Journal of Physical Studies 26(4), Article 4401 [16 pages] (2022)
DOI: https://doi.org/10.30970/jps.26.4401

THERMOMAGNETIC INSTABILITIES IN A NONUNIFORMLY ROTATING ELECTRICALLY CONDUCTIVE FLUID

M. I. Kopp{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, du Colonel Roche Ave., BP 44346, 31028 Toulouse Cedex 4, France

Received 11 April 2022; in final form 10 August 2022; accepted 21 September 2022; published online 17 November 2022

The paper investigates the stability of small axisymmetric disturbances in a nonuniformly rotating viscous electrically conductive fluid taking into account galvanometric and thermo-magnetic phenomena. In the local geometrical optics approximation, we obtained a dispersion equation taking into account the Hall, the Nernst, the Righi-Leduc effects and gradients of temperature $\nabla T_0$ and thermo-electromotive force coefficient $\nablaα $ in constant magnetic field ${\bf{B}}_0$ and gravitational field ${\bf{g}}$. The growth rates of thermomagnetic instability (TMI) in a nonuniformly rotating electrically conducting fluid without an external magnetic field (${\bf{B}}_0 =0$) are obtained for the case of “smooth” (a weakly inhomogeneous medium) gradients ($\nabla T_0$ and $\nablaα $ ). The regions of the development of TMI are established depending on the profile of the angular velocity of rotation (Rossby number Ro) and the radial wave number $k_R$. The conditions under which the generation of a magnetic field with sharp gradients of temperature and thermo-electromotive force coefficient in the media with low $(σ → 0)$ and high $(σ → ∞)$ conductivity are found. The regions of the development of the Hall magnetorotational instability in an external magnetic field (${\bf{B}}_0\neq 0$) are established depending on the profile of the angular rotation velocity (Rossby number Ro) and the axial wavenumber $k_z$. The growth rates of TM instabilities for the propagation of perturbations with a wave vector ${\bf{k}}$ in the radial direction ${\bf{k}}\| {\bf{e}}_R$ are obtained taking into account the Nernst effect in an external magnetic field ${\bf{B}}_0$, the Righi-Leduc effect, the inhomogeneity of the equilibrium temperature and specific thermopower, and the buoyancy force in a temperature-stratified medium.

Key words: thermoelectromotive force, generation of magnetic fields, thermomagnetic instability, Boussinesq approximation, nonuniformly rotating electrically conductive fluid.

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