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Sheet-like and plume-like thermal flow in a spherical convection experiment performed under microgravity

  • B. Futterer (a1) (a2), A. Krebs (a1), A.-C. Plesa (a3), F. Zaussinger (a1), R. Hollerbach (a4), D. Breuer (a3) and C. Egbers (a1)...


We introduce, in spherical geometry, experiments on electro-hydrodynamic driven Rayleigh–Bénard convection that have been performed for both temperature-independent (‘GeoFlow I’) and temperature-dependent fluid viscosity properties (‘GeoFlow II’) with a measured viscosity contrast up to 1.5. To set up a self-gravitating force field, we use a high-voltage potential between the inner and outer boundaries and a dielectric insulating liquid; the experiments were performed under microgravity conditions on the International Space Station. We further run numerical simulations in three-dimensional spherical geometry to reproduce the results obtained in the ‘GeoFlow’ experiments. We use Wollaston prism shearing interferometry for flow visualization – an optical method producing fringe pattern images. The flow patterns differ between our two experiments. In ‘GeoFlow I’, we see a sheet-like thermal flow. In this case convection patterns have been successfully reproduced by three-dimensional numerical simulations using two different and independently developed codes. In contrast, in ‘GeoFlow II’, we obtain plume-like structures. Interestingly, numerical simulations do not yield this type of solution for the low viscosity contrast realized in the experiment. However, using a viscosity contrast of two orders of magnitude or higher, we can reproduce the patterns obtained in the ‘GeoFlow II’ experiment, from which we conclude that nonlinear effects shift the effective viscosity ratio.


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Androvandi, S., Davaille, A., Limarea, A., Foucquiera, A. & Marais, C. 2011 At least three scales of convection in a mantle with strongly temperature-dependent viscosity. Phys. Earth Planet. Inter. 188, 132141.
Bahloul, A., Mutabazi, I. & Ambari, A. 2000 Codimension 2 points in the flow inside a cylindrical annulus with a radial temperature gradient. Eur. Phys. J., Appl. Phys. 9, 253264.
Baumgardner, J. P. 1985 Three-dimensional treatment of convective flow in the Earth’s mantle. J. Stat. Phys. 39, 501511.
Bayer Leverkusen (now GE Bayer Silicones Germany). 2002 Bayer Silicones: Baysilone Fluids M. Technical Data Sheet, 11.11.2002 (delivered with the liquids).
Bercovici, D., Schubert, G. & Glatzmaier, G. A. 1989a Three-dimensional spherical models of convection in the Earth’s mantle. Science 244, 950955.
Bercovici, D., Schubert, G. & Glatzmaier, G. A. 1991 Modal growth and coupling in three-dimensional spherical convection. Geophys. Astrophys. Fluid Dyn. 61, 149159.
Bercovici, D., Schubert, G. & Glatzmaier, G. A. 1992 Three-dimensional convection of an infinite-Prandtl-number compressible fluid in a basally heated spherical shell. J. Fluid Mech. 239, 683719.
Bercovici, D., Schubert, G., Glatzmaier, G. A. & Zebib, A. 1989b Three-dimensional thermal convection in a spherical shell. J. Fluid Mech. 206, 75104.
Booker, J. R. 1976 Thermal convection with strongly temperature-dependent viscosity. J. Fluid Mech. 76, 741754.
Breuer, M., Wessling, S., Schmalzl, J. & Hansen, U. 2004 Effects of inertia in Rayleigh–Bénard convection. Phys. Rev. E 69, 026302.
Busse, F. H. 1975 Patterns of convection in spherical shells. J. Fluid Mech. 72, 6785.
Busse, F. H. 1978 Non-linear properties of thermal convection. Rep. Prog. Phys. 41, 19301967.
Busse, F. H. 2002 Convective flows in rapidly rotating spheres and their dynamo action. Phys. Fluids 14, 13011313.
