Skip to main content Accessibility help
×
×
Home

Experimental study of the convection in a rotating tangent cylinder

  • Kélig Aujogue (a1), Alban Pothérat (a1), Binod Sreenivasan (a2) and François Debray (a3)
Abstract

This paper experimentally investigates the convection in a rapidly rotating tangent cylinder (TC), for Ekman numbers down to $E=3.36\times 10^{-6}$ . The apparatus consists of a hemispherical fluid vessel heated in its centre by a protruding heating element of cylindrical shape. The resulting convection that develops above the heater, i.e. within the TC, is shown to set in for critical Rayleigh numbers and wavenumbers respectively scaling as $Ra_{c}\sim E^{-4/3}$ and $a_{c}\sim E^{-1/3}$ with the Ekman number $E$ . Although exhibiting the same exponents as for plane rotating convection, these laws reflect much larger convective plumes at onset. The structure and dynamics of supercritical plumes are in fact closer to those found in solid rotating cylinders heated from below, suggesting that the confinement within the TC induced by the Taylor–Proudman constraint influences convection in a similar way as solid walls would do. There is a further similarity in that the critical modes in the TC all exhibit a slow retrograde precession at onset. In supercritical regimes, the precession evolves into a thermal wind with a complex structure featuring retrograde rotation at high latitude and either prograde or retrograde rotation at low latitude (close to the heater), depending on the criticality and the Ekman number. The intensity of the thermal wind measured by the Rossby number $Ro$ scales as $Ro\simeq 5.33(Ra_{q}^{\ast })^{0.51}$ with the Rayleigh number based on the heat flux $Ra_{q}^{\ast }\in [10^{-9},10^{-6}]$ . This scaling is in agreement with heuristic predictions and previous experiments where the thermal wind is determined by the azimuthal curl of the balance between the Coriolis force and buoyancy. Within the range $Ra\in [2\times 10^{7},10^{9}]$ which we explored, we also observe a transition in the heat transfer through the TC from a diffusivity-free regime where $Nu\simeq 0.38E^{2}Ra^{1.58}$ to a rotation-independent regime where $Nu\simeq 0.2Ra^{0.33}$ .

