The role of tertiary wave interactions in wave–body problems

Abstract

Results from experiments on wave interaction with a rigid plate are reported. The plate is projected from one of the sidewalls of the basin. The sidewall acts as a plane of symmetry, thereby doubling the widths of the plate and of the basin. The tests are carried out in regular waves of varying periods and steepnesses. At wavelengths comparable with the width of the plate, strong run-ups are observed at the plate–wall intersection, increasing with the wave steepness. These run-ups take many wave cycles to develop, with no steady state being reached in some cases. It is advocated that these phenomena result from third-order interactions between the incident and reflected wave fields, over a wide area on the weather side of the plate. A theoretical model is proposed, based on tertiary wave interaction. A parabolic equation is derived that describes the transformation of the incoming waves through their interaction with the reflected wave field. A steady-state solution is obtained through iterations. Results from the theoretical model are compared with the experimental data, with good agreement.