Complex Analysis Of Rotating Boundary Layer Flows

A comprehensive study of the linear stability of laminar-turbulent transitions is presented in this thesis for high-Reynolds-number boundary layer flows over a rotating disk, with particular focus on the influence of axial flow in the surface-normal direction. The original contribution of this research lies in the detailed analysis of how axial flow interacts with the boundary layer in both steady and non-steady regimes, alongside the effects of uniform suction and injection. The study introduces a novel asymptotic and numerical framework for analysing the behavior of inviscid Type I and viscous Type II modes under varying conditions. A key aspect of this work is the development of new formulations for the wavenumber and waveangle for Type II modes, and their comparison with Type I modes under stationary conditions. The findings demonstrate that positive axial flow has a stabilising effect on the boundary layer, while negative axial flow leads to destabilisation a result that confirms and extends prior research. The influence of suction and injection is further explored, with original insights revealing that suction consistently stabilises the flow, while injection destabilises it, with distinct impacts on Type I and Type II modes. Furthermore, this study contributes a new analysis of the critical Reynolds number and how parameter variations impact flow stability. The effects of travelling modes, which move faster or slower relative to the disk’s rotation, are also explored in detail. A significant finding is the discovery that negative frequency values entirely eliminate Type II modes, while positive frequency values destabilise them by reducing the critical Reynolds number. These results highlight the complex interplay between axial flow, suction, and travelling modes, providing new insights into the control and stability of boundary layer flows over rotating disks. Of note, the work conducted in this thesis has been published in two papers 1, 2, while the remaining part of the travelling mode is submitted to the Physical Review Fluids 3.