A numerical model is applied to analyze the mixing characteristics of an axisymmetric turbulent buoyant jet discharged into flowing stratified ambients. The numerical model is a Gaussian-vortex model which incorporates the effects of the vortex pair known as the representative characteristics of far-field in flowing ambients. Six ocean outfalls that have field data for the initial dilution at the water surface are selected for testing the applicability of the developed numerical model. The comparisons of the observed initial dilutions and the simulated ones show that the developed numerical model could be used for the analyses of the initial mixings induced by the sewage diffuser discharged into the ocean.