Analytical modeling of contaminant transport along sloping coastal beaches in presence of tidal waves and exponential rainfall infiltration

Coastal beaches are the most important part of the marine environment and are highly influenced by the interactions taking place between groundwater and surface water of any form. Generally, the purity index of the groundwater is based on the concentration of Total Dissolved Solids (TDS) in it. Analytical solutions are the best tools for groundwater flow and transport modeling. However, contaminant transport along the sloping coastal beaches with complex boundaries cannot be addressed with available analytical solutions. In the present study, new analytical models are developed for groundwater flow and contaminant transport for sloping coastal beaches with continuity and tidal boundary conditions. To assess the performance of the new analytical solution and to validate the range of aquifer parameters, numerical simulation is performed using Du-Fort Frankel (DFF) Scheme. Numerical experimentation is carried out using the Tchebycheff and L2 norms. It is observed that the new analytical solution for the contaminant transport gives acceptable results over the wide range of the aquifer parameters. To show the effectiveness of the developed models, two case studies from Indian coastal aquifers namely, Kalpakkam, Tamil Nadu, and Bhavnagar, Gujarat are considered. The profiles of the contaminant concentration are obtained to study the TDS behavior along these complex coastal beaches in the spatiotemporal directions. The results are compared with numerical model results and found to be satisfactory. The combined effect of the initial rainfall and rainfall decay constants showed a significant impact on the concentration of TDS. TDS concentrations are observed to be varying highly with the variation in the tidal constituents and bed slope.