Journal of Physical Studies 27(2), Article 2403 [17 pages] (2023)
DOI: https://doi.org/10.30970/jps.27.2403

CHAOTIC DYNAMICS OF MAGNETIC FIELDS GENERATED BY THERMOMAGNETIC INSTABILITY IN A NONUNIFORMLY ROTATING ELECTRICALLY CONDUCTIVE FLUID

M. I. Kopp1} , A. V. Tur3 , V. V. Yanovsky1,2 

1Institute for Single Crystals, NAS Ukraine, 60, ave. Nauky, Kharkov, UA–61072, Ukraine,
2V. N. Karazin Kharkiv National University, 4, Svobody Sq., Kharkov, UA–61022, Ukraine
3Université de Toulouse [UPS], CNRS, Institut de Recherche en Astrophysique et Planétologie,
9, ave. du Colonel Roche, BP 44346, 31028 Toulouse Cedex 4, France

Received 10 2023; in final form 18 May 2023; accepted 26 May 2023; published online 15 June 2023

The chaotic behavior of thermal convection in a nonuniformly rotating electrically conductive fluid under the action of a constant vertical magnetic field ${\bf B}_0$ is studied. In the presence of vertical temperature gradients $\nabla T_0$ and the thermo-electromotive force coefficient $\nablaα $, thermomagnetic (TM) instability arises, leading to the generation of magnetic fields. The magnetic field ${\bf B}_1$ excited by the effect of the Biermann battery is directed perpendicular to the plane of the vectors $\nabla T_0$, $\nablaα $, and the gradient of temperature disturbances $\nabla T_1$. This magnetic field changes the heat transfer regime, and due to the effects of convective heat transfer and Righi-Leduc, a positive feedback is established, which leads to an increase in magnetic field disturbances. Using the truncated Galerkin method, a nonlinear dynamic system of equations is obtained, which describes the processes of generation and regeneration of the magnetic field. Numerical analysis of these equations showed the existence of a regular, quasi-periodic, and chaotic behavior of magnetic field disturbances, accompanied by its inversions. Applying the method of perturbation theory to the nonlinear dynamic system of equations, we obtained the Ginzburg-Landau equation for the weakly nonlinear stage of nonuniformly rotating magnetic convection, taking into account TM effects. The solution of this equation showed that the stationary level of the generated magnetic fields increases with allowance for the influence of the TM instability.

Key words: generation of magnetic fields, thermomagnetic instability, chaotic behavior, Ginzburg–Landau equation.

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