Hello,
With a level imposed and with the flow entering the domain, the problem is not well posed, it is the nagging difficulty of estuaries. A general advice is to put the open boundary in deep waters, so that the velocity remains small. Many tidal studies are done like this. When it is not sufficient the Thompson boundary conditions must be used, and the theory of characteristic hopefully gives the correct conditions (but actually if the velocities and elevations are not both prescribed there is still a small risk).
With best regards,
Jean-Michel Hervouet