Experiments and calculations of cnoidal wave loads on a flat plate in shallow-water

Horizontal and vertical wave forces due to the interaction of cnoidal waves with a two-dimensional, horizontal flat plate located in shallow-water are studied through laboratory experiments and calculations. The experiments are conducted for a combination of two water depths, five wavelengths and four wave heights, corresponding to the propagation of nonlinear waves in shallow-water depth. The model is located at six different elevations and submergence depths such that all possible cases of a coastal bridge deck fully above the still-water level, a deck on the surface and a fully submerged deck are considered in the study. Calculations are performed for the same cases as in the laboratory experiments and include the results of a nonlinear shallow-water wave model based on the Level I Green–Naghdi equations for the fully submerged cases, and Euler’s equations coupled with the Volume of Fluid interface tracking method for one submerged case, one elevated case, and one case at the water surface. Comparison of existing theoretical solutions are also provided, including the Long-Wave Approximation based on linear potential theory for the submerged cases, and empirical relations for the elevated cases. The set of data presented here provides an insight into storm wave loads on the decks of coastal bridges, jetties and piers located in shallow-water areas.