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  • Open Access

Strong and Weak Dynamo Regimes in Taylor-Couette Flows

Ashish Mishra1,*, George Mamatsashvili1,2, and Frank Stefani1

  • *Contact author: a.mishra@hzdr.de
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Phys. Rev. Lett. 135, 124001 – Published 16 September, 2025

DOI: https://doi.org/10.1103/fvv6-7pr2

Abstract

We reveal a nonlinear magnetic dynamo in a Taylor-Couette flow at small magnetic Prandtl numbers Pm≤1, which has been previously believed to exist only at higher Pm≳10 in this flow. The amplitude of initial perturbations, Pm, and domain aspect ratio play a key role in the onset and evolution of the dynamo. It exists in two main states: a weak state dominated by large-scale modes and a strong, turbulent state with higher amplitude dominated by small-scale modes. These findings can be important for dynamo processes in various astrophysical objects with small Pm.

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References (53)

  1. H. Ji, J. Goodman, and A. Kageyama, Magnetorotational instability in a rotating liquid metal annulus, Mon. Not. R. Astron. Soc. 325, L1 (2001).
  2. J. Goodman and H. Ji, Magnetorotational instability of dissipative Couette flow, J. Fluid Mech. 462, 365 (2002).
  3. G. Rüdiger and Y. Zhang, MHD instability in differentially-rotating cylindric flows, Astron. Astrophys. 378, 302 (2001).
  4. X. Wei, H. Ji, J. Goodman, F. Ebrahimi, E. Gilson, F. Jenko, and K. Lackner, Numerical simulations of the Princeton magnetorotational instability experiment with conducting axial boundaries, Phys. Rev. E 94, 063107 (2016).
  5. H. W. Winarto, H. Ji, J. Goodman, F. Ebrahimi, E. P. Gilson, and Y. Wang, Parameter space mapping of the Princeton magnetorotational instability experiment, Phys. Rev. E 102, 023113 (2020).
  6. A. Mishra, G. Mamatsashvili, and F. Stefani, From helical to standard magnetorotational instability: Predictions for upcoming liquid sodium experiments, Phys. Rev. Fluids 7, 064802 (2022).
  7. Y. Wang, E. P. Gilson, F. Ebrahimi, J. Goodman, and H. Ji, Observation of axisymmetric standard magnetorotational instability in the laboratory, Phys. Rev. Lett. 129, 115001 (2022).
  8. A. Mishra, G. Mamatsashvili, and F. Stefani, Nonlinear evolution of magnetorotational instability in a magnetized Taylor-Couette flow: Scaling properties and relation to upcoming DRESDYN-MRI experiment, Phys. Rev. Fluids 8, 083902 (2023).
  9. A. Mishra, G. Mamatsashvili, and F. Stefani, Nonaxisymmetric modes of magnetorotational and possible hydrodynamical instabilities in the upcoming DRESDYN-MRI experiments: Linear and nonlinear dynamics, Phys. Rev. Fluids 9, 033904 (2024).
  10. R. Hollerbach and G. Rüdiger, New type of magnetorotational instability in cylindrical Taylor-Couette flow, Phys. Rev. Lett. 95, 124501 (2005).
  11. F. Stefani, T. Gundrum, G. Gerbeth, G. Rüdiger, M. Schultz, J. Szklarski, and R. Hollerbach, Experimental evidence for magnetorotational instability in a Taylor-Couette flow under the influence of a helical magnetic field, Phys. Rev. Lett. 97, 184502 (2006).
  12. W. Liu, J. Goodman, I. Herron, and H. Ji, Helical magnetorotational instability in magnetized Taylor-Couette flow, Phys. Rev. E 74, 056302 (2006).
  13. F. Stefani, G. Gerbeth, T. Gundrum, R. Hollerbach, J. Priede, G. Rüediger, and J. Szklarski, Helical magnetorotational instability in a Taylor-Couette flow with strongly reduced Ekman pumping, Phys. Rev. E 80, 066303 (2009).
  14. O. N. Kirillov and F. Stefani, On the relation of standard and helical magnetorotational instability, Astrophys. J. 712, 52 (2010).
