Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-30T20:36:52.998Z Has data issue: false hasContentIssue false
  • English
  • Français

Convection in an internally heated stratified heterogeneous reservoir

Published online by Cambridge University Press:  07 May 2019

Angela Limare Open the ORCID record for Angela Limare [Opens in a new window] ,
Claude Jaupart ,
Edouard Kaminski ,
Loic Fourel  and
Cinzia G. Farnetani
Angela Limare*
Affiliation:
Institut de Physique du Globe, Université de Paris, CNRS, F-75005 Paris, France
Claude Jaupart
Affiliation:
Institut de Physique du Globe, Université de Paris, CNRS, F-75005 Paris, France
Edouard Kaminski
Affiliation:
Institut de Physique du Globe, Université de Paris, CNRS, F-75005 Paris, France
Loic Fourel
Affiliation:
Solid Earth Geology Team, Geological Survey of Norway (NGU), Trondheim NO-7491, Norway
Cinzia G. Farnetani
Affiliation:
Institut de Physique du Globe, Université de Paris, CNRS, F-75005 Paris, France
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The Earth’s mantle is chemically heterogeneous and probably includes primordial material that has not been affected by melting and attendant depletion of heat-producing radioactive elements. One consequence is that mantle internal heat sources are not distributed uniformly. Convection induces mixing, such that the flow pattern, the heat source distribution and the thermal structure are continuously evolving. These phenomena are studied in the laboratory using a novel microwave-based experimental set-up for convection in internally heated systems. We follow the development of convection and mixing in an initially stratified fluid made of two layers with different physical properties and heat source concentrations lying above an adiabatic base. For relevance to the Earth’s mantle, the upper layer is thicker and depleted in heat sources compared to the lower one. The thermal structure tends towards that of a homogeneous fluid with a well-defined time constant that scales with $Ra_{H}^{-1/4}$, where $Ra_{H}$ is the Rayleigh–Roberts number for the homogenized fluid. We identified two convection regimes. In the dome regime, large domes of lower fluid protrude into the upper layer and remain stable for long time intervals. In the stratified regime, cusp-like upwellings develop at the edges of large basins in the lower layer. Due to mixing, the volume of lower fluid decreases to zero over a finite time. Empirical scaling laws for the duration of mixing and for the peak temperature difference between the two fluids are derived and allow extrapolation to planetary mantles.

JFM classification

Geophysical and Geological Flows: Mantle convection
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 870 , 10 July 2019 , pp. 67 - 105
Copyright
© 2019 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

