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, 132–141.

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, 253–264.

Baumgardner, J. P.
1985
Three-dimensional treatment of convective flow in the Earth’s mantle. J. Stat. Phys.
39, 501–511.

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, 950–955.

Bercovici, D., Schubert, G. & Glatzmaier, G. A.
1991
Modal growth and coupling in three-dimensional spherical convection. Geophys. Astrophys. Fluid Dyn.
61, 149–159.

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, 683–719.

Bercovici, D., Schubert, G., Glatzmaier, G. A. & Zebib, A.
1989b
Three-dimensional thermal convection in a spherical shell. J. Fluid Mech.
206, 75–104.

Booker, J. R.
1976
Thermal convection with strongly temperature-dependent viscosity. J. Fluid Mech.
76, 741–754.

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, 67–85.

Busse, F. H.
1978
Non-linear properties of thermal convection. Rep. Prog. Phys.
41, 1930–1967.

Busse, F. H.
2002
Convective flows in rapidly rotating spheres and their dynamo action. Phys. Fluids
14, 1301–1313.

Busse, F. H. & Frick, H.
1985
Square-pattern convection in fluids with strongly temperature-dependent viscosity. J. Fluid Mech.
150, 451–465.

Busse, F. H. & Riahi, N.
1982
Patterns of convection in spherical shells. Part 2. J. Fluid Mech.
182, 283–301.

Chandrasekhar, S.
1981
Hydrodynamic and Hydromagnetic Stability. Dover.

Christensen, U. & Harder, H.
1991
Three-dimensional convection with variable viscosity. Geophys. J. Intl
104, 213–226.

Cullen, M.
2007
Modelling atmospheric flows. Acta Numerica
16, 67–154.

Davaille, A. & Jaupart, C.
1994
Onset of thermal convection in fluids with temperature-dependent viscosity: application to the oceanic mantle. J. Geophys. Res.
99, 19 843–19 866.

Davaille, A. & Limare, A.
2009
Laboratory studies of mantle convection. In Mantle Dynamics (ed. Schubert, G. & Bercovici, D.), Treatise on Geophysics, 7, pp. 89–165. 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, 934–945.

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, 171–180.

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.

Futterer, B., Brucks, A., Hollerbach, R. & Egbers, C.
2007
Thermal blob convection in spherical shells. Intl J. Heat Mass Transfer
50, 4079–4088.

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, 11–19.

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, 193–200.

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, 2191–2194.

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, 205–221.

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, 519–544.

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, 380–391.

Hollerbach, R.
2000
A spectral solution of the magneto-convection equations in spherical geometry. Intl J. Numer. Meth. Fluids
32, 773–797.

Houseman, G. A.
1990
The thermal structure of mantle plumes: axisymmetric or triple junction?. Geophys. J. Intl
102, 15–24.

Hüttig, C. & Breuer, D.
2011
Regime classification and planform scaling for internally heated mantle convection. Phys. Earth Planet. Inter.
186, 111–124.

Hüttig, C. & Stemmer, K.
2008a
Finite volume discretization for dynamic viscosities on Voronoi grids. Phys. Earth Planet. Inter.
171, 137–146.

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, 107–148.

Kameyama, M. & Ogawa, M.
2000
Transitions in thermal convection with strongly temperature-dependent viscosity in a wide box. Earth Planet. Sci. Lett.
180, 355–367.

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, 13–26.

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, 563–569.

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, 355–377.

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, 320–329.

Ogawa, M.
2008
Mantle convection: a review. Fluid Dyn. Res.
40, 379–398.

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, 299–328.

Ratcliff, J. T., Schubert, G. & Zebib, A.
1996
Effects of temperature-dependent viscosity on thermal convection in a spherical shell. Physica D
97, 242–252.

Ratcliff, J. T., Tackley, P. J., Schubert, G. & Zebib, A.
1997
Transitions in thermal convection with strongly variable viscosity. Phys. Earth Planet. Inter.
102, 201–212.

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, 173–192.

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, 381–403.

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, 1928–1932.

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, 266–274.

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, 223–249.

Stengel, K. C., Oliver, D. S. & Booker, J. R.
1982
Onset of convection in a variable-viscosity fluid. J. Fluid Mech.
120, 411–431.

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, 2187–2190.

Tackley, P. J.
1996
Effects of strongly variable viscosity on three-dimensional compressible convection in planetary mantles. J. Geophys. Res.
101, 3311–3332.

Travnikov, V., Egbers, C. & Hollerbach, R.
2003
The GEOFLOW-experiment on ISS (Part II): numerical simulation. Adv. Space Res.
32, 181–189.

White, D. B.
1988
The planforms and onset of convection with a temperature-dependent viscosity. J. Fluid Mech.
191, 247–286.

Yanagisawa, T. & Yamagishi, Y.
2005
Rayleigh–Bénard convection in spherical shell with infinite Prandtl number at high Rayleigh number. J. Earth Sim.
4, 11–17.

Yavorskaya, I. M., Fomina, N. I. & Balyaev, Y. N.
1984
A simulation of central symmetry convection in microgravity conditions. Acta Astronaut.
11, 179–183.

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, 1034–1042.

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), 11 063–11 082.