Run-up of surface waves on a sea wall built on a convex bottom profile

Abstract

Wave run-up on a sea wall built on a convex bottom profile is studied in the framework of linear shallow water theory. When the wall is located in “deeper water,” a wave is reflected from the wall without changing its shape and phase, which is fully consistent with classical considerations. If the wall is shifted towards the shore, the shape of the wave changes in a complex way. Note that the wave phase changes to the opposite in the limiting case when the wall is located right on the shore. The role of nonlinear effects is studied by means of numerical simulations using nonlinear shallow water theory. It is shown that the contribution of nonlinear effects and breaking is high on a convex-shaped beach, which makes the structure of the wave field rather complicated.