Mathematical modeling of seepage flows in coastal pressure water-bearing strata

We study mathematical models of certain two-dimensional steady-state seepage flows of sweet groundwater. We assume that the flows go out of a rectangular pressure water-bearing stratum and enter a sea with saline water, which has a water sheet above its surface. On the base of these models we propose algorithms, calculating the intrusion of sea saline water into shoaling sweet water strata in cases, when flows of groundwater enter the sea sidewise (the scheme of P. Ya. Polubarinova-Kochina and M. K. Mikhailov) or from below (the scheme of J. Bear and G. Dagan). Using exact analytic dependencies established with the help of the Polubarinova-Kochina method and numerical computations, we study the influence of all physical parameters of the models onto the type of the intrusion and its degree. In a particular case, with no fresh water stratum over the sea surface, we compare the results for both inflow schemes and consider the intrusion specificity, depending on the initial location of fluids interface. We study the limit cases of flows. We prove that a certain particular choice of values of unknown parameters of the conformal mapping, which enter in a solution, leads to the well-known results of P. Ya. Polubarinova-Kochina for the classical filtration problem in a rectangular dam.