Turbulent radial and plane wall jets have been extensively investigated both experimentally and numerically over the past few decades. Previous studies mostly focused on the heat and mass transfers involved in jet flows. In this study, a comprehensive investigation was conducted on turbulent radial and plane wall jets, considering both jet spread and velocity decay for different parameters. The numerical results were compared with existing experimental measurements. The comparison focused on the velocity profile, jet spread, and velocity decay, and revealed that the Reynolds stress model (RSM) performs well in the simulation of both radial and plane wall jets. The results show that with a typical ratio of cloud base height to diameter for most downburst events, the effects of nozzle height and Reynolds number on the evolution of the radial wall jet are not significant. Both the jet spread and velocity decay exhibit a clear dependence on the Reynolds number below a critical value. Above this critical value, the plane wall jet becomes asymptotically independent of the Reynolds number. The co-flow was found to have a significant influence on the evolution of the plane wall jet. Comparatively, the jet spread and velocity of the radial wall jet were faster than those of the plane jet. For applications in civil engineering, it is valid to approximate the downburst outflow with a two-dimensional (2D) assumption from the perspective of longitudinal evolution of the flows.