  15. G. Mamatsashvili and F. Stefani, Linking dissipation-induced instabilities with nonmodal growth: The case of helical magnetorotational instability, Phys. Rev. E 94, 051203(R) (2016).
  16. G. Mamatsashvili, F. Stefani, A. Guseva, and M. Avila, Quasi-two-dimensional nonlinear evolution of helical magnetorotational instability in a magnetized Taylor-Couette flow, New J. Phys. 20, 013012 (2018).
  17. G. Mamatsashvili, F. Stefani, R. Hollerbach, and G. Rüdiger, Two types of axisymmetric helical magnetorotational instability in rotating flows with positive shear, Phys. Rev. Fluids 4, 103905 (2019).
  18. R. Hollerbach, V. Teeluck, and G. Rüdiger, Nonaxisymmetric magnetorotational instabilities in cylindrical Taylor-Couette flow, Phys. Rev. Lett. 104, 044502 (2010).
  19. M. Seilmayer, V. Galindo, G. Gerbeth, T. Gundrum, F. Stefani, M. Gellert, G. Rüdiger, M. Schultz, and R. Hollerbach, Experimental evidence for nonaxisymmetric magnetorotational instability in a rotating liquid metal exposed to an azimuthal magnetic field, Phys. Rev. Lett. 113, 024505 (2014).
  20. A. Mishra, G. Mamatsashvili, V. Galindo, and F. Stefani, Convective, absolute and global azimuthal magnetorotational instabilities, J. Fluid Mech. 922, R4 (2021).
  21. A. Mishra, G. Mamatsashvili, M. Seilmayer, and F. Stefani, One-winged butterflies: Mode selection for azimuthal magnetorotational instability by thermal convection, J. Fluid Mech. 992, R1 (2024).
  22. G. Rüdiger, M. Gellert, R. Hollerbach, M. Schultz, and F. Stefani, Stability and instability of hydromagnetic Taylor-Couette flows, Phys. Rep. 741, 1 (2018).
  23. H. Ji and J. Goodman, Taylor-Couette flow for astrophysical purposes, Phil. Trans. R. Soc. A 381, 20220119 (2023).
  24. F. Stefani, Liquid-metal experiments on geophysical and astrophysical phenomena, Nat. Rev. Phys. 6, 409 (2024).
  25. F. Rincon, Dynamo theories, J. Plasma Phys. 85, 205850401 (2019).
  26. F. Rincon, G. I. Ogilvie, and M. R. E. Proctor, Self-sustaining nonlinear dynamo process in Keplerian shear flows, Phys. Rev. Lett. 98, 254502 (2007).
  27. G. Lesur and G. I. Ogilvie, On self-sustained dynamo cycles in accretion discs, Astron. Astrophys. 488, 451 (2008).
  28. J. Herault, F. Rincon, C. Cossu, G. Lesur, G. I. Ogilvie, and P. Y. Longaretti, Periodic magnetorotational dynamo action as a prototype of nonlinear magnetic-field generation in shear flows, Phys. Rev. E 84, 036321 (2011).
  29. A. Riols, F. Rincon, C. Cossu, G. Lesur, G. I. Ogilvie, and P. Y. Longaretti, Dissipative effects on the sustainment of a magnetorotational dynamo in Keplerian shear flow, Astron. Astrophys. 575, A14 (2015).
  30. J. Walker, G. Lesur, and S. Boldyrev, On the nature of magnetic turbulence in rotating, shearing flows, Mon. Not. R. Astron. Soc. 457, L39 (2016).
  31. J. Walker and S. Boldyrev, Magnetorotational dynamo action in the shearing box, Mon. Not. R. Astron. Soc. 470, 2653 (2017).
  32. J.-M. Shi, J. M. Stone, and C. X. Huang, Saturation of the magnetorotational instability in the unstratified shearing box with zero net flux: Convergence in taller boxes, Mon. Not. R. Astron. Soc. 456, 2273 (2016).
  33. F. Nauman and M. E. Pessah, Sustained turbulence in differentially rotating magnetized fluids at a low magnetic Prandtl number, Astrophys. J. 833, 187 (2016).
  34. A. Riols, F. Rincon, C. Cossu, G. Lesur, G. I. Ogilvie, and P. Y. Longaretti, Magnetorotational dynamo chimeras. The missing link to turbulent accretion disk dynamo models?, Astron. Astrophys. 598, A87 (2017).
