Linear stability of a rotating channel flow subjected to a static magnetic field

Abstract

Magnetohydrodynamics is effective to control the instabilities of fluid flows. This control process is cost-effective and compact because it does not require extra mechanical components. In the present study, the effect of a constant uniform magnetic field on the linear stability of a rotating channel flow is investigated. The electromagnetic field is applied in the spanwise direction alongside the axis of rotation. The Hartmann and rotation numbers characterize the magnetic and rotational effects. The axial flow is governed by the centrifugal force, and the Coriolis force due to rotation makes the flow unstable at relatively low Reynolds numbers concerning spanwise disturbances. The modal instabilities of the flow are captured by solving the Orr–Sommerfeld–Squire eigenvalue problem. Numerical results confirm that the employed magnetic force has a prominent stabilizing role on the linear instabilities of the rotating channel flow. Notably, the higher Hartmann numbers suppress the temporal growth of the most unstable mode and decrease the area of neutral stability boundaries. The onset of rotational instability occurs at a higher critical Reynolds number for a stronger magnetic field. Further, the presence of Lorentz force restricts the co-existence of multiple unstable modes and the mode competition phenomenon, which results in structure modification of roll-cells and tardy secondary flow. The findings of this investigation would be useful in designing bio-medical and mechanical tools where the rotational instabilities are harmful. Furthermore, it is hoped that the obtained results will motivate the experimental verification and look for worthy applications.