ASPECTS OF A COMPUTATIONAL MODEL FOR LONG-PERIOD WATER-WAVE PROPAGATION

The model is based upon numerical integration of the hydrodynamic equations governing the long-period wave motions of the sea. The basis of computation is the vertically integrated equations of motion and continuity in an Eulerian system. The partial-differential equations, which include the effects of earth rotation and bottom roughness, are approximated by two sets of difference equations. The two sets are used in succession for a step-by-step solution in time. An analytical investigation of simplified sets of difference equations indicates that this multioperation method is unconditionally stable. The discreteness of the representation of the waves in time and in two spatial dimensions influences the computed velocity of wave propagation but not (or insignificantly, through terms of a second order of magnitude) the amplitude of the wave. The computational method, which is presented in FORTRAN, permits modeling of long waves, such as tides, surges, seiches, and tsunamis, in areas with complicated boundaries in an expedient manner and is particularly suited for hydraulic engineering research. A guide is given for use of the model, and computational effects are discussed in detail. The use of the computational procedure is illustrated with results of tidal computations of the southern North Sea and of the Haringvliet in the estuary of the Rhine River. (Author)