Asymptotic analysis of nonlinear tides in Wadden systems - the role of momentum sinks.

Abstract

This study aims to contribute to a better understanding of physical mechanisms in tidal channels as present in, for example, the Dutch Wadden Sea. Understanding these mechanisms will contribute to effective management of the Wadden Sea and help preventing flooding in coastal areas. In this study we consider a tidal channel with tidal flats on both sides, that is connected on two sides to an open sea. The model is an idealized version of the channel connecting the Marsdiep and the Vlie in the Netherlands.

The specific mechanism studied is that of momentum dissipation on tidal flats. Rising water level leads to water masses flowing onto the flats, carrying momentum. The water flows back into the channel during the falling tide after being temporarily stored on the flats. However, due to large friction on the shallow flats, the momentum dissipates rapidly. This is a momentum sink. The terms arising from the mass storage and the momentum dissipation are nonlinear and give rise to overtides of the primary (semi-diurnal lunar) tide, which in turn affect net sediment transport.

Here, we build on and extend a recent numerical study so as to better understand the effect of momentum sink on characteristics of the primary tide and of its overtides. This is done by constructing an asymptotic approximation to the solution of the cross sectionally averaged shallow water equations that model the hydrodynamics in a tidal channel. The analytic approach enables assessment of the effect of the momentum sink and quantification of the differences between solutions that do or do not account for it. Multiple effects of the momentum sink on the hydrodynamics are found. In particular, when the tidal flats are approximately of the same width as the main channel no significant effects of momentum sink are found. However, when the tidal channel has wide tidal flats compared to the main channel, the momentum sink causes significant tidal distortion.