model of the horseshoe vortex in juncture flows

When a boundary-layer flow, either laminar or turbulent, encounters a hemispherical body extending from a surface, a horseshoe-shaped vortex forms at the juncture. In this thesis, we study the evolution of this vortex using a numerical inviscid model and laboratory experiments. The numerical model is based on determining the evolution of the filament using the cut-off method. The assumption is that although the generation of the vortex depends on viscous effects, the dynamic evolution is well described by inviscid equations of motion. It is found that the vortex filament is fairly steady on the upstream side but on the downstream side, travelling waves appear on it which cannot be suppressed through evolution. For a range of Reynolds number, steady horseshoe-shaped vortex was obtained in the experiments, revealing the shape past the hemisphere. This is compared with the numerical results.