Small-Scale Analysis of Hydrodynamical Helicity Suppression in the Mean-Field Dynamo-Model
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TICAL, NONLINEAR, AND SOFT MATTER PHYSICS
Small-Scale Analysis of Hydrodynamical Helicity Suppression in the Mean-Field Dynamo-Model E. V. Yushkova,b,c,*, A. S. Lukina,d, and D. D. Sokoloffb,c,e aSpace
Research Institute, Russian Academy of Sciences, Profsoyuznaya ul. 84/32, Moscow, 117997 Russia bMoscow State University, Moscow, 119991 Russia c Moscow Center of Fundamental and Applied Mathematics, Moscow, 119991 Russia dHigher School of Economics, National Research University, Myasnitskaya ul. 20, Moscow, 101100 Russia e Institute of Terrestrial Magnetism, Ionosphere, and Radio Wave Propagation, Russian Academy of Sciences, Troitsk, Moscow, 108840 Russia *e-mail: [email protected] Received November 6, 2019; revised January 9, 2020; accepted January 9, 2020
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 smallscale 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. DOI: 10.1134/S1063776120050118
1. INTRODUCTION The transfromation of the kinetic energy of fluid motions into magnetic energy, which leads, in particular, to the generation of the magnetic fields of the Earth, the Sun, stars, and galaxies, is commonly called a magnetohydrodynamic (MHD) dynamo (for a review, see, e.g., [1]). Two channels through which this conversion occurs can be distinguished. One of them, which is commonly called a largescale dynamo or mean-field dynamo, requires a mirror asymmetry of convection/turbulence and gives rise to a magnetic field whose scale is comparable to the sizes of the body itself. Simultaneously with the largescale generation, this mechanism also creates a smallscale component with characteristic sizes smaller than the sizes of the body. Remarkably, the mean-field dynamo equations can be formulated in such a way that they contain only the large-scale
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