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Numerical investigation of quasistatic magnetoconvection with an imposed horizontal magnetic field

Michael A. Calkins1,*, Talal AlRefae1, Angel Hernandez1, Ming Yan1, and Stefano Maffei2

  • 1Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
  • 2Institute of Geophysics, ETH Zurich, Sonneggstrasse 5, 8092 Zürich, Switzerland

  • *michael.calkins@colorado.edu
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Phys. Rev. Fluids 8, 123501 – Published 11 December, 2023

DOI: https://doi.org/10.1103/PhysRevFluids.8.123501

Abstract

Quasistatic Rayleigh-Bénard convection with an imposed horizontal magnetic field is investigated numerically for Chandrasekhar numbers up to Q=106 with stress-free boundary conditions. Both Q and the Rayleigh number (Ra) are varied to identify the various dynamical regimes that are present in this system. We find three primary regimes: (i) a two-dimensional (2D) regime in which the axes of the convection rolls are oriented parallel to the imposed magnetic field; (ii) an anisotropic three-dimensional (3D) regime; and (iii) a mean flow regime characterized by a large scale horizontal flow directed transverse to the imposed magnetic field. The transition to 3D dynamics is preceded by a series of 2D transitions in which the number of convection rolls decreases as Ra is increased. For sufficiently large Q, there is an eventual transition to two rolls just prior to the 2D-3D transition. The 2D-3D transition occurs when inertial forces become comparable to the Lorentz force, i.e., when Q/Re=O(1); 2D, magnetically constrained states persist when Q/Re≳O(1). Within the 2D regime, we find heat and momentum transport scalings that are consistent with the hydrodynamic asymptotic predictions of Chini and Cox [Phys. Fluids 21, 083603 (2009)]: the Nusselt number (Nu) and Reynolds number (Re) scale as Nu∼Ra1/3 and Re∼Ra2/3, respectively. For Q=106, we find that the scaling behavior of Nu and Re breaks down at large values of Ra due to a sequence of bifurcations and the eventual manifestation of mean flows.

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References (51)

