An aggregate model for the adaptation of the morphology and sand bypassing after basin reduction of the Frisian Inlet

Abstract

To study the adaptation of the morphology of the Frisian Inlet after basin reduction an aggregate model is developed. In the model, especial attention is given to the sand transport to the down-drift coast. In developing the model the inlet system is divided into three elements, the ebb tidal delta, the Zoutkamperlaag and the tidal flats. Based on observations during the first 18 years after basin reduction the adaptation time scale of the tidal flats is expected to be much larger than that of the ebb tidal delta and the Zoutkamperlaag, essentially reducing the inlet schematization to a two-element system. The dependent variables in the model are the sand volume of the ebb tidal delta and the water volume of the channel. The governing equations are non-linear and for quantitative accurate results are solved numerically. To demonstrate the nature of the solution the equations are linearized assuming the morphological state is close to equilibrium. The linearized equations are solved analytically and the solution is applied to a hypothetical case where the tidal prism of the Frisian Inlet is reduced by 10%. From the analytical solution it follows that the adaptation of the volumes of the two elements, delta and channel, is governed by two system time scales. These system time scales are functions of two local time scales. The local time scales pertain to the adaptation of one element assuming the other element has reached equilibrium. Because there are two system scales the adaptation of the volumes of the delta and channel is not exponential and is not necessarily monotonic. For example, initially the transport of sand to the down-drift coast is larger than the long-shore sand transport entering the inlet system from the up-drift coast, then becomes smaller and after some time increases again to reach the value of the up-drift long-shore sand transport. Comparison of the numerical solution for the actual reduction in tidal prism of 30% with the analytical solution for the 10% reduction in tidal prism shows qualitatively the same results.