With the aid of a three-dimensional direct-numerical simulation (using pseudospectral methods) at high resolution (1283 grid points in a cubic box containing four fundamental longitudinal wavelengths), the origin and topology of the longitudinal vortex filaments which appear in the temporally growing mixing layer are investigated. The basic velocity field is a hyperbolic-tangent profile U tanh 2y/δi, with a Reynolds number Uδi/ν=100. The basic flow is forced initially by two small Gaussian random perturbations: a three-dimensional one, of kinetic energy ε3D U2, and a two-dimensional one, of kinetic energy ε2D U2. For ε2D=10−4 and ε3D=10−5, quasi-two-dimensional large coherent Kelvin–Helmholtz rolls form and merge. Because of unstable oblique modes, they oscillate slightly as in the translative instability proposed by Pierrehumbert and Widnall [J. Fluid Mech. 114, 59 (1982)], but not exactly in phase. Between these big rollers, weak vortex lines are stretched. For ε2D=0 and ε3D=10−4 the oblique modes observed in the previous case yield local roll-ups and pairings occurring in certains regions of the span only, giving rise to a large-scale vortex lattice similar to that observed by Nygaard and Glezer in forced experiments [Phys. Fluids A 2, 461 (1990)]. This is numerical evidence of Pierrehumbert and Widnall’s helical-pairing instability. Furthermore, a thin and intense streamwise hairpin vortex appears, stretched in between the large vortices of the lattice. A low Reynolds number counterpart of the mixing transition occurs during the second pairing, characterized by short k−5/3 subranges in the spectra, intense vorticity extrema, and intermittent distributions of local helicity.