle Scholar
Monnereau, M. & Quéré, S. 2001 Spherical shell models of mantle convection with tectonic plates. Earth Planet. Sci. Lett. 184, 575–587.CrossRefGoogle Scholar
O'Neill, C., Lenardic, A., Jellinek, A.M. & Moresi, L. 2009 Influence of supercontinents on deep mantle flow. Gondwana Res. 15, 276–287.CrossRefGoogle Scholar
Patankar, S.V. 1980 Numerical Heat Transfer and Fluid Flow. Taylor & Francis.Google Scholar
Peirce, J.W. 1978 The northward motion of India since the late Cretaceous. Geophys. J. R. Astron. Soc. 52, 277–311.CrossRefGoogle Scholar
Phillips, B.R. & Bunge, H.-P. 2005 Heterogeneity and time dependence in 3D spherical mantle convection models with continental drift. Earth Planet. Sci. Lett. 233, 121–135.CrossRefGoogle Scholar
Pollack, H.N., Hurter, S.J. & Johnson, J.R. 1993 Heat flow from the earth's interior: analysis of the global data set. Rev. Geophys. 31, 267–280.CrossRefGoogle Scholar
Puster, P., Hager, B.H. & Jordan, T.H. 1995 Mantle convection experiments with evolving plates. Geophys. Res. Lett. 22, 2223–2226.CrossRefGoogle Scholar
Ritsema, J., van Heijst, H.J. & Woodhouse, J.H. 1999 Complex shear wave velocity structure imaged beneath Africa and Iceland. Science 286, 1925–1928.CrossRefGoogle ScholarPubMed
Schult, F.R. & Gordon, R.G. 1984 Root Mean square velocities of the continents with respect to the hot spots since the early Jurassic. J. Geophys. Res. 89, 1789–1800.CrossRefGoogle Scholar
Shiomi, K., Sato, H. & Obara, K. 2004 Configuration of subducting Philippine Sea plate beneath southwest Japan revealed from receiver function analysis based on the multivariate autoregressive model. J. Geophys. Res. 109, B04308.Google Scholar
Sparrow, E.M., Husar, R.B. & Goldstein, R.J. 1970 Observations and other characteristics of thermals. J. Fluid Mech. 41, 793–800.CrossRefGoogle Scholar
Suggate, R.P., Stevens, G.R. & te Punga, M.T. 1978 The Geology of New Zealand. Department of Scientific and Industrial Research.Google Scholar
Sutherland, R. 1999 Basement geology and tectonic development of the greater New Zealand region: an interpretation from regional magnetic data. Tectonophysics 308, 341–362.CrossRefGoogle Scholar
Tackley, P.J. 1996 On the ability of phase transitions and viscosity layering to induce long wavelength heterogeneity in the mantle. Geophys. Res. Lett. 23, 1985–1988.CrossRefGoogle Scholar
Torsvik, T.H., Burke, K., Steinberger, B., Webb, S.J. & Ashwal, L.D. 2010 Diamonds sampled by plumes from the core-mantle boundary. Nature 466, 352–355.CrossRefGoogle ScholarPubMed
Torsvik, T.H., Steinberger, B., Cocks, L.R.M. & Burke, K. 2008 Longitude: linking earth's ancient surface to its deep interior. Earth Planet. Sci. Lett. 276, 273–282.CrossRefGoogle Scholar
Turcotte, D. & Oxburgh, E. 1967 Finite amplitude convection cells and continental drift. J. Fluid Mech. 28, 29–42.CrossRefGoogle Scholar
Turcotte, D. & Schubert, G. 2002 Geodynamics. Cambridge University Press.CrossRefGoogle Scholar
Whitehead, J.A. 1972 Moving heaters as a model of continental drift. Phys. Earth Planet. Intl 5, 199–212.CrossRefGoogle Scholar
Whitehead, J.A. & Behn, M.D. 2015 The continental drift convection cell. Geophys. Res. Lett. 42, 4301–4308.CrossRefGoogle Scholar
Zhang, J. & Libchaber, A. 2000 Periodic boundary motion in thermal turbulence. Phys. Rev. Lett. 84, 4361–4364.CrossRefGoogle ScholarPubMed
Zhong, S. & Gurnis, M. 1993 Dynamic feedback between a continent like raft and thermal convection. J. Geophys. Res. 98, 12219–12232.CrossRefGoogle Scholar
Zhong, J.-Q. & Zhang, J. 2005 Thermal convection with a freely moving top boundary. Phy. Fluids 17, 115105.CrossRefGoogle Scholar
Zhong, J.-Q. & Zhang, J. 2007 a Dynamical states of a mobile heat blanket on a thermally convecting fluid. Phys. Rev. E 75, 055301.CrossRefGoogle ScholarPubMed
Zhong, J.-Q. & Zhang, J. 2007 b Modeling the dynamics of a free boundary on turbulent thermal convection. Phys. Rev. E 76, 016307.CrossRefGoogle ScholarPubMed
Zhong, S., 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, 11063–11082.CrossRefGoogle Scholar