Equilibrium and cross-sectional stability of tidal inlets: application to the Frisian Inlet before and after basin reduction

Abstract

The focus of this paper is on the adaptation of the inlet cross-sectional area after basin reduction. To calculate the new equilibrium and degree of stability, use is made of a method first proposed by Escoffier. As part of this study his largely empirical approach is expanded and given a physical basis. The inlet channel is divided in an entrance and interior section. Sand enters the entrance section on the flood and is removed by the ebb tidal current. On annually average basis, the volume of sand entering the inlet is assumed to be a constant fraction of the littoral drift. A theoretical expression for the ebb tidal sand transport as a function of the tidal velocity amplitude and a length dimension of the cross-section is derived. An important ingredient in the stability analysis is the empirical cross-sectional area versus tidal prism relationship for inlets in equilibrium and the related equilibrium velocity. A physical justification for this relationship is presented. As a measure for cross-sectional stability, a stability index, S, is introduced. For S≥1, the inlet is very stable. Stability increases with increasing values of S. For inlets that are very stable, the value of S can be related to P/ V, i.e. the ratio of tidal prism and volume of littoral drift. A method to determine the time scale for the entrance section to return to a new equilibrium after a change in basin surface area is presented. To illustrate its practical use, the Escoffier method is applied to the Frisian Inlet before and after basin reduction. In 1969, the basin area and tidal prism were reduced by approximately 30%. Based on the Escoffier method, the original equilibrium cross-sectional area of 22,000 m 2 is expected to reduce to 15,500 m 2. The adaptation time scale is estimated to be 30 years. Even after basin reduction, the inlet remains very stable with S=31 and P/ V=585.