Recent natural extreme events, such as Hurricane Ike in the U.S. (2008), Tohoku tsunami in Japan (2011), and Typhoon Haiyan in Southeast Asia (2013), have caused significant damage to the decks of coastal bridges. The failure of the structure occurs when wave-induced loads on the decks of coastal bridges exceed the bridge capacity, resulting in partial removal or a complete collapse of bridge decks. Tsunami, storm waves, and storm surge are known to be the ultimate agents of such failures. An understanding of the failure mechanism and possible solutions require a better knowledge of the destructive loads on the structure. Interaction of surface waves with the bridge deck is a complex problem, involving fluid–structure interaction, wave breaking, and overtopping. Possible submergence of the deck and entrapment of air pockets between girders can increase destructive forces and add to the complexities of the problem. In recent years, remarkable progress has been made on this topic, resulting in some new findings about the failure mechanism and the destructive wave loads. A review of the key studies on wave loads on the coastal bridge decks, including those in the past and very recently, is presented here. Emphasis is given to the pioneering works that have significantly improved our understanding of the problem. Challenges associated with the existing solutions are highlighted, and suggestions for future studies are provided.

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.

The diffraction of highly nonlinear Stokes waves by vertical cylinders of circular cross section is numerically simulated in the time domain. A finite-element method, based on Hamilton’s principle, is used to discretize the fluid domain. The Stokes waves, input at the numerical wave maker, are obtained numerically from the two-dimensional steady solution of the finite element model. A new matching scheme is developed to match the two-dimensional wave at the far field and the three-dimensional diffracted wave in the near field. The method developed here can easily be extended to the diffraction of irregular, nonlinear waves. Numerical examples are presented for the diffraction of Stokes waves with various steepnesses by single and multiple circular cylinders. The wave elevation and runup on the cylinder are calculated and compared with the available theoretical and experimental results.

Large-amplitude internal solitary waves in a two-layer fluid system with a free surface are investigated in this paper. Laboratory experiments on strongly nonlinear internal solitary waves with a free surface for a deep configuration are conducted. After comparing the experimental data with the results of the Miyata–Choi–Camassa model that includes the free-surface effects (MCC-FS), we find that the MCC-FS model does not calculate accurately the internal solitary waves with a free surface. Thus, we develop a strongly nonlinear model for a deep configuration, namely the two-layer high-level Green–Naghdi (HLGN-FS) model that includes the free-surface effects. Numerical results of the HLGN-FS model, including the wave profile, velocity field and wave speed, are presented for three cases. The first case is a shallow configuration with . It is shown that the MCC-FS model can provide accurate results for the shallow configurations. Meanwhile, the HLGN-FS model is shown to be accurate for describing the internal solitary waves for both shallow and deep configurations.

A nonlinear theoretical model for deformations, oscillations, and drift motions of multiple elastic ice sheets in shallow waters due to combined nonlinear waves and uniform current is presented. The model is based on the Green–Naghdi theory for the fluid motion and the thin plate theory for the deformation of the ice sheets. In principle, there are N number of the floating sheets with arbitrary lengths, drafts, and rigidities, which may be located at arbitrary distances from each other. Nonlinear waves of solitary and cnoidal types are considered, and there are no restrictions on the wave properties (wave height or wave period). The sheets, located at different positions, are shown to drift with different speeds, but surge in most of the wave conditions with equal amplitudes. It is shown systematically that wavelength and spacing between the sheets are the critical parameters determining the drift response of a set of freely floating ice sheets. When wavelength is equal to the distance between the centers of the sheets, they bend and drift in resonance, causing the largest wave reflection. The ambient current is found to affect the drift motion of the sheets nonlinearly. This work complements the part I paper of the same title, where drift motion of a single ice sheet was investigated.