Formula omitted] attractor bifurcation analysis for an electrically conducting fluid flow between two rotating cylinders

Abstract

This work formulates the simplified governing equations for an electrically conducting fluid flow between two concentric rotating cylinders. We consider the case where the flow is under the influence of an electric current (axial current) of suitable constant density passing axially through the fluid and a line current (center current) moving along the axis of the two concentric cylinders. Furthermore, we show that the simplified governing equations bifurcate to an S1 attractor (a 1-dimensional sphere) when the magnetic Taylor number crosses a critical value. Notably, the S1 attractor contains precisely eight singular points, four of which are stable nodes and the remaining are saddle points, with the impact of the magnetic field generated only by the axial electric current. If the magnetic field is mainly produced by the center electric current, the number of singular points of the S1 attractor can only be four, with two saddle points, and two stable nodes. In addition, our research shows that the axial current accelerates the S1 attractor bifurcation but the center current has the opposite effect, in comparison with the flow without the influence of a magnetic field.