Absolute Instability of the Rotating-Disk Boundary Layer — Theory and Experiment

Abstract

The rotating-disk boundary layer is studied. The inviscid stability of the flow and the stability with viscous, Coriolis and streamline curvature effects included have been studied. In both cases, the flow is radially absolutely unstable for certain parameters. The critical Reynolds number for absolute instability is R ≈ 510 In the experimental study, the flow was perturbed impulsively at a value of R below that at which laminar-turbulent transition is observed. Convectively unstable modes were excited, which form a wave packet that initially convects away from the source. However, the radial propagation of the trailing edge of the wave packet tended towards zero as it approached R c ; the predicted critical R for the onset of absolute instability. The accumulation of energy at a well-defined radius, may cause the onset of transition, which has been consistently observed at an average value of 513 with only a small scatter. Here, transition was observed at about this value, with and without artificial excitation of the boundary layer. This lack of sensitivity to the exact form of the disturbance environment is characteristic of an absolutely unstable flow, because absolute growth of disturbances can start from either noise or artificial sources to reach the same final state, which is determined by nonlinear effects.