Surfactant effects on the interaction of a three dimensional vortex pair with a free surface; and,

Abstract

In part I of the thesis, a canonical problem of three dimensional surfactant hydrody namics, the three-dimensional laminar interaction between a clean or contaminated free surface and a vortical flow underneath is considered. Initially, the vortical flow is in the form of two modulated finite-core vortex tubes parallel to the free surface. The vortex tubes break down via instability and helical vorticity is generated. The most prominent feature at the surface is that associated with the connection of helical vorticity to the free surface. For clean surface, the helical vorticity would interact fully with the free surface and reconnects to it under the influence of the primary vorticity. The presence of surfactant leads to substantial increase in the generation of free-surface secondary vorticity which results from large gradients in the surface surfactant distribution created by induced velocities at the free surface due to the primary vortex tubes. The secondary structure in the bulk interacts with the he lical vorticity, which totally alters the vortex pattern and connection process. The presence of contamination considerably weakens the connection in terms of strength, location and duration. The degree of secondary vorticity generation by the surfac tant is limited by a closed-loop interaction between the flow field (primary flow and secondary flow) and surfactant transport.

(cont.) The presence of secondary vorticity tends to smooth out the surfactant distribution on the free surface and consequently leads to a reduction in the generation of secondary vorticity itself associated with the sur factant gradient (together with surfactant diffusion). This negative feedback process and the rebounding of the primary vorticity by the secondary vorticity are the key processes underlying effects of insoluble surfactant. For contaminated free surface, the secondary and helical vortical structures interact strongly and new structures are generated. The split of helical vorticity because of the strong secondary vorticity leads to the new structures. When the surfactant is soluble, the effects are generally diminished due to the sorption kinetics between the surface and the bulk phase. Both vorticity isosurfaces and vortex filaments are used to describe vortex structures and their evolution. In Part II of the thesis, we investigated the turbulent flow over a smooth wavy wall undergoing traveling wave motion in the mean flow direction. Results are presented from direct numerical simulation with periodic and non-periodic streamwise boundary conditions. The Reynolds number in terms of mean velocity and motion wavelength is in the range of 3000-6500 and wave phase speed c relative to incoming flow velocity U is in the range of -0.5 and 2.0. The flow pattern is a strong function of c/U.For c = 0, there are features like separated region, attached boundary layer, and free shear layer ...