  35. G. Mamatsashvili, G. Chagelishvili, M. E. Pessah, F. Stefani, and G. Bodo, Zero net flux MRI turbulence in disks: Sustenance scheme and magnetic Prandtl number dependence, Astrophys. J. 904, 47 (2020).
  36. L. E. Held and G. Mamatsashvili, MRI turbulence in accretion discs at large magnetic Prandtl numbers, Mon. Not. R. Astron. Soc. 517, 2309 (2022).
  37. J. Guilet, A. Reboul-Salze, R. Raynaud, M. Bugli, and B. Gallet, MRI-driven dynamo at very high magnetic Prandtl numbers, Mon. Not. R. Astron. Soc. 516, 4346 (2022).
  38. A. P. Willis and C. F. Barenghi, A Taylor-Couette dynamo, Astron. Astrophys. 393, 339 (2002).
  39. R. Laguerre, C. Nore, J. Leorat, and J. L. Guermond, Cyclic nonlinear dynamo action in a finite Taylor Couette flow, J. Phys. Conf. Ser. 137, 012019 (2008).
  40. C. Nore, J. L. Guermond, R. Laguerre, J. Léorat, and F. Luddens, Nonlinear dynamo in a short Taylor-Couette setup, Phys. Fluids 24, 094106-094106-15 (2012).
  41. C. Gissinger, The Taylor-vortex dynamo, Phys. Fluids 26, 044101 (2014).
  42. F. Marcotte, B. Gallet, F. Pétrélis, and C. Gissinger, Enhanced dynamo growth in nonhomogeneous conducting fluids, Phys. Rev. E 104, 015110 (2021).
  43. A. Guseva, R. Hollerbach, A. P. Willis, and M. Avila, Dynamo action in a quasi-Keplerian Taylor-Couette flow, Phys. Rev. Lett. 119, 164501 (2017).
  44. H. Ji, M. Burin, E. Schartman, and J. Goodman, Hydrodynamic turbulence cannot transport angular momentum effectively in astrophysical disks, Nature (London) 444, 343 (2006).
  45. M. Avila, Stability and angular-momentum transport of fluid flows between corotating cylinders, Phys. Rev. Lett. 108, 124501 (2012).
  46. L. Shi, B. Hof, M. Rampp, and M. Avila, Hydrodynamic turbulence in quasi-Keplerian rotating flows, Phys. Fluids 29, 044107 (2017).
  47. G. Rüdiger and M. Schultz, Large-scale dynamo action of magnetized Taylor-Couette flows, Mon. Not. R. Astron. Soc. 493, 1249 (2020).
  48. L. Petitdemange, F. Marcotte, and C. Gissinger, Spin-down by dynamo action in simulated radiative stellar layers, Science 379, 300 (2023).
  49. D. Gogichaishvili, G. Mamatsashvili, W. Horton, G. Chagelishvili, and G. Bodo, Nonlinear transverse cascade and sustenance of MRI turbulence in Keplerian disks with an azimuthal magnetic field, Astrophys. J. 845, 70 (2017).
  50. G. Lesur, M. Flock, B. Ercolano, M. K. Lin, C. Yang, J. A. Barranco, P. Benitez-Llambay, J. Goodman, A. Johansen, H. Klahr, G. Laibe, W. Lyra, P. S. Marcus, R. P. Nelson, J. Squire, J. B. Simon, N. J. Turner, O. M. Umurhan, and A. N. Youdin, Hydro-, magnetohydro-, and dust-gas dynamics of protoplanetary disks, in Protostars and Planets VII, Astronomical Society of the Pacific Conference Series Vol. 534, edited by S. Inutsuka et al. (Astronomical Society of the Pacific, San Francisco, 2023), p. 465.
  51. S. M. Tobias, P. H. Diamond, and D. W. Hughes, β-plane magnetohydrodynamic turbulence in the solar tachocline, Astrophys. J. Lett. 667, L113 (2007).
  52. L. Jouve, F. Lignières, and M. Gaurat, Interplay between magnetic fields and differential rotation in a stably stratified stellar radiative zone, Astron. Astrophys. 641, A13 (2020).
  53. D. G. Meduri, L. Jouve, and F. Lignières, Angular momentum and chemical transport by azimuthal magnetorotational instability in radiative stellar interiors, Astron. Astrophys. 683, A12 (2024).

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Phys. Rev. Lett. 135, 124001– Published 16 September, 2025
  • Received 19 January 2025
  • Revised 30 May 2025
  • Accepted 15 August 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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