|M.Sc Thesis||Department of Aerospace Engineering|
|Supervisors:||Prof. Cohen Jacob|
|Dr. Vladimir Levinski|
Hydrodynamic stability of swirling flows has been a primary subject for research since the discovery of vortex breakdown phenomenon on slender wings at high angles of attack.
In this work we investigate the growth of optimal disturbances in swirling and non-swirling columnar flow. First we study non-rotating circular pipe flow. Optimal disturbances are found for spatial and temporal stability analysis. For both cases, the initial disturbance that yields maximum transient growth, has a similar character. It is further shown that in both cases the transient growth mechanism is based on the interference between pairs of the least stable modes. In particular, the distance (for the spatial case) and the time (for the temporal case) at which the maximum growth is obtained is well predicted analytically. The spatial analysis is also used to find optimal disturbances in circular rotating pipe flow. It is shown that initial disturbances, composed of both growing and decaying modes, can achieve significant growth which is orders of magnitude larger than the maximum growth that can be achieved by the most unstable mode only. Finally, unlike the case of non-rotating flow, in swirling pipe flow the growth mechanism of optimal disturbances is found to be a multiple-mode phenomenon, and not a pair-mode mechanism.