Busse, F. H. & Frick, H. 1985 Square-pattern convection in fluids with strongly temperature-dependent viscosity. J. Fluid Mech. 150, 451465.
Busse, F. H. & Riahi, N. 1982 Patterns of convection in spherical shells. Part 2. J. Fluid Mech. 182, 283301.
Chandrasekhar, S. 1981 Hydrodynamic and Hydromagnetic Stability. Dover.
Christensen, U. & Harder, H. 1991 Three-dimensional convection with variable viscosity. Geophys. J. Intl 104, 213226.
Cullen, M. 2007 Modelling atmospheric flows. Acta Numerica 16, 67154.
Davaille, A. & Jaupart, C. 1994 Onset of thermal convection in fluids with temperature-dependent viscosity: application to the oceanic mantle. J. Geophys. Res. 99, 19 84319 866.
Davaille, A. & Limare, A. 2009 Laboratory studies of mantle convection. In Mantle Dynamics (ed. Schubert, G. & Bercovici, D.), Treatise on Geophysics, 7, pp. 89165. Elsevier.
Dubois, F., Johannes, L., Dupont, O., Dewandel, J. L. & Legros, J. C. 1999 An integrated optical set-up for fluid physics experiments under microgravity conditions. Meas. Sci. Technol. 10, 934945.
Dutton, J. A. 1995 Dynamics of Atmospheric Motion. Dover.
Egbers, C., Beyer, W., Bonhage, A., Hollerbach, R. & Beltrame, P. 2003 The GEOFLOW-experiment on ISS (Part I): Experimental preparation and design. Adv. Space Res. 32, 171180.
Feudel, F., Bergemann, K., Tuckerman, L., Egbers, C., Futterer, B., Gellert, M. & Hollerbach, R. 2011 Convection patterns in a spherical fluid shell. Phys. Rev. E 83, 046304.
FIZ Chemie (Fachinformationszentrum Chemie GmbH, Berlin). 2010 Relative permittivity at zero frequency. 2010-03-29, ID 1972shkgal0,
Futterer, B., Brucks, A., Hollerbach, R. & Egbers, C. 2007 Thermal blob convection in spherical shells. Intl J. Heat Mass Transfer 50, 40794088.
Futterer, B., Dahley, N., Koch, S., Scurtu, N. & Egbers, C. 2012 From isoviscous convective experiment ‘GeoFlow I’ to temperature-dependent viscosity in ‘GeoFlow II’ – Fluid physics experiments on-board ISS for the capture of convection phenomena in Earth’s outer core and mantle. Acta Astronaut. 71, 1119.
Futterer, B., Egbers, C., Dahley, N., Koch, S. & Jehring, L. 2010 First identification of sub- and supercritical convection patterns from GeoFlow, the geophysical flow simulation experiment integrated in Fluid Science Laboratory. Acta Astronaut. 66, 193200.
Futterer, B., Scurtu, N., Egbers, C., Plesa, A.-C. & Breuer, D. 2009 Benchmark on Prandtl number influence for GeoFlow II, a mantle convection experiment in spherical shells. In Proceedings of the 11th International Workshop on Modelling of Mantle Convection and Lithospheric Dynamics, Braunwald, Switzerland.
Hansen, U. & Yuen, D. A. 1993 High Rayleigh number regime of temperature-dependent viscosity convection and the Earth’s nearly thermal history. Geophys. Res. Lett. 20, 21912194.
Hansen, U. & Yuen, D. A. 1994 Effects of depth-dependent thermal expansivity on the interaction of thermal chemical plumes with a compositional boundary. Phys. Earth Planet. Inter. 86, 205221.
Hart, J. E., Glatzmaier, G. A. & Toomre, J. 1986 Space-Laboratory and numerical simulations of thermal convection in a rotating hemispherical shell with radial gravity. J. Fluid Mech. 173, 519544.
