Modèle mathématique de marées littorales. Calcul numérique sur l'exemple de la Manche

A mathematical model of coastal tides. Digital computation on the example of the English Channel

¹ Maître-assistant à la Faculté des Sciences, Laboratoire de Mécaniqne des fluides de l'Université de Grenoble.
² Professeur à la Faculté des Sciences, Laboratoire de Mécanique des Fluides de l'Université de Grenoble.

Résumé

The authors review a few standard ideas on coastal tides for which they give a more restrictive definition than the generally accepted one. They set out the basic equations in standard form to within the friction terme, which is quadratic with respect to velocity. They oblain a quasi-linear system of partial differential equations of the hyperbolic type with non-analytical coefficients. With the theory of tides, this system becomes a composite problem which is still awaiting rigorous discussion. By extrapolation of data from simpler cases to this problem some of the properties of tides can be interpreted qualitatively and the digital methods applied for their calculation to some extent justified. The authors then describe their digital computation scheme for mean Channel tides, which is an application of the finite-difference method relying on a predetermined 'discretization' of the variation range of the unknowns. The mean tide given by the mathematical model reflects the real-life tide to within a satisfactory degree of approximation, also such specific properties as amphidrom of currents, high-tide persistence at Le Havre and the tide configuration in Saint-Malo Bay.