Magnetic Convection in a Nonuniformly Rotating Electroconducting Medium
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TICAL, NONLINEAR, AND SOFT MATTER PHYSICS
Magnetic Convection in a Nonuniformly Rotating Electroconducting Medium M. I. Koppa, A. V. Tourc,*, and V. V. Yanovskya,b,** a
Institute of Single Crystals, National Academy of Sciences of Ukraine, Kharkov, 61001 Ukraine b Karazin Kharkov National University, Kharkov, 61000 Ukraine c Université de Touluse [USP], CNRS, Institut de Recherche en Astrophysique et Planétologie, BP 44346, Toulouse Cedex 4, 31028 France *e-mail: [email protected] **e-mail: [email protected] Received June 24, 2018
Abstract—We study the stability of a convective flow in a nonuniformly rotating plasma layer in an axially uniform magnetic field. The stationary and oscillating regimes of magnetic convection are considered depending on the angular velocity profile (Rossby number Ro) of the electroconducting medium. Using the Galerkin method for describing the weakly nonlinear stage of evolution of convection, we have obtained a nonlinear dynamic system of Lorentz-type equations. Numerical analysis of these equations has revealed the chaotic behavior of convective flows. The criteria for the emergence of chaotic flows are obtained depending on parameters of convection (Rayleigh number Ra), magnetic field (Chandrasekhar number Q), and rotation (Taylor number Ta) for the Rayleigh (Ro = –1) and Kepler (Ro = –3/4) angular velocity profiles of the medium. DOI: 10.1134/S106377611812018X
1. INTRODUCTION Convective flows induced by thermal processes in a gravitational field are important for explaining many phenomena occurring in the interior of planets, stars, and other space objects. It is generally accepted that convection is the source of generation of large-scale magnetic fields as well as large-scale vortex structures irrespective of the choice of the model (laminar [1–4] or turbulent dynamo [5–7]). Rotation and magnetic fields undoubtedly strongly affect the convective flows of electroconducting media. The theory of such processes (Rayleigh– Bénard problem) for 1D rotation and constant magnetic field was described in detail in monographs [8, 9]. However, the rotation of most cosmic objects consisting of high-density gases or liquid (Jupiter, Saturn, Sun, galaxies, etc.), as well as electroconducting media in the planetary interior, is nonuniform. In many hydrodynamic problems, the differential rotation of the medium is simulated by the Couette flow confined between two cylinders rotating with different angular velocities (Fig. 1a), which is found to be convenient for performing laboratory experiments [10]. The stability of such a flow for a perfectly conducting medium in a magnetic field was considered for the first time in [11, 12]. It was shown that a weak axial magnetic field destabilizes the azimuthal differential
rotation of the plasma; when condition dΩ2/dR < 0 is satisfied, the magnetorotational instability (MRI) of the standard magnetorotational instability (SMRI) appears in a nondissipative plasma (see Fig. 1a). Since this condition also holds for Kepler flows with Ω ~ R–3/2, the
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