Time averaged groundwater table above the mean sea level has been observed in unconfined coastal aquifers. Several theoretical solutions were presented to investigate the groundwater table overheight (super-elevation) in response to tidal oscillations. Nevertheless, previous analytical solutions are generally limited to Dupuit-Forchheimer assumptions or a two-dimensional free surface model. In this paper, we introduced a more general condition that a three-dimensional kinematic boundary condition is considered. An exact analytical solution of the groundwater table overheight under the multi-tidal constituents was derived using the Fourier transform method. The solution shows the local groundwater table overheight is related to the mean aquifer thickness, tidal amplitude, damping coefficient as well as its positions in sand beaches. In addition, the analytical solution illustrates the simple linear superposition is not applicable to the multi-tidal components condition, whose groundwater table overheight becomes weak due to the non-linear effect of the three-dimensional kinematic boundary condition. In addition, concentrations were focused on the time averaged total flux density illustrating the groundwater exchange occurs both in the shore normal and shore parallel directions, which however is missing in the previous two-dimensional solution. Further cognitions on the groundwater circulation mechanism were also achieved, which originates from the large tidal amplitude region and fans out towards the small tidal amplitude region. These new findings are of great importance to extend our understandings of the groundwater hydrodynamics in unconfined coastal aquifers.

在无限制的沿海含水层中已观察到平均海平面以上的时间平均地下水位。提出了几种理论解决方案来研究响应潮汐振荡的地下水位超高（超高）。尽管如此，以前的分析解决方案通常仅限于Dupuit-Forchheimer假设或二维自由表面模型。在本文中，我们介绍了一个更通用的条件，即考虑了三维运动学边界条件。利用傅立叶变换法，得出了多潮因素作用下地下水位超高的精确解析解。该解决方案表明，当地地下水位超高与平均含水层厚度，潮汐振幅，阻尼系数及其在沙滩中的位置有关。此外，解析解表明，简单的线性叠加不适用于多潮分量条件，由于三维运动边界条件的非线性作用，其地下水位超高值变弱。此外，浓度集中在时间平均总通量密度上，说明地下水交换发生在海岸法线和海岸平行方向，但是在先前的二维解决方案中却没有。对地下水循环机制的认识也更多，其起源是大的潮汐幅度区域，然后向小的潮汐幅度区域扩展。这些新发现对于扩展我们对无限制沿海含水层中地下水流体动力学的理解具有重要意义。