Direct numerical simulation of a counter-rotating vortex pair interacting with a wall

The influence of a horizontal wall on the evolution of the long-wave instability in equal strength counter-rotating vortex pairs is studied with direct numerical simulation. The two vortices descend under mutual induction and interact with a ground plane, as would aircraft trailing vortices in ground effect. Both the linear and nonlinear development of the pair is studied for three initial heights above the wall, representative of three modes of interaction identified by experiment. A study of two vortex core sizes over a range of Reynolds numbers (1000 <= Re <= 2500) is used to verify parameter independence. The vortex system undergoes complex topological changes in the presence of a wall, with the separation of wall generated vorticity into hairpin-like vortex tongues and axial flow development in the primary pair. The secondary structures are rotated and stretched around the primary vortices, strongly influencing the resultant flow evolution and are comparable with those observed for oblique ring-wall interaction. Of the three modes, the small-amplitude mode shows the formation of four principal tongues per long wavelength of the Crow instability, with the secondary vortex remaining connected. The large-amplitude mode undergoes a re-connective process to form two non-planar secondary vortex structures per wavelength, and a simulation of the large ring mode in its first formation develops six tongues per wavelength. These secondary structures `rebound' from the wall and interact at the symmetry plane prior to dissipation, governing the bending, stretching and trajectory of the primary vortex pair.