Two-Dimensional Semi-Analytical Solution of Land-Derived Solute Transport under Tidal Fluctuations Considering Variable Boundary Conditions on the Seaward Boundary

Transport of contaminants in coastal aquifers subject to tidal fluctuations is an important topic and a growing problem due to increasing populations and development in coastal areas. Many studies have used variable boundary conditions to simulate transport behavior at the interface between seawater and groundwater. However, to the best of our knowledge, no analytical solution accounting for variable-concentration boundary conditions exists for plume migration of land-derived contaminants passing through the inland zone of aquifers under tidally induced periodic flow. Here, a two-dimensional (2D) semi-analytical solution for land-derived solute transport was developed with variable boundary conditions at the seaward boundary under tidal fluctuations. The proposed 2D semi-analytical solution was verified through comparison with an existing one-dimensional semi-analytical solution and a 2D numerical solution developed using the finite-element method. Sensitivity analysis was performed to explore factors including hydraulic properties, tidal amplitude, and the location and distribution of initial contaminants, which affect the characteristics of land-derived pollutant transport in coastal aquifers. Through comparison of the calculated masses remaining over time in the aquifer using the proposed semi-analytical solution under two types of variable boundary conditions (Dirichlet-Neumann and Cauchy-Neumann variable boundary conditions), we found that the Cauchy-Neumann variable boundary conditions reflected reality better than did the Dirichlet-Neumann variable boundary conditions. The proposed analytical solution will be useful for obtaining insights into the mechanisms that drive the plume behavior of contaminants such as radionuclides or toxic chemicals released into coastal aquifers of tidally affected systems. This dataset contains Supplementary Sections A to E. In Supplementary Sections A to E, the details of mathematical derivations are included to derive a two-dimensional semi-analytical solution for land-derived solute transport subject to tidal fluctuations in a confined coastal aquifer: Supplementary Section A provides the detailed derivations of x- and y-directional eigenfunctions, x- and y-directional eigenvalues, and x- and y-directional norms for using the general transformation technique (GITT). Supplementary Sections B and C detail the derivation of the matrix integrals within the matrix exponential of Eqs. (24a) and (29a) in the main text, respectively. Supplementary Sections D and E explain the calculations of x-axis integrals inside the matrix exponential of Eq. (B.26) in Supplementary Section B and Eq. (C.18) in Supplementary Section C, respectively