Effects of the suction/injection and external free stream on the instability of a boundary layer over a rotating disk

In this paper, we investigated the effectiveness of the strength of axial flow and suction/injection for the viscous mode (type II) instability within the boundary layer of a rotating disk. To investigate the lower branch, we scaled the viscous mode by using a familiar triple-deck structure analogous to that which was found for Blasius flow over a flat plate. We also analyzed the linear stability behavior of high-Reynolds laminar-turbulent transition. To describe the stationary type II wavenumber and waveangle, we conducted an asymptotic analysis followed by a comparison with the type I mode. We found that a positive axial flow had a stabilizing effect and vice versa a negative axial flow exhibited a destabilizing effect. The results were consistent with previous studies in the literature for positive axial flow, as disturbances were advected downstream in the radial direction. Regarding the suction/injection study, we found suction to be stabilizing, which aligns with previous results in the literature although, conversely, the injection was found to be destabilizing. For the numerical analysis, we found that parameters which result in an increase or decrease of the critical Reynolds number led to a stabilization or destabilization of the flow, respectively. Finally, we compared the asymptotic and numerical stability results for both types I and II followed by the critical Reynolds numbers comparisons, which were found to be consistent in general with results in the literature.