  1. J. M. Aurnou and P. Olson, Experiments on Rayleigh-Bénard convection, magnetoconvection, and rotating magnetoconvection in liquid gallium, J. Fluid Mech. 430, 283 (2001).
  2. U. Burr and U. Müller, Rayleigh–Bénard convection in liquid metal layers under the influence of a horizontal magnetic field, J. Fluid Mech. 453, 345 (2002).
  3. E. M. King and J. M. Aurnou, Magnetostrophic balance as the optimal state for turbulent magnetoconvection, Proc. Natl. Acad. Sci. USA 112, 990 (2015).
  4. Y. Tasaka, K. Igaki, T. Yanagisawa, T. Vogt, T. Zuerner, and S. Eckert, Regular flow reversals in Rayleigh-Bénard convection in a horizontal magnetic field, Phys. Rev. E 93, 043109 (2016).
  5. X.-X. Yu, J. Zhang, and M.-J. Ni, Numerical simulation of the Rayleigh-Bénard convection under the influence of magnetic fields, Int. J. Heat Mass Transf. 120, 1118 (2018).
  6. T. Vogt, W. Ishimi, T. Yanagisawa, Y. Tasaka, A. Sakuraba, and S. Eckert, Transition between quasi-two-dimensional and three-dimensional Rayleigh-Bénard convection in a horizontal magnetic field, Phys. Rev. Fluids 3, 013503 (2018).
  7. W. Liu, D. Krasnov, and J. Schumacher, Wall modes in magnetoconvection at high Hartmann numbers, J. Fluid Mech. 849, R2 (2018).
  8. M. Yan, M. A. Calkins, S. Maffei, K. Julien, S. M. Tobias, and P. Marti, Heat transfer and flow regimes in quasi-static magnetoconvection with a vertical magnetic field, J. Fluid Mech. 877, 1186 (2019).
  9. Z. L. Lim, K. L. Chong, G.-Y. Ding, and K.-Q. Xia, Quasistatic magnetoconvection: Heat transport enhancement and boundary layer crossing, J. Fluid Mech. 870, 519 (2019).
  10. T. Zürner, F. Schindler, T. Vogt, S. Eckert, and J. Schumacher, Flow regimes of Rayleigh-Bénard convection in a vertical magnetic field, J. Fluid Mech. 894, A21 (2020).
  11. N. O. Weiss and M. Proctor, Magnetoconvection (Cambridge University Press, Cambridge, UK, 2014).
  12. U. Burr and U. Müller, Rayleigh-Bénard in liquid metal layers under the influence of a vertical magnetic field, Phys. Fluids 13, 3247 (2001).
  13. P. Matthews, M. Proctor, and N. Weiss, Compressible magnetoconvection in three dimensions: Planforms and nonlinear behaviour, J. Fluid Mech. 305, 281 (1995).
  14. P. C. Matthews, Asymptotic solutions for nonlinear magnetoconvection, J. Fluid Mech. 387, 397 (1999).
  15. S. Cioni, S. Chaumat, and J. Sommeria, Effect of a vertical magnetic field on turbulent Rayleigh-Bénard convection, Phys. Rev. E 62, 4520(R) (2000).
  16. N. E. Hurlburt, P. C. Matthews, and M. R. Proctor, Nonlinear compressible convection in oblique magnetic fields, Astrophys. J. 457, 933 (1996).
  17. J. A. Nicoski, M. Yan, and M. A. Calkins, Quasistatic magnetoconvection with a tilted magnetic field, Phys. Rev. Fluids 7, 043504 (2022).
  18. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Oxford University Press, Oxford, UK, 1961).
  19. O. Andreev, A. Thess, and C. Haberstroh, Visualization of magnetoconvection, Phys. Fluids 15, 3886 (2003).
  20. J. C. Yang, T. Vogt, and S. Eckert, Transition from steady to oscillating convection rolls in Rayleigh-Bénard convection under the influence of a horizontal magnetic field, Phys. Rev. Fluids 6, 023502 (2021).
  21. G. Ahlers, S. Grossmann, and D. Lohse, Heat transfer and large scale dynamics in turbulent Rayleigh-Bénard convection, Rev. Mod. Phys. 81, 503 (2009).
  22. J. S. Cheng, S. Stellmach, A. Ribeiro, A. Grannan, E. M. King, and J. M. Aurnou, Laboratory-numerical models of rapidly rotating convection in planetary cores, Geophys. J. Int. 201, 1 (2015).
  23. W. V. Malkus, The heat transport and spectrum of thermal turbulence, Proc. R. Soc. London A 225, 196 (1954).
  24. R. H. Kraichnan, Turbulent thermal convection at arbitrary Prandtl number, Phys. Fluids 5, 1374 (1962).
  25. D. Lohse and F. Toschi, Ultimate state of thermal convection, Phys. Rev. Lett. 90, 034502 (2003).
  26. B. Castaing, G. Gunaratne, F. Heslot, L. Kadanoff, A. Libchaber, S. Thomae, X.-Z. Wu, S. Zaleski, and G. Zanetti, Scaling of hard thermal turbulence in Rayleigh-Bénard convection, J. Fluid Mech. 204, 1 (1989).
