Magnetic convection in a nonuniformly rotating electrically conductive medium in an external spiral magnetic field
M. I. Kopp, A. V. Tur, Vladimir Yanovsky
Abstract
Abstract The research is devoted to the stability of convective flow in a nonuniformly rotating layer of an electrically conducting fluid in a spiral magnetic field. The stationary and oscillatory modes of magnetic convection are considered depending on the profile of the angular rotation velocity (Rossby number Ro) and on the profile of the external azimuthal magnetic field (magnetic Rossby number Rb). The non-linear dynamic system of Lorentz type equations is obtained by using the Galerkin method. Numerical analysis of these equations has shown the presence of chaotic behavior of convective flows. The criteria of the occurrence of chaotic movements are found. It depends on the parameters of convection: dimensionless numbers of Rayleigh Ra, Chandrasekhar Q, Taylor Ta, and external azimuthal magnetic field with the Rossby magnetic number Rb for Rayleigh (Ro = −1) and Kepler <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:mtext>Ro</mml:mtext> </mml:mrow> <mml:mo>=</mml:mo> <mml:mo>−</mml:mo> <mml:mn>3</mml:mn> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>4</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:math> profiles of the angular rotation velocity of the medium.