Effect of a radial magnetic field on the stability of Dean flow

Abstract

The effect of a radial magnetic field on the stability of an electrically conducting incompressible fluid between two concentric non-conducting cylinders is considered. The cylinders are at rest and the motion of the fluid is due to a pressure gradient acting in the transverse direction. For arbitrary gap widths between the cylinders, the equations governing the marginal stability state of the flow are derived and solved numerically. The calculated critical parameters characterizing the onset of instability of the flow indicate that the presence of a radial magnetic flow contributes to a more stable now. It also causes the Taylor cells to contract in the axial direction of the cylinders. These effects depend on the gap width between the cylinders and are more pronounced in the presence of a strong magnetic field.