Bloomfield, V. A. & Dewan, R. K. 1971 Viscosity of liquid mixtures. J. Phys. Chem. 75 (20), 3113–3119.Google Scholar
Dadarlat, D. & Neamtu, C. 2009 High accuracy photopyroelectric calorimetry of liquids. Acta Chim. Slov. 56, 225–236.Google Scholar
Davaille, A. 1999a Simultaneous generation of hotspots and superswells by convection in a heterogeneous planetary mantle. Nature 402, 756–760.Google Scholar
Davaille, A. 1999b Two-layer thermal convection in miscible viscous fluids. J. Fluid Mech. 379, 223–253.Google Scholar
Davaille, A., Girard, F. & Le Bars, M. 2002 How to anchor hotspots in a convecting mantle? Earth Planet. Sci. Lett. 203 (2), 621–634.Google Scholar
Davaille, A., Le Bars, M. & Carbonne, C. 2003 Thermal convection in a heterogeneous mantle. C. R. Geosci. 335 (1), 141–156.Google Scholar
Davaille, A. & Limare, A. 2015 7.03 - Laboratory studies of mantle convection. In Treatise on Geophysics, 2nd edn. (ed. Schubert, G.), pp. 73–144. Elsevier.Google Scholar
Deschamps, F., Cobden, L. & Tackley, P. J. 2012 The primitive nature of large low shear-wave velocity provinces. Earth Planet. Sci. Lett. 349, 198–208.Google Scholar
Deschamps, F. & Tackley, P. J. 2008 Searching for models of thermochemical convection that explain probabilistic tomography. I. Principles and influence of rheological parameters. Phys. Earth Planet. Inter. 171, 357–373.Google Scholar
Deschamps, F. & Tackley, P. J. 2009 Searching for models of thermochemical convection that explain probabilistic tomography. II. Influence of physical and compositional parameters. Phys. Earth Planet. Inter. 176, 1–18.Google Scholar
England, P., Molnar, P. & Richter, F. 2007 John Perry’s neglected critique of Kelvin’s age for the Earth: a missed opportunity in geodynamics. GSA Today 17 (1), 4–9.Google Scholar
Fourel, L., Limare, A., Jaupart, C., Surducan, E., Farnetani, C. G., Kaminski, E. C., Neamtu, C. & Surducan, V. 2017 The Earth’s mantle in a microwave oven: thermal convection driven by a heterogeneous distribution of heat sources. Exp. Fluids 58 (8), 90.Google Scholar
French, S. W. & Romanowicz, B. 2015 Broad plumes rooted at the base of the Earth’s mantle beneath major hotspots. Nature 525, 95–113.Google Scholar
Gale, A., Dalton, C. A., Langmuir, C. H., Su, Y. & Schilling, J.-G. 2013 The mean composition of ocean ridge basalts. Geochem. Geophys. Geosyst. 14 (3), 489–518.Google Scholar
Garnero, E. J. & Helmberger, D. V. 1996 Seismic detection of a thin laterally varying boundary layer at the base of the mantle beneath the central-pacific. Geophys. Res. Lett. 23 (9), 977–980.Google Scholar
Garnero, E. J., McNamara, A. K. & Shim, S.-H. 2016 Continent-sized anomalous zones with low seismic velocity at the base of Earth’s mantle. Nature Geosci. 9, 481–489.Google Scholar
Goluskin, D. 2016 Internally Heated Convection and Rayleigh-Bénard Convection. Springer.Google Scholar
Herzberg, C., Condie, K. & Korenaga, J. 2010 Thermal history of the Earth and its petrological expression. Earth Planet. Sci. Lett. 292, 79–88.Google Scholar
van der Hilst, R. D. & Kárason, H. 1999 Compositional heterogeneity in the bottom 1000 kilometers of earth’s mantle: toward a hybrid convection model. Science 283 (5409), 1885–1888.Google Scholar
Hofmann, A. W. 2003 Sampling mantle heterogeneity through oceanic basalts: isotopes and trace elements. Treatise Geochem. 2, 568.Google Scholar
Jackson, M. G. & Carlson, R. W. 2012 Homogeneous superchondritic 142Nd/144Nd in the mid-ocean ridge basalt and ocean island basalt mantle. Geochem. Geophys. Geosyst. 13 (6), Q06011.Google Scholar
Jaupart, C., Labrosse, S., Lucazeau, F. & Mareschal, J.-C.2015 Temperatures, heat and energy in the mantle of the Earth. In Treatise of Geophysics, 2nd edn. (ed. G. Schubert), vol. 7, pp. 223–270. Elsevier.Google Scholar
Javoy, M. & Kaminski, E. 2014 Earth’s Uranium and Thorium content and geoneutrinos fluxes based on enstatite chondrites. Earth Planet. Sci. Lett. 407, 1–8.Google Scholar
Jellinek, A. M. & Manga, M. 2002 The influence of a chemical boundary layer on the fixity, spacing and lifetime of mantle plumes. Nature 418, 760–763.Google Scholar
Katsaros, K. B., Liu, W. T., Businger, J. A. & Tillman, J. E. 1977 Heat thermal structure in the interfacial boundary layer measured in an open tank of water in turbulent free convection. J. Fluid Mech. 83, 311–335.Google Scholar
Kulacki, F. A. & Goldstein, R. J. 1972 Thermal convection in a horizontal fluid layer with volumetric heat sources. J. Fluid Mech. 271, 271–287.Google Scholar
Labrosse, S. & Jaupart, C. 2007 Thermal evolution of the earth: secular changes and fluctuations of plate characteristics. Earth Planet. Sci. Lett. 260 (3), 465–481.Google Scholar
