The majority of this work is concerned with the <i>local</i>-linear stability of the incompressible boundary-layer flows over rotating spheres and rotating cones; convective and absolute instabilities are investigated and the effects of viscosity and streamline-curvature are included in each analysis. Preliminary investigations into the linear <i>global</i>-mode behaviour of the rotating-disk, rotating-cone and rotating-sphere boundary layers are also presented. The local rotating-sphere analyses are conducted at various latitudes from the axis of rotation (<i>q</i>), and the local rotating-cone analyses are conducted at points along cones of various half-angles (<i>ψ</i>), in each case convective and absolute instabilities are found within specific parameter spaces. The predictions of the Reynolds number, vortex angle and vortex speed at the onset of convective instability are consistent with existing experimental measurements for both boundary-layer types. Axial flow is found to stabilize each boundary layer with respect to convective and absolute instabilities. The global behaviour of the boundary-layer flows over rotating disks, cones and spheres is considered by taking into account the slowly varying basic state along each body surface. The locations of saddle points in the absolute frequency are determined which give the leading-order estimate of the global frequency. For the rotating disk and rotating cones, the global frequency indicates the disturbances in the boundary-layer flow are globally damped; and for rotating spheres, the global frequency indicates the boundary layer may support neutrally stable global modes when a region of absolute instability exists.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:599330 |
| Date | January 2002 |
| Creators | Garrett, S. J. |
| Publisher | University of Cambridge |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
Page generated in 0.0018 seconds