Mathematical models for calculation of mixing zones for coastal effluent discharges

The potential long-term environmental impacts of coastal effluent discharges can be addressed and regulated using a mixing zone concept to control and manage the mixing capacity of the receiving coastal waters. The standard regulatory guidelines consist of two key elements: a concentration limit and a point of compliance expressed as a radius centered at the end of the outfall pipe. Modeling studies of the effect of seabed depth upon dispersion of coastal effluent discharges into the sea in the far-field are investigated analytically using the solutions of two-dimensional advection-diffusion equations with a point source on the simple depth profiles of a flat seabed and a uniformly sloping seabed. Solutions are then illustrated graphically by plotting contours of concentration, showing that the effluent discharged plumes are spreading downstream and heading towards the shoreline. Based on the location of maximum value of concentration at the shoreline, the imposed radius of and limit of concentration level within the circular mixing zone are formulated to be used as a measure for assessing the impact of effluent discharges in the coastal environment. The results found agreed with the mixing zones implemented in practice as the environmental quality standards by the regulatory authorities to minimize the impact. As the sea outfall's long pipeline may go beyond the continental shelf, a sudden step change in the seabed depth profiles is introduced, where the solutions of the advection-diffusion equations are obtained using the method of images. An extended formulation of the mixing zones radius and concentration limit are also presented.