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Subcritical transition to turbulence triggered by a magnetic dynamo

F. Daniel1,*, L. Petitdemange2,†, and C. Gissinger1,3,‡

  • 1Laboratoire de Physique de l'Ecole normale superieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, Paris, France
  • 2Laboratoire d'Etudes du Rayonnement et de la Matière en Astrophysique et Atmosphères (LERMA), Observatoire de Paris, PSL, CNRS, Sorbonne Université, Paris, France
  • 3Institut Universitairé de France (IUF), Paris, France

  • *florentin.daniel@phys.ens.fr
  • †ludovic.petitdemange@upmc.fr
  • ‡christophe.gissinger@phys.ens.fr
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Phys. Rev. Fluids 8, 123701 – Published 5 December, 2023

DOI: https://doi.org/10.1103/PhysRevFluids.8.123701

Abstract

It has recently been shown that a significant slowdown of many stars can be attributed to the emergence of a strong magnetic field within the radiative region, where heat is transferred through radiation in a stably stratified layer. Here we describe how this transition can be understood as a subcritical bifurcation to small-scale turbulence in linearly stable flows. The turbulence is sustained by a nonlinear mean-field dynamo and can be observed down to relatively small differential rotation, arbitrarily far from the linear onset of any hydrodynamic instability. In this regime, turbulent fluctuations provide diffusivity-free transfer of angular momentum that increases the transport generated by the magnetic field triggering the turbulence. Finally, we present a simple nonlinear model that captures this scenario and can be used as a general description of the transition to turbulence in astrophysical flows, as long as it involves a competition between a large-scale dynamo and a small-scale magnetic instability.

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References (66)

