Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-23T12:12:43.981Z Has data issue: false hasContentIssue false
  • English
  • Français

An insulating plate drifting over a thermally convecting fluid: the effect of plate size on plate motion, coupling modes and flow structure

Published online by Cambridge University Press:  06 April 2021

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, Wuhan430074, PR China
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

As a simplified model to study continental drift over the convective mantle, a thermally insulating plate is introduced to float freely over a bottom-heated thermally convecting fluid. Results of numerical simulations reveal that plate size plays an essential role in plate motion and the flow--structure interaction. The insulating plate exerts a thermal blanket effect on the flow underneath by locally accumulating heat and modifying the flow structure. As the thermal blanket effect enhances with plate size, the plate becomes increasingly capable of overcoming the impeding flow and continue its movement. As plate size increases, plate motion transitions from long durations of stagnancy over cold downwelling, to short-term stagnancy over newly formed hot upwelling and eventually to a unidirectionally moving mode (UMM) with no stagnancy. For the UMM, a hot ‘propelling plume’ is always observed near the trailing edge of the plate, moving with the plate and generating a convection cell that propels the plate. However, it moves toward the plate centre as the plate extends to cover almost the entire flow domain. The average plate speed is revealed to be proportional to the multiplication of the average plume distance and the open surface area. The critical plate sizes for the UMM predicted by a simplified model agree well with results of the full numerical simulations. Moreover, spectra of the streamfunction field show that an increase in plate size induces longer-wavelength structure, and an increase in plate speed is accompanied by an enhanced dominance of longer-wavelength structure.

JFM classification

Geophysical and Geological Flows: Mantle convection Nonlinear Dynamical Systems: Low-dimensional models
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 916 , 10 June 2021 , A18
Check for updates
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

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
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, A.M. & Baumgardner, J.R. 1997 A sensitivity study of three-dimensional 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
Burke, 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
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
Goluskin, D., Johnston, H., Flierl, G.R. & Spiegel, E.A. 2014 Convectively driven shear and decreases heat flux. J. Fluid Mech. 759, 360–385.CrossRefGoogle 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
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
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., 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., 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
Lowman, J.P. & Jarvis, G.T. 1995 Mantle convection models of continental collision and breakup incorporating finite thickness plates. Phys. Earth Planet. Intl 88, 53–68.CrossRefGoogle Scholar
Lowman, J., 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., 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
Patankar, S.V. 1980 Numerical Heat Transfer and Fluid Flow. Taylor & Francis.Google 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
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
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
Sutherland, R. 1999 Basement geology and tectonic development of the greater New Zealand region: an interpretation from regional magnetic data. Tectonophys. 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. & Schubert, G. 2002 Geodynamics. Cambridge University Press.CrossRefGoogle Scholar
Wang, Q., Chong, K.L., Stevens, R.J.A.M., Verzicco, R. & Lohse, D. 2020 From zonal flow to convection rolls in Rayleigh–Bénard convection with free-slip plates. J. Fluid Mech. 905, A21.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
Whitehead, J.A., Shea, E. & Behn, M.D. 2011 Cellular convection in a chamber with a warm surface raft. Phys. Fluids 23, 104103.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