Â© 2014 AIP Publishing LLC. The liquid jet from a round orifice during the transient start-up and steady mass flux periods of a high pressure injector is studied via Navier-Stokes and level-set computations. Via post-processing, the role of vorticity dynamics is examined and shown to reveal crucial new insights. A brief review of relevant literature is made. An unsteady, axisymmetric full-jet case is solved. Then, a less computationally intensive case is studied with a segment of the jet core undergoing temporal instability; agreement with the full-jet calculation is satisfactory justifying the segment analysis for three-dimensional computation. The results for surface-shape development are in agreement with experimental observations and other three-dimensional computations; the initial, axisymmetric waves at the jet surface created by Kelvin-Helmholtz (KH) instability distort to cone shapes; next, three-dimensional character develops through an azimuthal instability that leads to the creation of streamwise vorticity, lobe shapes on the cones, and formation of liquid ligaments which extend from lobes on the cones. The cause of this azimuthal instability has been widely described as a Rayleigh-Taylor instability. However, additional and sometimes more important causes are identified here. Counter-rotating, streamwise vortices within and around the ligaments show a relationship in the instability behavior for jets flowing into like-density fluid; thus, density difference cannot explain fully the three-dimensional instability as previously suggested. Furthermore, the formation of ligaments that eventually break into droplets and the formation of streamwise vorticity are caused by the same vortical dynamics. Waviness is identified on the ligaments which should result in droplet formation. The nonlinear development of the shorter azimuthal waves and ligament waves explains the experimental results that droplet sizes are usually smaller than KH wavelengths. The higher the relative velocity and/or the lower the surface tension the shorter are the values of the most unstable wavelengths.