  1. N. Brummell, F. Cattaneo, and J. Toomre, Turbulent dynamics in the solar convection zone, Science 269, 1370 (1995).
  2. J. M. Aurnou, M. A. Calkins, J. S. Cheng, K. Julien, E. M. King, D. Nieves, K. M. Soderlund, and S. Stellmach, Rotating convective turbulence in earth and planetary cores, Phys. Earth Planet. Inter. 246, 52 (2015).
  3. S. A. Balbus and J. F. Hawley, A powerful local shear instability in weakly magnetized disks. I. Linear analysis, Astrophys. J. 376, 214 (1991).
  4. R. Rosner and E. Deluca, On the galactic dynamo, Symp. Intl. Astro. Union 136, 319 (1989).
  5. Lord Rayleigh, Containing papers of a mathematical and physical character, Proc. R. Soc. London A 93, 148 (1917).
  6. H. H. Klahr and P. Bodenheimer, Turbulence in accretion disks: Vorticity generation and angular momentum transport via the global baroclinic instability, Astrophys. J. 582, 869 (2003).
  7. G. Lesur and G. I. Ogilvie, On the angular momentum transport due to vertical convection in accretion discs, Mon. Not. R. Astron. Soc. Lett. 404, L64 (2010).
  8. A. Toomre, On the gravitational stability of a disk of stars, Astrophys. J. 139, 1217 (1964).
  9. L. F. Richardson, The supply of energy from and atmospheric eddies, Proc. R. Soc. London 97, 354 (1920).
  10. E. Chang and P. Garaud, Modelling coexisting GSF and shear instabilities in rotating stars, Mon. Not. R. Astron. Soc. 506, 4914 (2021).
  11. P. Garaud, Journey to the center of stars: The realm of low Prandtl number fluid dynamics, Phys. Rev. Fluids 6, 030501 (2021).
  12. S. A. Balbus and J. F. Hawley, Instability, turbulence, and enhanced transport in accretion disks, Rev. Mod. Phys. 70, 1 (1998).
  13. S. Ji, J. Fuller, and D. Lecoanet, Magnetohydrodynamic simulations of the Tayler instability in rotating stellar interiors, Mon. Not. R. Astron. Soc. 521, 5372 (2023).
  14. R. J. Tayler, The adiabatic stability of stars containing magnetic fields, Mon. Not. R. Astron. Soc. 161, 365 (1973).
  15. A. Guseva, A. P. Willis, R. Hollerbach, and M. Avila, Transition to magnetorotational turbulence in Taylor-Couette flow with imposed azimuthal magnetic field, New J. Phys. 17, 093018 (2015).
  16. K. Moffatt and E. Dormy, Self-exciting Fluid Dynamos (Cambridge University Press, Cambridge, 2019).
  17. F. Rincon, G. I. Ogilvie, M. R. E. Proctor, and C. Cossu, Subcritical dynamos in shear flows, Astron. Nachr. 329, 750 (2008).
  18. F. Rincon, Dynamo theories, J. Plasma Phys. 85, 205850401 (2019).
  19. A. Riols, F. Rincon, C. Cossu, G. Lesur, P. Y. Longaretti, G. I. Ogilvie, and J. Herault, Global bifurcations to subcritical magnetorotational dynamo action in Keplerian shear flow, J. Fluid Mech. 731, 1 (2013).
  20. 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).
  21. D. W. Hughes and N. O. Weiss, Double-diffusive convection with two stabilizing gradients: Strange consequences of magnetic buoyancy, J. Fluid Mech. 301, 383 (1995).
  22. S. A. Balbus, Enhanced angular momentum transport in accretion disks, Annu. Rev. Astron. Astrophys. 41, 555 (2003).
  23. B. Mosser, M. J. Goupil, K. Belkacem, J. P. Marques, P. G. Beck, S. Bloemen, J. De Ridder, C. Barban, S. Deheuvels, Y. Elsworth et al., Spin down of the core rotation in red giants, Astron. Astrophys. 548, A10 (2012).
  24. C. Aerts, S. Mathis, and T. Rogers, Angular momentum transport in stellar interiors, Annu. Rev. Astron. Astrophys. 57, 35 (2019).
  25. S. Mathis, Transport processes in stellar interiors, in Studying Stellar Rotation and Convection Theoretical Background and Seismic Diagnostics, edited by M. Goupil, k. Belkacem, C. Neiner, F. Lignières, and J. Green, Lecture Notes in Physics Vol. 865 (Springer, Berlin Heidelberg, 2013) pp. 23–42.
  26. C. Pinçon, K. Belkacem, M. J. Goupil, and J. P. Marques, Can plume-induced internal gravity waves regulate the core rotation of subgiant stars? Astron. Astrophys. 605, A31 (2017).
  27. J. Fuller, A. L. Piro, and A. S. Jermyn, Slowing the spins of stellar cores, Mon. Not. R. Astron. Soc. 485, 3661 (2019).
  28. H. C. Spruit, Dynamo action by differential rotation in a stably stratified stellar interior, Astron. Astrophys. 381, 923 (2002).
  29. M. Avila, Stability and angular-momentum transport of fluid flows between corotating cylinders, Phys. Rev. Lett. 108, 124501 (2012).
  30. R. Ostilla-Mónico, E. P. van der Poel, R. Verzicco, S. Grossmann, and D. Lohse, Boundary layer dynamics at the transition between the classical and the ultimate regime of Taylor-Couette flow, Phys. Fluids 26, 015114 (2014).
  31. M. Vernet, S. Fauve, and C. Gissinger, Angular momentum transport by Keplerian turbulence in liquid metals, Phys. Rev. Lett. 129, 074501 (2022).
  32. M. S. Paoletti, D. P. M. Van Gils, B. Dubrulle, C. Sun, D. Lohse, and D. P. Lathrop, Angular momentum transport and turbulence in laboratory models of Keplerian flows, Astron. Astrophys. 547, A64 (2012).
  33. D. Lathrop, J. Fineberg, and H. Swinney, Turbulent flow between concentric rotating cylinders at large Reynolds number, Phys. Rev. Lett. 68, 1515 (1992).
  34. S. G. Huisman, D. P. M. Van Gils, S. Grossmann, C. Sun, and D. Lohse, Ultimate turbulent Taylor-Couette flow, Phys. Rev. Lett. 108, 024501 (2012).
