Wavy wall induced three-dimensionality in vortex-pair wall interaction

We investigate the onset of three-dimensional (3D) flow features resulting from the impingement of a nominally 2D counter-rotating vortex pair (VP) onto a sinusoidal wavy wall using direct numerical simulations. The VP is initialized at a circulation-based Reynolds number of 1000. The wall geometry consists of spanwise undulations with amplitude 0.1b₀ and wavelength 3b₀, where b₀ denotes the initial spacing between the vortices. The VP induces secondary vorticity at the wall, which subsequently separates and rolls up into hairpin-like vortex loops that advect away from the surface. The origin of these hairpin structures can be traced to the 3D, time-evolving pressure gradients generated by the interaction of the descending VP with the wavy wall. This spatially and temporally evolving separation results in differential vortex interactions along the span, culminating in the formation of the observed hairpin structures. These findings provide new insights into the mechanisms by which large-scale vortices interacting with wavy surfaces generate smaller-scale coherent features in wall-bounded flows, with direct relevance to flow control strategies. The interaction also causes a marked reduction in the circulation of the primary VP, highlighting implications for ground-induced