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Numerical simulations aim to investigate the bifurcation caused by swirling flow between two coaxial vertical cylinders, and the fluid layers produced by the thermal gradient. The stability of both bifurcation and fluid layers by an axial magnetic field is analyzed. The finite-volume method is used to solve the governing Navier–Stokes, temperature and potential equations. A conducting viscous fluid characterized by a small Prandtl number [Formula: see text] is placed in the gap between two coaxial cylinders. The combination of aspect ratio, [Formula: see text] and Reynolds number, [Formula: see text] for three annular gaps ([Formula: see text] and [Formula: see text]) is compared in terms of flow stability, and heat transfer rates. Without a magnetic field, the vortex breakdown takes place near the inner cylinder due to the increased pumping action of the Ekman boundary layer. Fluid layered structures are developed by the competition between buoyancy and viscous forces. The increase in the magnitude of the magnetic field retarders the onset of the oscillatory instability caused by the disappearance of the vortex breakdown and reduces the number of fluid layers. The limits in which a vortex breakdown bubble manifests and the limits of transition from the multiple fluid layers to the single fluid layer are established.

This research aims to investigate the vortex breakdown zone, the stability margin, and the fluid layers of the rotating flow between two vertical coaxial cylinders under the effect of thermal gradient and an axial magnetic field. The governing Navier-Stokes, temperature, and potential equations are solved using the finitevolume method. Three combinations of aspect ratios (γ) and Reynolds numbers (Re) are compared. The pumping action sets up a secondary circulation along the meridional plane of the annular gap. For certain combinations, the vortex breakdown bubble occurred near the inner wall. Bifurcation in form of multiple fluid layers becomes apparent when the temperature difference exceeds a critical value. These fluid layers play the role of thermal insulation and limit the heat transfer between the hot top and cold bottom of the coaxial cylinders. Both the vortex breakdown and fluid layers could be suppressed by the magnetic field; the increasing of Hartmann number (Ha) would reduce the number of fluid layers. Diagrams represent the effect of increasing Richardson number (Ri) on fluid layers are established. Then stability diagrams corresponding to the transition from the multiple fluid layers zone to the one fluid layer zone for increasing Prandtl number (Pr) are obtained.