The interaction of a counter-rotating vortex pair (dipole) with a flat plate in its path is studied numerically. The vortices are initially separated by a distance $D$ (dipole size) and placed far upstream of a plate of length $L$. The plate is centered on the dipole path and inclined relative to it at an incident angle ${\beta }_i$. At first, the plate is held fixed in place. The vortices approach the plate, travel around it, and then leave as a dipole with unchanged velocity but generally a different travel direction, measured by a transmitted angle ${\beta }_t$. For certain plate angles the transmitted angle is highly sensitive to changes in the incident angle. The sensitivity increases as the dipole size decreases relative to the plate length. In fact, for sufficiently small values of $D/L$, singularities appear: near critical values of ${\beta }_i$, the dipole trajectory undergoes a topological discontinuity under changes of ${\beta }_i$ or $D/L$. The discontinuity is characterized by a jump in the winding number of one vortex around the plate, and in the time that the vortices take to leave the plate. The jumps occur repeatedly in a self-similar, fractal fashion, within a region near the critical values of ${\beta }_i$, showing the existence of incident angles that trap the vortices, which never leave the plate. The number of these trapping regions increases as the parameter $D/L$ decreases, and the dependence of the motion on ${\beta }_i$ becomes increasingly complex. The simulations thus show that even in this apparently simple scenario, the inviscid dynamics of a two-point-vortex system interacting with a stationary wall is surprisingly rich. The results are then applied to separate an incoming stream of dipoles by an oscillating plate.

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• Vortex flows