There are many types of marine outfall systems operated along the Omani coasts to discharge (treated) municipal wastewaters, cooling waters, or desalination brine effluents to the Oman Sea. The outfall's system varies from a simple open channel at the shoreline, a short single port outfall and to modern long multiport diffusers. Discharged effluents are primarily seawater but at a more concentrated level and warmer, and may also contain some unknown chemical components which are subject to significant loss due to temporal decay that varies with water depth. Due to the complexity and uncertainty in sea conditions, mathematical models have been widely applied to study dispersion and spreading of discharged effluent in coastal waters, and to assess the potential environmental impacts of steady effluent discharge from sea outfalls. In the far-field where the effluent plume is observed drifting away with the currents, seabed depth profiles play an important role since in deeper water the current tends to be faster, mixing is stronger, and there is a greater depth over which to dilute the effluents. For nearshore discharges in particular, due to relatively weak cur rent and shallow water depth, the effluent plumes are observed to be spreading along the shoreline and cause a build-up of concentration to higher levels. The analytical solutions of two-dimensional advection-diffusion equation with multiple sources in a continuous and discontinuous seabed depth profiles are presented to investigate the effect of variability of water depth and decay. To replicate the merging overlapping process of discharged effluent plumes in coastal waters, the solutions are illustrated graphically by plotting contours. The concentration at the shoreline and at the discontinuity line are formulated and used as a measure for assessing the impacts of nearshore steady effluent discharge.