ABSTRACT
In the conventional approach to describing tidal fluctuations in coastal aquifers, it is often assumed that the upper free surface is a sharp boundary between saturated and dry aquifer material. This assumption is an oversimplification in many situations as the upper boundary is not abrupt, but a diffuse transition zone of partially unsaturated material. Therefore, a capillarity correction was proposed to describe the effect of the diffuse transition zone based on the Boussinesq equation. Previous studies conclude that the capillarity correction is important at high frequencies. However, all these investigations considered only the zeroth-order capillarity correction for a vertical beach, not for a sloping beach. In this chapter, we will discuss a higher-order capillarity correction to free surface flow of groundwater in a sloping beach. First, based on the existing definition of capillarity correction, the second-order capillarity correction is derived. Then, a new definition of the capillarity fringe is proposed for the case of small capillarity number, and a simplified model is derived. With the two new analytical solutions, the effects of the capillarity correction and sloping beaches on watertable fluctuations in coastal aquifers are discussed in detail.
