On Non-Saturated Breakers and the Wave Run-Up

Some theoretical results pertaining to the physical behavior of gravity waves on a sloped plane are presented. The notion of "saturated" breakers and "non-saturated" breakers which follow the breaking index curve is introduced. Criteria for different kinds of breaking and successive breaking of waves are presented. Some considerations on the wave run-up are deduced. Then a critical analysis of the method of characteristics is presented, with some possible refinements. Path curvature effect is taken into account and the problem of waves climbing on a dry bed is solved. Criteria for determining saturated and non-saturated breakers and the wave run-up by the method of characteristics are proposed.