The effects of surface mass flux on the instability of the BEK system of rotating boundary-layer flows

We consider the effect of mass flux through the lower boundary of the general class of rotating BEK boundary-layer flows. This class includes the Bödewadt, Ekman and von Kármán flows as particular cases. A theoretical study is presented which considers the onset of convective instability modes (both stationary and travelling relative to the rotating system) and local absolute instability. Suction is found to be universally stabilising in terms of both the delayed onset and reduced amplification rates of both instability types. Furthermore, the radial span of convective instability preceding the onset of local absolute instability is extended with increased suction. Slowly travelling modes are predicted to be more dangerous than stationary modes within the convectively unstable region of each flow. Such modes are expected to be selected over highly polished lower disks. Extensive theoretical data is presented for future comparison to experiment.