Tidal computations in shallow water - Report on hydrostatic levelling across the Westerschelde

A survey is given of the established practice of tidal computations in the Netherlands. The dynamical analysis of tidal elevations and currents in shallow waters is of great practical interest when coastal engineering projects are undertaken, like the Zuiderzee or the Delta project, both in the Netherlands. Tidal computations have to be based upon a careful schematization of the region considered. The water is assumed la move substantially in the length direction of a channel with variabie cross-section or in a channel network. The problem is then governed by two partial differential equations, the continuity equation and one dynamical equation. These equations generally are too complicated to admit solutions in closed form. Several methods of numerical approach have therefore been devised. First among these methods are the harmonie methods, by which one or more tidal constituents are computed. If confined to one single constituent (M2), this method is relatively simple to handle and it requires a moderate effort of calculation. The computation of further constituents leads to progressively increasing efforts, so that the method is seldom extended beyond the second harmonie (M4). For the immediate numerical integration of the continuity and the dynamicaI equation, several ways may be followed. A method based on an iterative process has been extensively used for practical problems in the Netherlands and abroad. This method is particularly suited to analyse tidal motions in connection with the problem of schematization. A third group of methods is based upon the properties ofthe characteristicelements ofthe differential equations. lntegration, performed either graphically or numerically, is in particular used in specific propagation problems, such as wave motions produced by sluicing operations and bores. The employment of large computers, either analogue or digital, is here mentioned only briefly, since more detailed information on the development is being prepared