Ph.D Thesis


Ph.D StudentVictoria Suponitsky
SubjectThe Generation of Streaks and Hairpin Vortices from a
Localized Vortex Disturbance Embedded in
Unbounded Uniform Shear Flow
DepartmentDepartment of Aerospace Engineering
Supervisors Full Professors Cohen Jacob
Professor Emeritus Bar-Yoseph Pinhas


Abstract

Since the coherent structures (streaks and hairpin vortices) have been discovered in turbulent boundary layers, an enormous amount of experimental, numerical and theoretical work has been carried out to investigate their generation and regeneration mechanisms. This thesis demonstrates the capability of a simple model of interaction between a localized vortical disturbance and laminar uniform unbounded shear flow, to reproduce the generation mechanism and characteristics of these coherent structures that naturally occur in fully developed turbulent boundary layers. The effects of the disturbance ‘localized character’ in streamwise and spanwise directions plus its initial orientation relative to the base flow are investigated by using several geometries of the initial disturbance. The results demonstrate that a small amplitude initial disturbance (linear case) eventually evolves into a streaky structure independent of its initial geometry and orientation, whereas, a large amplitude (strongly non-linear case) disturbance evolves into a hairpin vortex (or a packet of hairpin vortices) that is independent of its geometry over a wide range of the initial disturbance orientations. The main non-linear effects are: (i) self-induced motion, which results in movement of the vortical structure relative to the base flow and the destruction of its streamwise symmetry, (ii) the coincidence between the direction of the vorticity lines and the vortical structure. This is unlike the linear case, where there is a strong deviation of the vorticity vector from the direction of the vortical structure, i.e. the vortical structure cannot be represented as a vortex filament. The quantitative evolution of the disturbance has been found to be sufficiently independent of the initial disturbance geometry, whereas the quantitative characteristics, i.e. inclination angle, center and strength (which is governing by the transient growth mechanism), strongly depend on the disturbance geometry. The Reynolds number has been found to have a negligible effect on the kinematics of the vortical structure, but does have a significant effect on its transient growth. Finally, the formation of the asymmetric hairpin vortex is demonstrated.