  35. P. Charbonneau, Solar and Stellar Dynamos, edited by Oskar Steiner, Vol. 39 (Springer, Berlin, Heidelberg, 2013), pp. 187–212.
  36. L. Petitdemange, F. Marcotte, and C. Gissinger, Spin-down by dynamo action in simulated radiative stellar layers, Science 379, 300 (2023).
  37. E. Dormy, P. Cardin, and D. Jault, Mhd flow in a slightly differentially rotating spherical shell, with conducting inner core, in a dipolar magnetic field, Earth Planet. Sci. Lett. 160, 15 (1998).
  38. J. Aubert, J. Aurnou, and J. Wicht, The magnetic structure of convection-driven numerical dynamos, Geophys. J. Int. 172, 945 (2007).
  39. N. Schaeffer, Efficient spherical harmonic transforms aimed at pseudospectral numerical simulations, Geochem. Geophys. Geosyst. 14, 751 (2013).
  40. J. Christensen-Dalsgaard, Lecture Notes on Stellar Structure and Evolution (Institute for Fysik og Astronomi, Aarhus Universitet, 2008).
  41. H. C. Spruit, Differential rotation and magnetic fields in stellar interiors, Astronomy and Astrophysics 349, 189 (1999).
  42. O. N. Kirillov, F. Stefani, and Y. Fukumoto, Local instabilities in magnetized rotational flows: A short-wavelength approach, J. Fluid Mech. 760, 591 (2014).
  43. D. Biskamp and W. C. Müller, Scaling properties of three-dimensional isotropic magnetohydrodynamic turbulence, Phys. Plasmas 7, 4889 (2000).
  44. A. A. Schekochihin, S. C. Cowley, J. L. Maron, and J. C. McWilliams, Critical magnetic prandtl number for small-scale dynamo, Phys. Rev. Lett. 92, 054502 (2004).
  45. Y. Ponty, P. D. Mininni, D. C. Montgomery, J. F. Pinton, H. Politano, and A. Pouquet, Numerical study of dynamo action at low magnetic Prandtl numbers, Phys. Rev. Lett. 94, 164502 (2005).
  46. J. Wicht, Flow instabilities in the wide-gap spherical couette system, J. Fluid Mech. 738, 184 (2014).
  47. L. Petitdemange, F. Marcotte, C. Gissinger, and F. Daniel, Tayler-Spruit dynamos in simulated radiative stellar layers, arXiv:2306.11711 [astro-ph.SR] (2023).
  48. S. Couvidat, R. A. García, S. Turck-Chiè, T. Corbard, C. J. Henney, and S. Jiménez-Reyes, The rotation of the deep solar layers, Astrophys. J. 597, L77 (2003).
  49. D. J. Acheson, On the instability of toroidal magnetic fields and differential rotation in stars, Philos. Trans. R. Soc. 289, 459 (1978).
  50. J. P. Zahn, A. S. Brun, and S. Mathis, On magnetic instabilities and dynamo action in stellar radiation zones, Astron. Astrophys. 474, 145 (2007).
  51. W. H. Press, Radiative and other effects from internal waves in solar and stellar interiors 1, Astrophys. J. 245, 286 (1981).
  52. J.-P. Zahn, A. S. Talon, and J. Matias, Angular momentum transport by internal waves in the solar interior, Astron. Astrophys. 322, 320 (1997) .
  53. F. Stefani, A. Giesecke, and T. Weier, A model of a tidally synchronized solar dynamo, Sol. Phys. 294, 60 (2019).
  54. K. S. Cline, N. H. Brummell, and F. Cattaneo, Dynamo action driven by shear and magnetic buoyancy, Astrophys. J. 599, 1449 (2003).
  55. M. Schrinner, L. Petitdemange, and E. Dormy, Dipole collapse and dynamo waves in global direct numerical simulations, Astrophys. J. 752, 121 (2012).
  56. J. Guckenheimer and P. Holmes, Nonlinear Oscillations Dynamical Systems and Bifurcations of Vector Fields (Springer, Verlag, New York, 1983).
  57. B. Young, S. Fauve, B. E. DeRemer, and S. Meacham, Summer study program in geophysical fluid dynamics: Patterns in fluid flow, Woods Hole Oceanographic Institution 92 (1991).
  58. M. Van Hecke, P. C. Hohenberg, and W. Van Saarloos, Amplitude equations for pattern forming systems, Fundamental Problems in Statistical Mechanics VIII (Elsevier, 1994), pp. 245–278.
  59. G. Krstulovic, G. Thorner, J.-P. Vest, S. Fauve, and M. Brachet, Axial dipolar dynamo action in the Taylor-Green vortex, Phys. Rev. E 84, 066318 (2011).
  60. F. Marcotte and C. Gissinger, Dynamo generated by the centrifugal instability, Phys. Rev. Fluids 1, 063602 (2016).
  61. F. Lignieres, P. Petit, M. Auriere, G. A. Wade, and T. Böhm, The dichotomy between strong and ultra-weak magnetic fields among intermediate-mass stars, Proc. Intl. Astron. Union 9, 338 (2013).
  62. J. Philidet, C. Gissinger, F. Lignières, and L. Petitdemange, Magnetohydrodynamics of stably stratified regions in planets and stars, Geophys. Astrophys. Fluid Dyn. 114, 336 (2020).
  63. P. Garaud, On rotationally driven meridional flows in stars, Mon. Not. R. Astron. Soc. 335, 707 (2002).
  64. 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).
  65. G. Rüdiger, M. Gellert, R. Hollerbach, M. Schultz, and F. Stefani, Stability and instability of hydromagnetic Taylor–Couette flows, Phys. Rep. 741, 1 (2018).
  66. U. Mitra-Kraev, L. K. Harra, D. R. Williams, and E. Kraev, The first observed stellar x-ray flare oscillation: Constraints on the flare loop length and the magnetic field, Astron. Astrophys. 436, 1041 (2005).

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Phys. Rev. Fluids 8, 123701– Published 5 December, 2023
  • Received 14 June 2023
  • Accepted 31 October 2023
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