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Stability of Oscillatory Rotating Disk Boundary Layers

The rotating disk boundary layer has long been considered as providing an archetypal model for studying the stability of three-dimensional boundary-layer flows, and the crossflow inflexion point instability mechanism is common to both the rotating disk boundary layer and the flow over a swept wing. Thus the investigation of strategies for controlling the behaviour of disturbances that develop in the rotating disk flow may prove to be helpful for the identification and assessment of aerodynamical technologies that have the potential to maintain laminar flow over swept wings.

We will consider the changes in the stability behaviour that arise when the rotating disk base-flow configuration is altered by imposing a periodic modulation in the rotation rate of the disk surface. Thomas et. al. [Proc. R. Soc. A (2011) 467:2643-2662] have previously demonstrated that Tollmien-Schlichting waves can be stabilised when a similarly induced Stokes layer is conjoined to a plane channel flow.

Current work encompasses three distinct investigatory approaches. Linearised direct numerical simulations have been conducted, using the vorticity-based methods that were first adopted by Davies & Carpenter [J. Comput. Phys (2001) 172:119-165]. These simulations are complemented by a local in time linear stability analysis, that is made possible by imposing an artificial frozen base-flow approximation. This localised analysis is deployed together with a more exact global treatment based upon Floquet theory, which avoids the need for any simplification of the temporal dependency of the base-flow.