Hostname: page-component-848d4c4894-sjtt6 Total loading time: 0 Render date: 2024-07-05T06:26:38.507Z Has data issue: false hasContentIssue false
  • English
  • Français

On magnetic helicity generation and transport in a nonlinear dynamo driven by a helical flow

Part of: Focus on Plasma Astrophysics

Published online by Cambridge University Press:  27 August 2020

F. Cattaneo ,
G. Bodo Open the ORCID record for G. Bodo [Opens in a new window]  and
S. M. Tobias Open the ORCID record for S. M. Tobias [Opens in a new window]
F. Cattaneo
Affiliation:
Department of Astronomy and Astrophysics, University of Chicago, 5640 S. Ellis Avenue, Chicago, IL60637, USA
G. Bodo
Affiliation:
INAF, Osservatorio Astrofisico di Torino, Strada Osservatorio 20, Pino Torinese, Italy
S. M. Tobias*
Affiliation:
Department of Applied Mathematics, University of Leeds, Woodhouse Lane, LeedsLS2 9JT, UK
*
†Email address for correspondence: smt@maths.leeds.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

The relationship between nonlinear large-scale dynamo action and the generation and transport of magnetic helicity is investigated at moderate values of the magnetic Reynolds number ($Rm$). The model consists of a helically forced, sheared flow in a Cartesian domain. The boundary conditions are periodic in the horizontal and impenetrable for the vertical. The magnetic field is required to be vertical at the upper and lower boundaries. There are two consequences of this choice; one is that the magnetic helicity is not gauge invariant, the second is that fluxes of magnetic helicity are allowed in and out of the domain. We select the winding gauge, define all the contributions to the evolution of the helicity in this gauge and measure these contributions for various solutions of the dynamo equations. We vary $Rm$ and the shear strength, and find a rich landscape of dynamo solutions including travelling waves, pulsating waves and non-wave-like solutions. We find that, at the $Rm$ considered, the main contribution to the growth of magnetic helicity comes from processes throughout the volume of the fluid and that boundary terms respond by limiting the growth. We find that, in this magnetic Reynolds number regime, helicity conservation is not a strong constraint on large-scale dynamo action. We speculate on what may happen at higher $Rm$.

