A theoretical study of the heat and momentum transfer resulting from a flow of power plant condenser effluent discharged vertically to shallow, quiescent coastal receiving water is presented. The complete partial differential equations governing steady, incompressible, turbulent flow driven by both initial momentum and buoyancy are solved using finite-difference techniques to obtain temperature and velocity distributions in the near field of the thermal discharge. Results were obtained for over 100 cases, using the computer program presented. These results ranged from cases of pure buoyancy to pure momentum and for receiving water depths from 1 to 80 discharge diameters deep. Various computed gross aspects of the flow were compared to published data and found to be in excellent agreement. Data for shallow water plumes and the ensuing lateral spread are not readily available; however, one computed surface temperature distribution was compared to proprietary data and found also to be in reasonable agreement. (Modfied author abstract)