A Comparative Study of Nonlinear Shallow-Water Wave Loads on a Submerged Horizontal Box

This paper is concerned with calculations of the two-dimensional nonlinear vertical and horizontal forces and overturning moment due to the unsteady flow of an inviscid, incompressible fluid over a fully-submerged horizontal, fixed box. The problem is approached on the basis of the Level I Green-Naghdi (GN) theory of shallow-water waves. The main objective of this paper is to present a comparison of the solitary and cnoidal wave loads calculated by use of the GN equations, with those computed by Euler’s equations and the recent laboratory measurements, and also with a linear solution of the problem for small-amplitude waves. The results show a remarkable similarity between the GN and Euler’s models and the laboratory measurements. In particular, the calculations predict that the thickness of the box has no effect on the vertical forces and only a slight influence on the two-dimensional horizontal positive force. The calculations also predict that viscosity of the fluid has a small effect on these loads. The results have applications to various physical problems such as wave forces on submerged coastal bridges and submerged breakwaters.