A NEW APPROACH FOR TIDAL COMPUTATIONS

During the twenty last years, tidal modelling has been intensively developed. Following the growth of engineering needs in coastal areas, more and more accurate models have been established, and this constant research of better accuracy in the representation of real phenomena bring*us to very expansive models. One way of reducing these costs is to use variable grids in space, in order to concentrate refined meshes in areas of interest. But the finite difference schemes are not well adapted to this kind of procedure : this is why several attempts have been made recently to use finite element technics : C. TAYLOR and J.M. DAVIS in 1975 DO , C.A. BREBBIA and P.W. PARTRIDGE in 1976 D 3 , ••• But these applications are not easy. During the same period, since 1975, more complex tentative have been made using Fourier transform of the equations, previously to any kind of numerical integration : tides are effectively quasi periodic phenomena, and their spectra are well known. Two important points arise in doing this : - time variable is eliminated from the hyperbolic problem of propagation, transformed into a set of elliptic problems. - for each elliptic problem, a variational formulation is available. It becomes thus possible to look at the various components of the real tides, and to use finite element technic to integrate numerically these problems in real basins. In this way, B.M.JAMART and D.F. WINTER have used recently a purely numerical procedure based upon the Fast Fourier Transform to carry their tidal computations in fjords, cf.fjsj, while A. ASKAR and A.S. CAKMAK introduced a perturbation technic to handle the non linearities, very important in such problems, cf. [j J . We have followed a similar approach to study the complete spectrum of the tides in shallow water areas for the european seas : North Sea and English Channel, cf.£9j . The aim of this paper is to illustrate the main ideas of our method applied on an academic one-dimensional problem.