Disturbance evolution in rotating-disk boundary layers: Competition between absolute instability and global stability

Results obtained from the numerical simulation of linearized disturbance evolution in various rotating disk boundary-layers can be modelled using impulse solutions of the Ginzburg-Landau equation. An explanation may thus be given of why there appears to be no unstable linear global mode for the von Kármán boundary layer, even though it is subject to a strong form of absolute instability. The stability effects of applying suction at the disk surface, or imposing an axial magnetic field, have also been investigated. In both of these cases, numerical simulation results indicated that local stabilization, which had previously been predicted to lead to a postponement of absolute instability to higher Reynolds numbers, could in fact be associated with the introduction of a new form of global instability. The modelling approach, based on comparisons with solutions of the Ginzburg-Landau equation, provides some insight into how such behaviour can arise.