Copyright
Corresponding author
Email address for correspondence: aujogue.kelig@gmail.com
References
Hide All
Aubert, J. 2005 Steady zonal flows in spherical shell dynamos. J. Fluid Mech. 542, 5367.
Aubert, J., Brito, D., Nataf, H.-C., Cardin, P. & Masson, J.-P. 2001 A systematic experimental study of rapidly rotating spherical convection in water and liquid gallium. Phys. Earth Planet. Inter. 128 (1), 5174.
Aujogue, K., Pothérat, A., Bates, I., Debray, F. & Sreenivasan, B. 2016 Little earth experiment: an instrument to model planetary cores. Rev. Sci. Instrum. 87 (8), 084502.
Aujogue, K., Pothérat, A. & Sreenivasan, B. 2015 Onset of plane layer magnetoconvection at low Ekman number. Phys. Fluids 27 (10), 106602.
Aurnou, J. 2007 Planetary core dynamics and convective heat transfer scaling. Geophys. Astrophys. Fluid Dyn. 101 (5–6), 327345.
Aurnou, J., Andreadis, S., Zhu, L. & Olson, P. 2003 Experiments on convection in Earth’s core tangent cylinder. Earth Planet. Sci. Lett. 212 (1), 119134.
Aurnou, J. M. & Olson, P. 2001 Experiments on Rayleigh–Bénard convection, magnetoconvection and rotating magnetoconvection in liquid gallium. J. Fluid Mech. 430, 283307.
Busse, F. H. 1970 Thermal instabilities in rapidly rotating systems. J. Fluid Mech. 44 (03), 441460.
Cardin, P. & Olson, P. 1994 Chaotic thermal convection in a rapidly rotating spherical shell: consequences for flow in the outer core. Phys. Earth Planet. Inter. 82 (3–4), 235259.
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Clarendon Press.
Cheng, J. S. & Aurnou, J. M. 2016 Tests of diffusion-free scaling behaviors in numerical dynamo datasets. Earth Planet. Sci. Lett. 436, 121129.
Cheng, J. S., Stellmach, S., Ribeiro, A., Grannan, A., King, E. M. & Aurnou, J. M. 2015 Laboratory-numerical models of rapidly rotating convection in planetary cores. Geophys. J. Intl 201 (1), 117.
Christensen, U. R. 2002 Zonal flow driven by strongly supercritical convection in rotating spherical shells. J. Fluid Mech. 470, 115133.
Christensen, U. R. & Aubert, J. 2006 Scaling properties of convection-driven dynamos in rotating spherical shells and application to planetary magnetic fields. Geophys. J. Intl 166 (1), 97114.
Clune, T. & Knoblauch, E. 1993 Pattern selection in rotating convection with experimental boundary conditions. Phys. Rev. E 47 (4), 25362540.
Cui, A. & Street, R. L. 2001 Large-eddy simulation of turbulent rotating convective flow development. J. Fluid Mech. 447, 5384.
Curbelo, J., Lopez, J. M., Mancho, A. M. & Marques, F. 2014 Confined rotating convection with large Prandtl number: centrifugal effects on wall modes. Phys. Rev. E 89, 013019.
Ecke, R. E., Zhong, F. & Knobloch, E. 1992 Hopf bifurcation with broken reflection symmetry in rotating Rayleigh–Bénard convection. Europhys. Lett. 19 (3), 177182.
Gastine, T., Wicht, J. & Aubert, J. 2016 Scaling regimes in spherical shell rotating convection. J. Fluid Mech. 808, 690732.
Gastine, T., Wicht, J. & Aurnou, J. M. 2015 Turbulent Rayleigh–Bénard convection in spherical shells. J. Fluid Mech. 778, 721764.
Glatzmaiers, G. A. & Roberts, P. H. 1995 A three-dimensional self-consistent computer simulation of a geomagnetic field reversal. Nature 377, 203209.
Goldstein, H. F., Knoblauch, E., Mercader, I. & Net, M. 1994 Convection in a rotating cylinder. Part 2. Linear theory for low Prandtl numbers. J. Fluid Mech. 262, 293324.
Goldstein, H. F., Knobloch, E., Mercader, I. & Net, M. 1993 Convection in a rotating cylinder. Part 1. Linear theory for moderate Prandtl numbers. J. Fluid Mech. 248, 583604.
Grossmann, S. & Lohse, D. 2000 Scaling in thermal convection: a unifying theory. J. Fluid Mech. 407, 2756.
Hollerbach, R. 1994 Imposing a magnetic field across a nonaxisymmetric shear layer in a rotating spherical shell. Phys. Fluids 6 (7), 25402544.
Horn, S. & Shishkina, O. 2014 Rotating non-Oberbeck–Boussinesq Rayleigh–Bénard convection in water. Phys. Fluids 26, 055111.
Hulot, G., Eymin, C., Langlais, B., Mandea, M. & Olsen, N. 2002 Small-scale structure of the geodynamo inferred from oersted and magsat satellite data. Nature 416 (6881), 620623.
Jacobs, P. & Ivey, G. N. 1998 The influence of rotation on shelf convection. J. Fluid Mech. 369, 2348.
Jones, C. A. 2007 Thermal and compositional convection in the outer core. In Treatise in Geophysics, Core Dynamics, vol. 8, pp. 131185. Elsevier.
Julien, K., Knobloch, E., Rubio, A. M. & Vasil, G. M. 2012 Heat transport in low-Rossby-number Rayleigh–Bénard convection. Phys. Rev. Lett. 109 (25), 254503.
King, E. M., Stellmach, S. & Aurnou, J. M. 2012 Heat transfer by rapidly rotating Rayleigh–Bénard convection. J. Fluid Mech. 691, 568582.
de Koker, N., Steinle-Neumann, G. & Vlček, V. 2012 Electrical resistivity and thermal conductivity of liquid Fe alloys at high P and T, and heat flux in Earths core. Proc. Natl Acad. Sci. USA 109 (11), 40704073.
Kraichnan, R. H. 1962 Turbulent thermal convection at arbitrary Prandtl number. Phys. Fluids 5, 13741389.
Kunnen, R. P. J., Geurts, B. J. & Clerx, H. J. H. 2010 Experimental and numerical investigation of turbulent convection in a rotating cylinder. J. Fluid Mech. 642, 445476.
Kunnen, R. P. J., Stevens, R. J. A. M., Overkamp, J., Sun, C., van Heijst, G. F. & Clercx, H. J. H. 2011 The role of Stewartson and Ekman layers in turbulent rotating Rayleigh–Bénard convection. J. Fluid Mech. 688, 422442.
Livermore, P. W. & Hollerbach, R. 2012 Successive elimination of shear layers by a hierarchy of constraints in inviscid spherical-shell flows. J. Math. Phys. 53 (7), 073104.
Livermore, P. W., Hollerbach, R. & Finlay, C. 2017 An accelerating high-latitude jet in earths core. Nat. Geo. 10, 6269.
Marques, F., Mercader, I., Batiste, O. & Lopez, J. M. 2007 Centrifugal effects in rotating convection: axisymmetric states and three-dimensional instabilities. J. Fluid Mech. 580, 303318.
Maxworthy, T. & Narimousa, S. 1994 Unsteady turbulent convection into a homogeneous rotating fluid with oceanic applications. J. Phys. Oceanogr. 24, 865887.
Pozzo, M., Davies, C., Gubbins, D. & Alfe, D. 2012 Thermal and electrical conductivity of iron at earth’s core conditions. Nature 485 (7398), 355358.
Schaeffer, N., Jault, D., Nataf, H.-C. & Fournier, A. 2017 Turbulent geodynamo simulations: a leap towards Earth’s core. Geophys. J. Intl 10.1093/gji/ggx265.
Schubert, G. & Soderlund, K. M. 2011 Planetary magnetic fields: observations and models. Phys. Earth Planet. Inter. 187 (3), 92108.
Sreenivasan, B. & Jones, C. A. 2006 Azimuthal winds, convection and dynamo action in the polar regions of planetary cores. Geophys. Astrophys. Fluid Dyn. 100 (4–5), 319339.
Stewartson, K. 1957 On almost rigid rotations. J. Fluid Mech. 3 (1), 1726.
Sumita, I. & Olson, P. 2003 Experiments on highly supercritical thermal convection in a rapidly rotating hemispherical shell. J. Fluid Mech. 492, 271287.
Trümper, T., Breuer, M. & Hansen, U. 2012 Numerical study on double-diffusive convection in the earths core. Phys. Earth Planet. Inter. 194, 5563.
Zhang, K. & Liao, X. 2009 The onset of convection in rotating circular cylinders with experimental boundary conditions. J. Fluid Mech. 622, 6373.
Zhong, F., Ecke, R. E. & Steinberg, V. 1993 Rotating Rayleigh–Bénard convection: asymmetric modes and vortex states. J. Fluid Mech. 249, 135159.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

JFM classification

Type Description Title
UNKNOWN
Supplementary materials

Aujogue et al. supplementary material
Aujogue et al. supplementary material 1

 Unknown (15 KB)
15 KB

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed