Interacting vortex and vortex layer: How length scale affects entrainment and ejection

A contour dynamics model of the interaction between a point vortex and a layer of constant vorticity, bounded below by a slip wall and above by irrotational flow, is studied. The height of the vortex above the layer establishes a length scale that is found to have a strong influence on both the evolution of the layer and the vertical displacement of the vortex. A vortex far above the boundary layer generates long-wavelength disturbances. These exhibit early-time growth, which saturates, taking on the shape of a vortex-like structure, suggesting that a vortex far above a boundary layer can create another one within the layer. Concurrently, entrainment of irrotational flow deep into the layer occurs within a narrow crevice. Alternatively, for a vortex initially placed close to the layer, a short-scale disturbance occurs that exhibits rapid, continuous growth that eventually rolls up around the vortex. Here, accounting for the vertical displacement of the vortex is necessary to accurately determine the interface evolution. The results support the contention that a vortex can induce ejection and roll up of the boundary layer and entrainment of irrotational flow into the layer.