Weakly Nonlinear Magnetic Convection in a Nonuniformly Rotating Electrically Conductive Medium Under the Action of Modulation of External Fields

  • Michael I. Kopp Institute for Single Cristals, NASU, Kharkiv, Ukraine https://orcid.org/0000-0001-7457-3272
  • Anatoly V. Tur Universite Toulouse [UPS], CNRS, Institute of Research for Astrophysics and Planetology, Toulouse, France https://orcid.org/0000-0002-3889-8130
  • Volodymyr V. Yanovsky Institute for Single Cristals, Nat. Academy of Science Ukraine, Kharkiv, Ukraine; V.N. Karazin Kharkiv National University, Kharkiv, Ukraine https://orcid.org/0000-0003-0461-749X
Keywords: magnetorotational instability, Rayleigh-Benard convection, critical Rayleigh numbers, weakly nonlinear theory

Abstract

In this paper we studied the weakly nonlinear stage of stationary convective instability in a nonuniformly rotating layer of an electrically conductive fluid in an axial uniform magnetic field under the influence of: a) temperature modulation of the layer boundaries; b) gravitational modulation; c) modulation of the magnetic field; d) modulation of the angular velocity of rotation. As a result of applying the method of perturbation theory for the small parameter of supercriticality of the stationary Rayleigh number nonlinear non-autonomous Ginzburg-Landau equations for the above types of modulation were obtaned. By utilizing the solution of the Ginzburg-Landau equation, we determined the dynamics of unsteady heat transfer for various types of modulation of external fields and for different profiles of the angular velocity of the rotation of electrically conductive fluid.

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Published
2020-04-03
Cited
0 article
How to Cite
Kopp, M., Tur, A., & Yanovsky, V. (2020). Weakly Nonlinear Magnetic Convection in a Nonuniformly Rotating Electrically Conductive Medium Under the Action of Modulation of External Fields. East European Journal of Physics, (2), 5-37. https://doi.org/10.26565/2312-4334-2020-2-01