Primary instability mechanisms on the magnetohydrodynamic boundary layer flow over a rotating disk subject to a uniform radial flow

Abstract

This paper is devoted to the investigation of three primary linear instability mechanisms due to the resonating disturbance waves present in the three-dimensional incompressible viscous/inviscid rotating disk boundary layer flow, extending our earlier still outer fluid work [M. Turkyilmazoglu, “Resonance instabilities on the boundary layer flow over a rotating-disk under the influence of a uniform magnetic field,” J. Eng. Math. 59, 337 (2007)] to a uniform nonzero radial flow. A spatiotemporal linear stability analysis is conducted to search for the influences of physical parameters on the possible important mechanisms of resonances leading to, respectively, the absolute instability, the direct spatial instability, and the direct temporal instability. The radial flow is shown to act in the way of stabilizing all the possible mechanisms considered, more pronouncedly as the magnetic field gets strengthened. The onset of absolute instability and convective temporal instability is found to be more sensitive to the variations in the radial flow than is the onset of convective direct spatial instability. Although a considerable delay of the onset of absolute instability as well as temporal instability can be achieved by increasing the magnitude of the radial flow, the direct spatial resonance instability mechanism persists to occur for low Reynolds numbers, while the flow is still in the laminar regime, which is expected to trigger nonlinearity just prior to transition to turbulence.