Hébert, F., Hufschmid, R., Scheel, J. & Ahlers, G. 2010 Onset of Rayleigh–Bénard convection in cylindrical containers. Phys. Rev. E 81, 046318.
Hernlund, J. W. & Tackley, P. J. 2008 Modelling mantle convection in the spherical annulus. Earth Planet. Sci. Lett. 274, 380391.
Hollerbach, R. 2000 A spectral solution of the magneto-convection equations in spherical geometry. Intl J. Numer. Meth. Fluids 32, 773797.
Houseman, G. A. 1990 The thermal structure of mantle plumes: axisymmetric or triple junction?. Geophys. J. Intl 102, 1524.
Hüttig, C. & Breuer, D. 2011 Regime classification and planform scaling for internally heated mantle convection. Phys. Earth Planet. Inter. 186, 111124.
Hüttig, C. & Stemmer, K. 2008a Finite volume discretization for dynamic viscosities on Voronoi grids. Phys. Earth Planet. Inter. 171, 137146.
Hüttig, C. & Stemmer, K. 2008b The spiral grid: a new approach to discretize the sphere and its application to mantle convection. Geochem. Geophys. Geosyst. 9, Q02018.
Jones, T. B. 1979 Electrohydrodynamically enhanced heat transfer in liquids – a review. Adv. Heat Transfer 14, 107148.
Kameyama, M. & Ogawa, M. 2000 Transitions in thermal convection with strongly temperature-dependent viscosity in a wide box. Earth Planet. Sci. Lett. 180, 355367.
Kellogg, L. H. & King, S. D. 1997 The effect of temperature dependent viscosity on the structure of new plumes in the mantle: results of a finite element model in a spherical, axisymmetric shell. Earth Planet. Sci. Lett. 148, 1326.
Landau, L. D., Lifshitz, E. M. & Pitaevskii, L. D. 1984 Course of Theoretical Physics – Electrodynamics of Continuous Media. Butterworth-Heinemann.
Lide, D. R. 2008 Handbook of Chemistry and Physics. CRC Press.
Malik, S. V., Yoshikawa, H. N., Crumeyrolle, O. & Mutabazi, I. 2012 Thermo-electro-hydrodynamic instabilities in a dielectric liquid under microgravity. Acta Astronaut. 81, 563569.
Mazzoni, S. 2011 GeoFlow II experiment scientific requirements. RQ 3. European Space Agency ESA, European Space Research and Technology Centre ESTEC, Noordwijk, The Netherlands, reference SCI-ESA-HSF-ESR-GEOFLOW II.
Merck (Merck KGaA Darmstadt, Germany). 2003 1-Nonanol zur Synthese. Safety Data Sheet 806866, 28.05.2003 (delivered with the liquids).
Merzkirch, W. 1987 Flow Visualization. Academic Press.
Morris, S. & Canright, D. R. 1984 A boundary-layer analysis of Bénard convection with strongly temperature-dependent viscosity. Earth Planet. Sci. Lett. 36, 355377.
Nataf, H. C. & Richter, F. M. 1982 Convection experiments in fluids with highly temperature-dependent viscosity and the thermal evolution of the planets. Phys. Earth Planet. Inter. 29, 320329.
Ogawa, M. 2008 Mantle convection: a review. Fluid Dyn. Res. 40, 379398.
Ogawa, M., Schubert, G. & Zebib, A. 1991 Numerical simulations of three-dimensioanl thermal convection a fluid with strongly temperature-dependent viscosity. J. Fluid Mech. 233, 299328.
Ratcliff, J. T., Schubert, G. & Zebib, A. 1996 Effects of temperature-dependent viscosity on thermal convection in a spherical shell. Physica D 97, 242252.
Ratcliff, J. T., Tackley, P. J., Schubert, G. & Zebib, A. 1997 Transitions in thermal convection with strongly variable viscosity. Phys. Earth Planet. Inter. 102, 201212.
