An analysis has been made to aid our understanding of various phenomena associated with turbulent plane jets that issue from river outlets and discharge into quiescent bays. An integrated form of the hydrodynamic equations of flow continuity and momentum balance, coupled with advective-difusion mass transport equations, has been formulated into a two-dimensional spatial domain. Closed-form analytical solutions are obtained with the aid of similarity functions for the velocity and sediment concentrations profiles. A numerical procedure for estimating the areal and volume deposition of the delta sediments is presented. The Atchafalaya River Delta, a newly developing delta in the south central Louisiana Coast, is used to illustrate analytical techniques. The results of analytical predictions are compared with the results predicted by other statistical and generic approaches; an agreement is found. A sensitivity analysis is performed to assess the relative importance of various parameters in the river-bay-delta system.