Rayleigh-Benard convection in a nonuniformly rotating electrically conductive medium in an external spiral magnetic field

TL;DR

This paper investigates the stability and chaotic behavior of convective flows in a nonuniformly rotating, electrically conducting fluid under a spiral magnetic field, revealing how various parameters influence flow chaos.

Contribution

It introduces a nonlinear Lorentz-type system modeling magnetic convection in rotating media and analyzes how parameters induce chaos, extending understanding of magnetoconvection stability.

Findings

Chaotic convective behavior depends on Rossby and magnetic Rossby numbers.

Criteria for chaos are derived based on dimensionless parameters.

Flow stability varies with rotation and magnetic field profiles.

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 $\textrm{Ro}$) and on the profile of the external azimuthal magnetic field (magnetic Rossby number $\textrm{Rb}$). The nonlinear 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 $\textrm{Ra}$, Chandrasekhar $\textrm{Q}$, Taylor $\textrm{Ta}$, and external azimuthal magnetic field with the Rossby magnetic number $\textrm{Rb}=-1$ for Rayleigh $(\textrm{Ro}=-1)$ and Kepler $(\textrm{Ro}=-3/4)$ profiles of the angular rotation velocity of the medium.