Le Bars, M. & Davaille, A. 2004a Large interface deformation in two-layer thermal convection of miscible viscous fluids. J. Fluid Mech. 499, 75–110.Google Scholar
Le Bars, M. & Davaille, A. 2004b Whole layer convection in a heterogeneous planetary mantle. J. Geophys. Res. 109, B03403.Google Scholar
Lepot, S., Aumaître, S. & Gallet, B. 2018 Radiative heating achieves the ultimate regime of thermal convection. Proc. Natl Acad. Sci. USA 115 (36), 8937–8941.Google Scholar
Li, M., McNamara, A. K., Garnero, E. J. & Yu, S. 2017 Compositionally-distinct ultra-low velocity zones on earths core-mantle boundary. Nature Commun. 8 (1), 177.Google Scholar
Limare, A., Vilella, K., Di Giuseppe, E., Farnetani, C., Kaminski, E., Surducan, E., Surducan, V., Neamtu, C., Fourel, L. & Jaupart, C. 2015 Microwave-heating laboratory experiments for planetary mantle convection. J. Fluid Mech. 1565, 14–18.Google Scholar
McKenzie, D. & Richter, F. M. 1981 Parametrized thermal convection in a layered region and the thermal history of the Earth. J. Geophys. Res. 86 (B12), 11667–11680.Google Scholar
Montelli, R., Nolet, G., Dahlen, F. A. & Masters, G. 2006 A catalogue of deep mantle plumes: new results from finite-frequency tomography. Geochem. Geophys. Geosyst. 7 (11), Q11007.Google Scholar
Nakagawa, T. & Tackley, P. J. 2005 Deep mantle heat flow and thermal evolution of the Earth’s core in thermochemical multiphase models of mantle convection. Geochem. Geophys. Geosyst. 6 (8), Q08003.Google Scholar
Nakagawa, T. & Tackley, P. J. 2014 Influence of combined primordial layering and recycled MORB on the coupled thermal evolution of Earth’s mantle and core. Geochem. Geophys. Geosyst. 15, 619–633.Google Scholar
Olson, P. 1984 An experimental approach to thermal convection in a two-layered mantle. J. Geophys. Res. 89 (B13), 11293–11301.Google Scholar
Olson, P. & Kincaid, C. 1991 Experiments on the interaction of thermal convection and compositional layering at the base of the mantle. J. Geophys. Res. 96 (B3), 4347–4354.Google Scholar
Parmentier, E. M., Sotin, C. & Travis, B. J. 1994 Turbulent 3-D thermal convection in an infinite Prandtl number, volumetrically heated fluid: implication for mantle dynamics. Geophys. J. Intl 116, 241–251.Google Scholar
Richter, F. M. & McKenzie, D. P. 1981 On some consequences and possible causes of layered mantle convection. J. Geophys. Res. 86 (B7), 6133–6142.Google Scholar
Ritsema, J., Deuss, A., Van Heijst, H. J. & Woodhouse, J. H. 2011 S40RTS: a degree-40 shear-velocity model for the mantle from new rayleigh wave dispersion, teleseismic traveltime and normal-mode splitting function measurements. Geophys. J. Intl 184 (3), 1223–1236.Google Scholar
Roberts, P. H. 1967 Convection in horizontal layers with internal heat generation. Theory. J. Fluid Mech. 30, 33–49.Google Scholar
Schubert, G., Turcotte, D. & Olson, P. 2001 Mantle Convection in the Earth and Planets. Cambridge University Press.Google Scholar
Surducan, E., Surducan, V., Limare, A., Neamtu, C. & di Giuseppe, E. 2014 Microwave heating device performing internal-heating convection experiments, applied to Earth’s mantle dynamics. Rev. Sci. Instrum. 85, 124702.Google Scholar
Torsvik, T. H., Smethurst, M. A., Burke, K. & Steinberger, B. 2006 Large igneous provinces generated from the margins of the large low-velocity provinces in the deep mantle. Geophys. J. Intl 167 (3), 1447–1460.Google Scholar
Townsend, A. A. 1964 Natural convection in water over an ice surface. Q. J. R. Meteorol. Soc. 90, 248–259.Google Scholar
Turcotte, D. L., Paul, D. & White, W. M. 2001 Thorium-uranium systematics require layered mantle convection. J. Geophys. Res. 106 (B3), 4265–4276.Google Scholar
Turner, J. S. 1974 Double-diffusive phenomena. Annu. Rev. Fluid Mech. 6 (1), 37–54.Google Scholar
Vilella, K., Limare, A., Jaupart, C., Farnetani, C., Fourel, L. & Kaminski, E. 2018 Fundamentals of laminar free convection in internally heated fluids at values of the Rayleigh-Roberts number up to 109 . J. Fluid Mech. 846, 966–998.Google Scholar

Limare et al. supplementary movie 1

Evolution of the lower layer topography in a ‘dome’ experiment (RaH=1.3 106, Bcond=0.9). Spatial dimensions are in mm.

Download Limare et al. supplementary movie 1(Video)
Video 824.9 KB

Limare et al. supplementary movie 2

Evolution of the lower layer topography in a ‘stratified’ experiment (RaH=5.9 105, Bcond=1.1). Spatial dimensions are in mm.

Download Limare et al. supplementary movie 2(Video)
Video 775.1 KB
Supplementary material: PDF

Limare et al. supplementary material

Supplementary figures and tables

Download Limare et al. supplementary material(PDF)
PDF 230.1 KB