  27. X. Zhu, V. Mathai, R. J. A. M. Stevens, R. Verzicco, and D. Lohse, Transition to the ultimate regime in two-dimensional Rayleigh-Bénard convection, Phys. Rev. Lett. 120, 144502 (2018).
  28. C. R. Doering, S. Toppaladoddi, and J. S. Wettlaufer, Absence of evidence for the ultimate regime in two-dimensional Rayleigh-Bénard convection, Phys. Rev. Lett. 123, 259401 (2019).
  29. J. M. Aurnou, S. Horn, and K. Julien, Connections between nonrotating, slowly rotating, and rapidly rotating turbulent convection transport scalings, Phys. Rev. Res. 2, 043115 (2020).
  30. E. A. Spiegel, Convective instability in a compressible atmosphere. I, Astrophys. J. 141, 1068 (1965).
  31. T. Vogt, S. Horn, A. M. Grannan, and J. M. Aurnou, Jump rope vortex in liquid metal convection, Proc. Natl. Acad. Sci. USA 115, 12674 (2018).
  32. T. Vogt, S. Horn, and J. M. Aurnou, Oscillatory thermal–inertial flows in liquid metal rotating convection, J. Fluid Mech. 911, A5 (2021).
  33. M. Yan, S. M. Tobias, and M. A. Calkins, Scaling behaviour of small-scale dynamos driven by Rayleigh–Bénard convection, J. Fluid Mech. 915, A15 (2021).
  34. G. P. Chini and S. M. Cox, Large Rayleigh number thermal convection: Heat flux predictions and strongly nonlinear solutions, Phys. Fluids 21, 083603 (2009).
  35. B. Wen, D. Goluskin, M. LeDuc, G. P. Chini, and C. R. Doering, Steady Rayleigh–Bénard convection between stress-free boundaries, J. Fluid Mech. 905, R4 (2020).
  36. F. Waleffe, A. Boonkasame, and L. M. Smith, Heat transport by coherent Rayleigh-Bénard convection, Phys. Fluids 27, 051702 (2015).
  37. A. Pandey, J. D. Scheel, and J. Schumacher, Turbulent superstructures in Rayleigh-Bénard convection, Nat. Commun. 9, 2118 (2018).
  38. D. Krug, D. Lohse, and R. J. Stevens, Coherence of temperature and velocity superstructures in turbulent Rayleigh–Bénard flow, J. Fluid Mech. 887, A2 (2020).
  39. T. Zürner, W. Liu, D. Krasnov, and J. Schumacher, Heat and momentum transfer for magnetoconvection in a vertical external magnetic field, Phys. Rev. E 94, 043108 (2016).
  40. T. Vogt, J.-C. Yang, F. Schindler, and S. Eckert, Free-fall velocities and heat transport enhancement in liquid metal magneto-convection, J. Fluid Mech. 915, A68 (2021).
  41. D. Goluskin, H. Johnston, G. R. Flierl, and E. A. Spiegel, Convectively driven shear and decreased heat flux, J. Fluid Mech. 759, 360 (2014).
  42. J. von Hardenberg, D. Goluskin, A. Provenzale, and E. A. Spiegel, Generation of large-scale winds in horizontally anisotropic convection, Phys. Rev. Lett. 115, 134501 (2015).
  43. Q. Wang, K. L. Chong, R. J. A. M. Stevens, R. Verzicco, and D. Lohse, From zonal flow to convection rolls in Rayleigh–Bénard convection with free-slip plates, J. Fluid Mech. 905, A21 (2020).
  44. B. Knaepen and R. Moreau, Magnetohydrodynamic turbulence at low magnetic Reynolds number, Annu. Rev. Fluid Mech. 40, 25 (2008).
  45. Y. Xu, S. Horn, and J. M. Aurnou, Thermoelectric precession in turbulent magnetoconvection, J. Fluid Mech. 930, A8 (2022).
  46. C. A. Jones and P. H. Roberts, Convection-driven dynamos in a rotating plane layer, J. Fluid Mech. 404, 311 (2000).
  47. P. Marti, M. A. Calkins, and K. Julien, A computationally efficient spectral method for modeling core dynamics, Geochem. Geophys. Geosys. 17, 3031 (2016).
  48. J. Hunt and J. Shercliff, Magnetohydrodynamics at high Hartmann number, Annu. Rev. Fluid Mech. 3, 37 (1971).
  49. K. Lüdemann and A. Tilgner, Transition to three-dimensional flow in thermal convection with spanwise rotation, Phys. Rev. Fluids 7, 063502 (2022).
  50. T. Yanagisawa, Y. Hamano, T. Miyagoshi, Y. Yamagishi, Y. Tasaka, and Y. Takeda, Convection patterns in a liquid metal under an imposed horizontal magnetic field, Phys. Rev. E 88, 063020 (2013).
  51. M. Ossendrijver, The solar dynamo, Astron. Astrophys. Rev. 11, 287 (2003).

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Information

Phys. Rev. Fluids 8, 123501– Published 11 December, 2023
  • Received 6 September 2021
  • Revised 11 October 2023
  • Accepted 15 November 2023
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