Détermination numérique des mouvements d'un coin salé

Abstract

Salt wedges are apt to form in river estuaries under certain flow conditions and eventually to extend several kilometres upstream. Where the river bed is fairly even and the tide not strong enough for sudden flow reversals to take place, there is little exchange between the two layers and an interface can be assumed to exist. Slight exchange does in fact frequently take place, however, and the interface can be defined as the locus of points at which the fluid density is the mean of those of the two layers. The problem is thus one of unsteady flow of two fluids of different densities with a free surface and an interface. The equations assuming gradually varying flows lead to a differential system comprising equations (7), (8), (10), (11), (14) and (15). Equation (23) gives the slopes of the four characteristics in each section and relationship (30) is satisfied on each characteristic. If condition (28) is satisfied the four characteristics are real and the problem is hyperbolic. Equation (23) enables the characteristics of the internal wave system to be distinguished from those of the external wave system ; relationship (29) gives an approximate value for the internal wave system slopes c. The considered region comprises an upstream part without a salt layer and a downstream part with the two layers one above the other ; the salt wedge front progressing at the same speed as the lower layer V1 comes between the two layers. The problem is solved numerically for the normal point with the aid of a Lax-wendroff explicit finite difference scheme. The characteristics are used at the ends of the integration domain, but as only those originating inside the domain are used, boundary conditions are required. A discharge/time or stage/time relationship is assumed upstream, and downstream (at the river mouth) a real surface variation relationship. If a second downstream condition is required, a critical section is assumed to become established at the mouth of the river. The steady flow conditions obtained by numerical integration of system (36) are taken as the initial conditions. A computation programme has been developed for a study of salt wedge movements in the Grand Rhone below Arles.