The development of a hydrogen jet injected into quiescent argon was investigated in a temporal jet configuration via direct numerical simulations (DNS). A case of argon mixing in argon was used as the basis for comparison. Both systems were computed at jet Reynolds numbers of 5000 and 10,000. Attention was focused on the mechanism driving the mixing process, as well as the turbulent momentum and scalar transport. The physical properties of argon are very different from those of hydrogen (density ratio (≈20), kinematic viscosity ratio (≈0.1), and Lewis number ratio), leading to significant differences between the two cases, in jet structure, instantaneous and mean profile characteristics. A common feature in all systems was the emergence of large quasi-two-dimensional rotating structures, responsible for the engulfment of surrounding fluid, which created elongated regions where most molecular mixing takes place, with one difference being faster mixing in the hydrogen cases. An a priori assessment of the classical gradient hypothesis for turbulent fluxes revealed that the turbulent Schmidt number () and C_µ are not constant in space nor time, with local values ranging from, and, respectively, contrasting with the constant values used in Reynolds-Averaged Navier-Stokes (RANS) modeling. Additionally, an evaluation of a two equation RANS model and a dynamic one-equation large eddy simulations (LES) model was made a posteriori by comparison of their predictions with the DNS results. Both approaches exhibited significant deviations from the DNS, primarily at the early stage, but relaxed to similar solutions as time progressed. The properties at the jet edge were less well predicted by the RANS model than by the LES model. This is attributed to both gradient diffusion modeling and the impact of a turbulent/non-turbulent interface. Possible model enhancements are discussed.