Richter, F. M., Nataf, H. C. & Daly, S. F. 1983 Heat transfer and horizontally averaged temperature of convection with large viscosity variations. J. Fluid Mech. 129, 173192.
Schmalzl, J., Breuer, M. & Hansen, U. 2002 The influence of the Prandtl number on the style of vigorous thermal convection. Geophys. Astrophys. Fluid Dyn. 96, 381403.
Schubert, G. & Bercovici, D. 2009 Mantle Dynamics, 7, Treatise on Geophysics, Elsevier.
Schubert, G., Glatzmaier, G. A. & Travis, B. 1993 Steady, three-dimensional, internally heated convection. Phys. Fluids A 5, 19281932.
Schubert, G. & Olson, P. 2009 Treatise on Geophysics – Core Dynamics. Elsevier.
Scurtu, N., Futterer, B. & Egbers, C. 2010 Pulsating and travelling wave modes of natural convection in spherical shells. Phys. Fluids 22, 114108.
Solomatov, V. S. 1995 Scaling of temperature and stress-dependent viscosity convection. Phys. Fluids 7, 266274.
Stemmer, K., Harder, H. & Hansen, U. 2006 A new method to simulate convection with strongly temperature- and pressure-dependent vicosity in a spherical shell: applications to the Earth’s mantle. Phys. Earth Planet. Inter. 157, 223249.
Stengel, K. C., Oliver, D. S. & Booker, J. R. 1982 Onset of convection in a variable-viscosity fluid. J. Fluid Mech. 120, 411431.
Sugiyama, K., Calzavarini, E., Grossmann, S. & Lohse, D. 2007 Non-Oberbeck–Boussinesq effects in two-dimensional Rayleigh–Bénard convection in glycerol. Europhys. Lett. 80, 34002.
Tackley, P. J. 1993 Effects of strongly temperature-dependent viscosity on time-dependent three-dimensional models of mantle convection. Geophys. Res. Lett. 20, 21872190.
Tackley, P. J. 1996 Effects of strongly variable viscosity on three-dimensional compressible convection in planetary mantles. J. Geophys. Res. 101, 33113332.
Travnikov, V., Egbers, C. & Hollerbach, R. 2003 The GEOFLOW-experiment on ISS (Part II): numerical simulation. Adv. Space Res. 32, 181189.
White, D. B. 1988 The planforms and onset of convection with a temperature-dependent viscosity. J. Fluid Mech. 191, 247286.
Yanagisawa, T. & Yamagishi, Y. 2005 Rayleigh–Bénard convection in spherical shell with infinite Prandtl number at high Rayleigh number. J. Earth Sim. 4, 1117.
Yavorskaya, I. M., Fomina, N. I. & Balyaev, Y. N. 1984 A simulation of central symmetry convection in microgravity conditions. Acta Astronaut. 11, 179183.
Yoshikawa, H. N., Crumeyrolle, O. & Mutabazi, I. 2013 Dielectrophoretic force-driven thermal convection in annular geometry. Phys. Fluids 25, 024106.
Zhang, J., Childress, S. & Libchaber, A. 1997 Non-Boussinesq effect: thermal convection with broken symmetry. Phys. Fluids 9, 10341042.
Zhang, P., Liao, X. & Zhang, K. 2002 Patterns in spherical Rayleigh–Bénard convection: a giant spiral roll and its dislocations. Phys. Rev. E 66, 055203.
Zhong, S., McNamara, A., Tan, E., Moresi, L. & Gurnis, M. 2008 A benchmark study on mantle convection in a 3-D spherical shell using CitcomS. Geochem. Geophys. Geosyst. 9, Q10017.
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 (B5), 11 06311 082.
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Sheet-like and plume-like thermal flow in a spherical convection experiment performed under microgravity

  • B. Futterer (a1) (a2), A. Krebs (a1), A.-C. Plesa (a3), F. Zaussinger (a1), R. Hollerbach (a4), D. Breuer (a3) and C. Egbers (a1)...


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