Boundary layers that are associated the motion of a rotating disk have been extensively studied for more than fifty years, both theoretically and in physical experiments. For the von Karman case, where the rotation is within a fluid that is stationary at large distances from the disk, the laminar-turbulent transition location has been found to be relatively constant in many physical experiments. One possible explanation for this constancy is that the flow is absolutely unstable near to the transition location.
We will discuss the connection between local absolute instability and global instability for rotating disk boundary layer flows. It turns out, rather intriguingly, that local temporal frequency variation can globally stabilize the flow, even when it is becoming more and more locally unstable. This frequency ‘detuning’ effect can also work in reverse. Flow control strategies which improve the local stability of the flow, such as the application of suction at the disk surface or the imposition of an axial magnetic field, can lead to a novel form of global instability. Unlike the case of wake flows, where absolute instability usually gives rise to a global mode with a well-defined frequency, globally unstable disturbances in rotating disk boundary layers appear to develop with a continually changing oscillation frequency.
The above phenomena will be illustrated using direct numerical simulation results. They will also be modelled with simple impulse solutions of the linearized GL equation, which prove to be surprisingly effective in capturing the essential features of the behavior. In particular, the introduction into the model of a single complex parameter suffices to capture the differences between the local and global disturbance evolution.