Influence of the tide on the mean watertable in an unconfined, anisotropic, inhomogeneous coastal aquifer

For an isotropic, homogeneous coastal aquifer, previous studies [Aust J Phys 26 (1973) 513; Water Resour Res 17 (4) (1981) 1222] have found that the mean watertable is influenced by the sea tide and will stand considerably above the mean sea level even in the absence of net inland recharge. This paper investigates the influence of the tide on the mean watertable for the case that the unconfined coastal aquifer is inhomogeneous and anisotropic. A two-dimensional free surface model is considered under the following assumptions: (a) the principle directions of the hydraulic conductivities are horizontal and vertical; (b) the horizontal hydraulic conductivity Kx(y) depends on the depth of the aquifer only and the vertical hydraulic conductivity Ky(x,y) is arbitrary; (c) the water–land boundary is vertical and there is no seepage face; (d) the specific storage is constant wherever the free surfaces are located; and (e) there is no net inland recharge. An integral equation satisfied by the asymptotic watertable as the landward distance approaches infinity is derived for multi-sinusoidal-component sea tide. This equation suggests that the asymptotic watertable is independent of Ky(x,y) and higher than mean sea level for arbitrary Kx(y). The asymptotic watertable is solved explicitly from the integral equation for three common patterns of Kx(y): constant, piecewise constant and linearly decreasing with the depth. Compared with the first two patterns, the third pattern has significant enhancing effect on the asymptotic watertable. Several previously published analytical solutions and the experiment data are in line with the analytical solution of this paper.