Journal of Physical Studies 25(2), Article 2401 [17 pages] (2021)
DOI: https://doi.org/10.30970/jps.25.2401

GENERATION OF MAGNETIC FIELDS BY THERMOMAGNETIC EFFECTS IN A NONUNIFORMLY ROTATING LAYER OF AN ELECTRICALLY CONDUCTIVE FLUID

M. I. Kopp{1} , K. N. Kulik{1}, A. V. Tur3 , V. V. Yanovsky{1,2} 

{1}Institute for Single Crystals, NAS Ukraine, 60, Nauky Ave., Kharkiv, UA–61001, Ukraine,
{2}V. N. Karazin Kharkiv National University, 4, Svobody Sq., Kharkiv, UA–61022, Ukraine,
{3}Université de Toulouse [UPS], CNRS, Institut de Recherche en Astrophysique et Planétologie, 9 avenue du Colonel Roche, BP 44346, 31028 Toulouse Cedex 4, France

Received 26 February 2021; accepted 03 April 2021; published online 03 June 2021

This paper studies, the generation of magnetic fields in a nonuniformly rotating layer of finite thickness of an electrically conducting fluid by thermomagnetic (TM) instability. This instability arises due to the temperature gradient $\nabla T_0$ and thermoelectromotive coefficient gradient $\nablaα $. The influence of the generation of a toroidal magnetic field by TM instability on the convective instability in a nonuniformly rotating layer of an electrically conductive fluid in the presence of a vertical constant magnetic field ${\bf{B}}_0 \| {\rm OZ}$ is established. By applying the method of perturbation theory for the small parameter $ ϵ = √ {(\textrm {Ra}-\textrm {Ra}_c) / \textrm {Ra}_c} $ of the supercriticality of the stationary Rayleigh number $\textrm {Ra}_c$, a nonlinear equation of the Ginzburg-Landau type was obtained. This equation describes the evolution of the finite amplitude of perturbations. Numerical solutions of this equation made it possible to determine the heat transfer in the fluid layer with and without TM effects. It is shown that the amplitude of the stationary toroidal magnetic field noticeably increases with allowance for TM effects.

Key words: thermoelectromotive force, generation of magnetic fields, Rayleigh–Benard convection, weakly nonlinear theory, Ginzburg–Landau equation

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