Numerical simulations of a three-dimensional temporally growing shear layer are obtained at high Reynolds number and zero Froude number using a vortex scheme modified for a variable-density flow. Attention is focused on the effect of initial vorticity and density distributions on the interaction between instability modes which lead to the generation and intensification of streamwise vorticity. Results show that the three-dimensional instabilities evolve following the formation of concentrated span wise vorticity cores. The deformation of each core along its span resembles the amplification of the translative instability. The generation of vortex rods, which wrap around individual cores while stretching between neighbouring cores, suggest a mode similar to the Corcos instability. The instability modes leading to the formation of both structures, energized by the extensional strain generated by the cores, grow simultaneously. A similar series of events occurs in variable-density shear layers and in shear layers which start with an asymmetric vorticity distribution. Baroclinic vorticity generation in the variable-density layer leads to the formation of asymmetric cores whose volumetric composition is biased towards the lighter fluid. The structures are propelled, by their asymmetric vorticity distribution, in the direction of the heavier stream while their eccentric spinning forces an uneven stretching of the vortex rods. The origin of the asymmetry is established by comparing these with the results of a shear layer with an initially asymmetric vorticity distribution in a uniform-density flow. The strong late-stage asymmetry exhibited by the former is not observed in the latter. Thus, baroclinic vorticity generation is responsible for the observed symmetry. We also find that initially asymmetric vorticity distribution does not, as suggested before, lead to asymmetric spacing between the streamwise rods, it is concluded that the experimentally observed asymmetric spacing must arise after pairing.