Nonlinear Wave Loads on a Submerged Deck by the Green-Naghdi Equations

We present a comparative study of the two-dimensional linear and nonlinear vertical and horizontal wave forces and overturning moment due to the unsteady flow of an inviscid, incompressible fluid over a fully submerged horizontal, fixed deck in shallow-water. The problem is approached on the basis of the level I Green-Naghdi (G-N) theory of shallow-water waves. The main objective of this paper is to present a comparison of the solitary and periodic wave loads calculated by use of the G-N equations, with those computed by the Euler equations and the existing laboratory measurements, and also with linear solutions of the problem for small-amplitude waves. The results show a remarkable similarity between the G-N and the Euler solutions and the laboratory measurements. In particular, the calculations predict that the thickness of the deck, if it is not "too thick," has no effect on the vertical forces and has 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.