On the effects of suction and injection on the absolute instability of the rotating-disk boundary layer

Abstract

In this paper we are concerned with the theoretical behavior of the laminar von Kármán boundary-layer flow, extending the work presented by Lingwood [J. Fluid Mech. 299, 17 (1995); 314, 373 (1996)] to the flow with mass transfer at the surface of the disk. It is known that, within specific regions of the parameter space, the flow is absolutely unstable in the radial direction, i.e. disturbances grow in time at every radial location within these regions. Uniform suction through the disk is shown to delay the onset of absolute instability, while uniform injection promotes the onset. By comparing suction and injection velocities of the same magnitude, it is shown that suction has a greater stabilizing effect on the absolute instability than the destabilizing effect of injection. Suction is also strongly stabilizing to both stationary and travelling inviscidly unstable branch-1 modes; injection is destabilizing. Stationary viscously unstable branch-2 modes are strongly stabilized and destabilized by suction and injection, respectively, but travelling branch-2 modes are shown to be much less sensitive to mass transfer through the disk.