The Interaction of a Point Vortex with a Boundary Layer Leading to Eruption

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Mathematics (HMC)

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A model for the entrainment of irrotational flow into a boundary layer, and the eruption and rollup of vorticity away from the wall, is studied. The model consists of a point vortex and a layer of constant vorticity, bounded below by a wall and above by an irrotational flow. Contour dynamics is used to compute the pathline of the vortex and the evolution of the interface which delineates vortical flow from irrotational flow. Four cases are studied for which the ratio of vortex strength to initial distance of the vortex above the interface is kept fixed. With this constraint, the intial vortex-induced velocity evaluated at a scaled distance along the interface is equal in all cases. Consequently, a vortex far above the boundary layer generates long-wavelength disturbances on the interface. These exhibit early-time growth which saturate as their amplitude becomes large. The interface takes the shape of a vortex-like structure as it overturns, 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. Though the vortex moves towards the layer during the course of its interaction, the change in its induced velocity on the interface is not dynamically significant. Alternatively, for a vortex initially placed close to the layer, a short-scale disturbance occurs for which the change in induced velocity due to the vertical displacement of the vortex is significant. The disturbance exhibits rapid, continuous growth that eventually rolls up around the vortex.

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© 1996 American Institute of Aeronautics and Astronautics, Inc.

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