Abstract
We compare the classical mean-field dynamo model proposed by Steenbeck, Krause, and Rädler to describe the generation of large-scale magnetic fields and the Kazantsev model that describes the small-scale dynamo in an unbounded homogeneous and isotropic flow. We consider the subcritical regime of small magnetic Reynolds numbers whereby there is no rapid generation. The same regime can also be understood as a process in which the small-scale generation is stopped due to its intrinsic mechanisms. Within both approaches we examine what distinguishes the spectra of the linear and nonlinear processes under the suppression of hydrodynamic (kinetic) helicity or, in other words, compare the alpha-quenchings. We check whether averaging the induction equation over scales larger than the velocity field correlation length leads to the loss of any features in the spectrum near the dissipative scale. We study the various types of dynamo stabilization using which seems more justified physically than the standard alpha-quenching, but more difficult within large-scale models containing limited information about the random velocity field. In particular, we compare the integral suppression whereby the total energy is conserved and the spectral suppression that suggests the conservation of energy and helicity in each spectral shell without assuming their redistribution over the spectrum.
Similar content being viewed by others
REFERENCES
D. D. Sokoloff, R. A. Stepanov, and P. G. Frick, Phys. Usp. 57, 292 (2014).
A. Ruzmaikin, D. Sokoloff, and A. Shukurov, Mon. Not. R. Astron. Soc. 241, 1 (1989).
K. Subramanian, Mon. Not. R. Astron. Soc. 294, 718 (1998).
Ya. B. Zeldovich, A. A. Ruzmaikin, and D. D. Sokoloff, Magnetic Fields in Astrophysics (Gordon and Breach, New York, 1983).
F. Krause and K.-H. Räadler, Mean-Field Magnetohydrodynamics and Dynamo Theory (Pergamon, Oxford, 1980).
S. A. Molchanov, A. A. Ruzmaikin, and D. D. Sokolov, Sov. Phys. Usp. 28, 307 (1985).
A. P. Kazantsev, Sov. Phys. JETP 26, 1031 (1967).
R. Kraichnan and S. Nagarajan, Phys. Fluids 10, 853 (1967).
S. Vainshtein and L. Kichatinov, J. Fluid Mech. 168, 73 (1986).
F. Cattaneo and S. I. Vainshtein, Astrophys. J. 376, L21 (1991).
A. V. Gruzinov and P. H. Diamond, Phys. Rev. Lett. 72, 1651 (1994).
A. Bhattacharjee and Y. Yuan, Astrophys. J. 449, 739 (1995).
A. Brandenburg and K. J. Donner, Mon. Not. R. Astron. Soc. 288, L29 (1997).
D. Sokoloff, A. Shukurov, and A. Ruzmaikin, Geophys. Astrophys. Fluid Dyn. 25, 293 (1983).
O. Artamonova and D. Sokolov, Vestn. MGU 27, 8 (1986).
D. Sokoloff, E. Yushkov, and A. Lukin, Geomagn. Aeron. 57, 844 (2017).
V. G. Novikov, A. A. Ruzmaikin, and D. D. Sokolov, Sov. Phys. JETP 58, 527 (1983).
E. Yushkov, Geomagn. Aeron. 109, 450 (2015).
E. Yushkov, A. Lukin, D. Sokoloff, and P. Frick, Geomagn. Aeron. 113, 184 (2018).
E. V. Yushkov, A. S. Lukin, and D. D. Sokoloff, J. Exp. Theor. Phys. 128, 952 (2019).
D. Sokoloff and N. Yokoi, J. Plasma Phys. 84, 7 (2018).
A. Brandenburg, S. H. Saar, and C. R. Turpin, Astrophys. J. Lett. 498, 51 (1998).
E. V. Yushkov and D. D. Sokoloff, Izv., Phys. Sol. Earth 54, 652 (2018).
F. Plunian, R. Stepanov, and P. Frick, Phys. Rep. 523, 1 (2013).
R. Beck, A. Brandenburg, D. Moss, A. Shukurov, and D. Sokoloff, Ann. Rev. Astron. Astrophys. 34, 155 (1996).
D. Sokoloff, A. Khlystova, and V. Abramenko, Mon. Not. R. Astron. Soc. 451, 6040 (2015).
Ya. B. Zel’dovich, S. A. Molchanov, A. A. Ruzmaikin, and D. D. Sokolov, Sov. Phys. Usp. 30, 353 (1987).
Funding
The work of D.D.S. and A.S.L. on the formulation of the problem and the search for methods of its solution was supported by the Russian Foundation for Basic Research (project no. 18-02-00085). The numerical experiment carried out by E.V.Y. and the interpretation of results by all authors were supported by the BAZIS Foundation (project no. 18-1-1-77-3)
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated by V. Astakhov
Rights and permissions
About this article
Cite this article
Yushkov, E.V., Lukin, A.S. & Sokoloff, D.D. Small-Scale Analysis of Hydrodynamical Helicity Suppression in the Mean-Field Dynamo-Model. J. Exp. Theor. Phys. 130, 935–944 (2020). https://doi.org/10.1134/S1063776120050118
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063776120050118