Numerical modelling of the initial spread of sewage from diffusers in the Bay of Piran (northern Adriatic)

A numerical model of initial dilution of sewage emerging from an orifice of a diffuser into stratified waters of the southern part of the Gulf of Trieste is presented. Municipial wastewater from the town of Piran empties into the sea from two diffusers at the end of adjacent submarine pipes (length 3.5 km), located at the open entrance of the shallow Bay of Piran (depth 21 m). First a numerical analysis of the hydraulics of each of the diffusers was developed to estimate the outflow through each of the diffusers’ orifices. Second, a numerical model was developed for the initial rising of sewage plumes in a marine environment with a complicated stratification. The model follows the conservation laws of mass, momentum and buoyancy, integrated over the cross-section of a buoyant plume. The system of equations is solved with the Runge-Kutta method with adaptive step-size, which keeps the local error bounded. The model was calibrated with known semi-analytical expressions for a linearly stratified sea. A sensitivity analysis of the model was also completed. Model simulations demonstrated that the initial inclination of a buoyant jet has low influence on dilution, but a high influence on rise height. On the other hand, the discharge velocity has a relatively low impact on the rise height, but affects the dilution much more. The model also showed that in a calm sea with typical summer stratification, plumes, which emerge from orifices spaced at 10 m, remain well separated until they reach a layer of neutral buoyancy below the sea-surface.