The flow passing over a trapezoidal tab mounted on a flat plate is studied using direct numerical simulation (DNS). Such a tab has been used to generate hairpin-like vortices to enhance cross-stream mixing. We attempt to provide a detailed account of the three-dimensional topology and dynamics of the hairpin vortices in the tab wake. Simulations are conducted for three tab inclination angles at Reynolds number $\hbox{\it Re}\,{=}\,600$ based on the free-stream velocity and the tab height. A finite-volume discretization scheme involving $2.6\,{\times}\, 10^6$ control volumes is employed for the simulations and the results are compared with PIV experimental data. Simulations captured all the experimentally observed near-field flow features including a pair of streamwise co-rotating vortices and its transition to hairpin vortices. Simulation results provide new insight into the vortex dynamics in the tab wake. It is shown that the hairpin vortex is capable of lifting up and entraining vorticity from the local boundary layer, thereby increasing its strength to counter the vorticity diffusion. It is also observed that the turbulence production is mostly accomplished by the hairpin heads/arches, while the highest kinetic energy is associated with hairpin vortex legs. The topological characteristics of the structures and the statistical characteristics of the flow are discussed in detail.