Keywords

astrophysical plasmas
Type
Research Article
Information
Journal of Plasma Physics , Volume 86 , Issue 4 , August 2020 , 905860408
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Berger, M. A. & Field, G. B. 1984 The topological properties of magnetic helicity. J. Fluid Mech. 147, 133–148.CrossRefGoogle Scholar
Blackman, E. G. & Field, G. B. 2000 Constraints on the magnitude of $\alpha$ in dynamo theory. Astrophys. J. 534 (2), 984–988.CrossRefGoogle Scholar
Blackman, E. G. & Field, G. B. 2002 New dynamical mean-field dynamo theory and closure approach. Phys. Rev. Lett. 89 (26), 265007.CrossRefGoogle ScholarPubMed
Bodo, G., Cattaneo, F., Mignone, A. & Rossi, P. 2017 Magnetic helicities and dynamo action in magneto-rotational turbulence. Astrophys. J. 843 (2), 86.CrossRefGoogle Scholar
Brandenburg, A. 2018 Advances in mean-field dynamo theory and applications to astrophysical turbulence. J. Plasma Phys. 84, 735840404.CrossRefGoogle Scholar
Brandenburg, A. & Subramanian, K. 2005 Astrophysical magnetic fields and nonlinear dynamo theory. Phys. Rep. 417, 1–209.CrossRefGoogle Scholar
Brummell, N. H., Cattaneo, F. & Tobias, S. M. 2001 Linear and nonlinear dynamo properties of time-dependent ABC flows. Fluid Dyn. Res. 28 (4), 237–265.CrossRefGoogle Scholar
Cattaneo, F. & Hughes, D. W. 1996 Nonlinear saturation of the turbulent $\alpha$ effect. Phys. Res. E 54, R4532–R4535.Google ScholarPubMed
Del Sordo, F., Guerrero, G., Brandenburg, A. 2013 Turbulent dynamos with advective magnetic helicity flux. Mon. Not. R. Astron. Soc. 429, 1686–1694.CrossRefGoogle Scholar
Ebrahimi, F. & Bhattacharjee, A. 2014 Helicity-flux-driven $\alpha$ effect in laboratory and astrophysical plasmas. Phys. Rev. Lett. 112 (12), 125003.CrossRefGoogle ScholarPubMed
Ebrahimi, F. & Blackman, E. G. 2016 Radially dependent large-scale dynamos in global cylindrical shear flows and the local cartesian limit. Mon. Not. R. Astron. Soc. 459 (2), 1422–1431.CrossRefGoogle Scholar
Field, G. B. & Blackman, E. G. 2002 Dynamical quenching of the $\alpha ^2$ dynamo. Astrophys. J. 572, 685–692.CrossRefGoogle Scholar
Galloway, D. J. & Proctor, M. R. E. 1992 Numerical calculations of fast dynamos in smooth velocity fields with realistic diffusion. Nature 356, 691–693.CrossRefGoogle Scholar
Gruzinov, A. V. & Diamond, P. H. 1994 Self-consistent theory of mean-field electrodynamics. Phys. Rev. Lett. 72, 1651–1653.CrossRefGoogle ScholarPubMed
Hubbard, A. & Brandenburg, A. 2010 Magnetic helicity fluxes in an $\alpha ^2$ dynamo embedded in a halo. Geophys. Astrophys. Fluid Dyn. 104, 577–590.CrossRefGoogle Scholar
Kulsrud, R. M. & Anderson, S. W. 1992 The spectrum of random magnetic fields in the mean field dynamo theory of the Galactic magnetic field. Astrophys. J. 396, 606–630.CrossRefGoogle Scholar
Moffatt, H. K. & Dormy, E. 2019 Self-Exciting Fluid Dynamos. Cambridge University Press.CrossRefGoogle Scholar
Nigro, G., Pongkitiwanichakul, P., Cattaneo, F. & Tobias, S. M. 2017 What is a large-scale dynamo? MNRAS 464, L119–L123.CrossRefGoogle Scholar
Pongkitiwanichakul, P., Nigro, G., Cattaneo, F. & Tobias, S. M. 2016 Shear-driven dynamo waves in the fully nonlinear regime. Astrophys. J. 825, 23.CrossRefGoogle Scholar
Prior, C. & Yeates, A. R. 2014 On the helicity of open magnetic fields. Astrophys. J. 787 (2), 100.CrossRefGoogle Scholar
Roberts, G. O. 1972 Dynamo action of fluid motions with two-dimensional periodicity. Phil. Trans. R. Soc. Lond. A 271, 411–454.Google Scholar
Shukurov, A., Sokoloff, D., Subramanian, K. & Brandenburg, A. 2006 Galactic dynamo and helicity losses through fountain flow. Astron. Astrophys. 448, L33–L36.CrossRefGoogle Scholar
Subramanian, K. & Brandenburg, A. 2004 Nonlinear current helicity fluxes in turbulent dynamos and alpha quenching. Phys. Rev. Lett. 93 (20), 205001.CrossRefGoogle ScholarPubMed
Sur, S., Shukurov, A. & Subramanian, K. 2007 Galactic dynamos supported by magnetic helicity fluxes. Mon. Not. R. Astron. Soc. 377, 874–882.CrossRefGoogle Scholar
Tobias, S. M. & Cattaneo, F. 2008 Limited role of spectra in dynamo theory: coherent versus random dynamos. Phys. Rev. Lett. 101 (12), 125003.CrossRefGoogle ScholarPubMed
Tobias, S. M. & Cattaneo, F. 2013 Shear-driven dynamo waves at high magnetic Reynolds number. Nature 497, 463–465.CrossRefGoogle ScholarPubMed
Tobias, S. M. & Cattaneo, F. 2015 The electromotive force in multi-scale flows at high magnetic Reynolds number. J. Plasma Phys. 81 (6), 395810601.CrossRefGoogle Scholar
Tobias, S. M., Cattaneo, F. & Brummell, N. H. 2011 On the generation of organized magnetic fields. Astrophys. J. 728, 153.CrossRefGoogle Scholar
Vainshtein, S. I. & Cattaneo, F. 1992 Nonlinear restrictions on dynamo action. Astrophys. J. 393, 165–171.CrossRefGoogle Scholar
Vishniac, E. T. & Cho, J. 2001 Magnetic helicity conservation and astrophysical dynamos. Astrophys. J. 550, 752.CrossRefGoogle Scholar
Woltjer, L. 1958 A theorem on force-free magnetic fields. Proc. Natl Acad. Sci. USA 44 (6), 489–491.CrossRefGoogle ScholarPubMed