The convective instability of the BEK system of rotating boundary-layer flows over rough disks

A numerical study investigating the effects of surface roughness on the stability properties of the BEK system of flows is introduced. The BEK system of flows occur in many engineering applications such as turbo-machinery and rotor-stator devices, therefore they have great practical importance. Recent studies have been concerned with the effects of surface roughness on the von Kármán flow. The aim of this thesis is to investigate whether distributed surface roughness could be used as a passive drag reduction technique for the broader BEK system of flows. If it can, what is “the right sort of roughness?" To answer these questions, a linear stability analysis is performed using the Chebyshev collocation method to investigate the effect of particular types of distributed surface roughness, both anisotropic and isotropic, on the convective instability characteristics of the inviscid Type I (cross-flow) instability and the viscous Type II instability. The results reveal that all roughness types lead to a stabilisation of the Type I mode in all flows within the BEK family, with the exception of azimuthally-anisotropic roughness (radial grooves) within the Bődewadt flow which causes a mildly destabilising effect. In the case of the Type II mode, the results reveal the destabilising effect of radially-anisotropic roughness (concentric grooves) on all the boundary layers, whereas both azimuthally-anisotropic and isotropic roughness have a stabilising effect on the mode for Ekman and von Kármán flows. Moreover, an energy analysis is performed to investigate the underlying physical mechanisms behind the effects of rough surfaces on the BEK system. The conclusion is that isotropic surface roughness is the most effective type of the distributed surface roughness and can be recommended as a passive-drag reduction mechanism for the entire BEK system of flows.