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This study considers two barges of different draughts in incident waves. Physical experiments are carried out in a wave flume to investigate the wave response at the gap between two barges. New experimental data are used to calibrate the artificial viscous coefficient of a typical time-domain potential-flow solver. Through a comparison between the experimental and numerical results, the artificial viscous coefficient that indicates dissipation effects at the gap is identified. It is found that the artificial viscous coefficient is determined not only by the relative barge draughts but also by the propagating direction of incident waves. Hydrodynamic characteristics of two barges with different draughts are further investigated. The wave frequency corresponding to the largest wave amplitude at the gap is found to decrease, as either barge draught grows. The maximum wave heights at the gap for different combination of barge draughts are analyzed. Corresponding physical explanation for the chart is given in detail.

A series of numerical simulations of wave run-up on four-cylinder array is performed at different spacing ratios 1.5 ≤ L/D ≤ 4.25, where L is the center-to-center distance between the adjacent cylinders and D is the cylinder diameter. The effects of spacing ratio and wave steepness on the wave run up ratio and wave force on the four cylinders are investigated. The results show that with variation of the spacing ratios and incident wave angles, different wave pattern regimes are observed among four cylinders. It is interesting to note that the maximum run-up ratio occurs at L/D = 2.0 with the large wave steepness H/λ=1/16, and approaches to 2.4 times of that for the single cylinder in the case of incident wave angle β = 45°. The spacing ratio has a significant effect on the horizontal wave forces for the four cylinders, however, the location of the maximum wave force is found to be not significantly related to that of the maximum run-up ratio.

This study examines the Bragg reflection of water waves by multiple submerged semi-circular breakwaters. The multipole expansions combined with the shift of polar coordinates are used to develop full linear potential solutions of the problem. In the full solutions, the obliquely and normally incident waves are independently considered. Experimental tests are carried out to measure the reflection and transmission coefficients of the breakwaters at different wave periods and body spacings. The analytical results are in reasonable agreement with the experimental data. The peak reflection coefficient of multiple submerged semi-circular breakwaters and the bandwidth of Bragg reflection are carefully examined by numerical examples. Some significant results for practical application are discussed.

Reliable estimations of overtopping rates are necessary for the design of vertical seawalls. Although many studies have been carried out to address this, few have paid attention to vertical seawalls built on coral reefs. In this study, a physical model was constructed with an idealized coral reef topography and vertical seawalls located on the middle or inner reef flat. A steep fore-reef slope in combination with a shallow and horizontal reef flat led to significant changes in wave heights, periods, spectra, and shapes across the reef. State-of-the-art overtopping formulas were tested against the experimental data, but none of them produced satisfying results. The reasons for the inapplicability of these formulas in this regard were discussed, which highlighted the necessity of distinguishing the significant influence of coral reefs on incident waves reaching engineered structures from structures fronted by relatively deep water and foreshores. A new formula for estimation of overtopping rates of vertical seawalls on coral reefs under non-impulsive conditions was derived. This formula is a function of the relative wave height at the seawall toe and the relative crest freeboard, whereas the spectral period is not incorporated. The performance of the new formula was investigated using various combinations of dimensional and dimensionless parameters.

This paper presents a semi-analytical solution methodology for the linear hydrodynamic diffraction induced by arrays of elliptical cylinders subjected to incident waves. The solution of the Laplace equation in elliptic coordinates for both the incident and the diffracted waves is formulated analytically in terms of the even and odd periodic and radial Mathieu functions. The main contribution herein is the employment of the so-called addition theorem for Mathieu functions, which for the purposes of the present work is properly modified and eventually expressed in terms of the even and odd periodic and radial Mathieu functions.

In recent years, local scour has been brought to attention because it may have a negative effect on coastal structures. This paper describes an experimental investigation of local scour in front of an impermeable submerged breakwater with a vertical offshore face. Experimental results show that the scour pattern in front of the submerged breakwater is similar to that in front of a vertical-wall breakwater, although there is a slight difference in the locations of the scour and the deposition. The maximum scour depth normalized by the incident wave height is found to decrease exponentially with relative water depth (the ratio of the water depth to wavelength of the incident wave height). Also, the scour depth is dependent on the reflection coefficient of the submerged breakwater. A new estimation method for evaluating scour depth is developed and provides excellent correlation with all experimental data available in the literature.

A new hybrid numerical-analytical method is developed for the evaluation of the second-order velocity potential associated with bichromatic incident waves attacking a floating long horizontal cylinder of arbitrary cross-section, in water of finite depth. The double sum or difference frequency velocity potentials may be obtained. An analytical treatment of the nonhomogeneous free surface condition makes the numerical solution accurate and efficient. The method is tested through a numerical example. Results showing the difference frequency sway force and sway response transfer function are presented for practical parameters of a moored vessel in a multi-buoy anchorage.

The wave-power absorption by an oscillating water column in a reflecting wall is studied within linear theory. We give numerical examples demonstrating how the performance depends on the geometry of the system as well as on the frequency and direction of the incident waves.

A simple mathematical model, based on the solution of the two-dimensional problem of a vertical floating plate and on rigid body dynamics, is used to investigate the influence of different characteristics (such as mass, draft and anchoring) on the breakwater performance. The results include information about the transmission coefficient as well as about the plate displacement and anchoring forces, as functions of the plate and incident wave parameters.

The effects are considered of short-crestedness of incident waves on the load which these exert on a long structure. The result is expressed as a frequency-dependent, directionally-averaged spectral multiplication factor for the load relative to the case of normally incident, long-crested waves. This is evaluated numerically for a cos2 θ-type directional incident spectrum, and various relative structure lengths. Calculated crest elevations, averaged over different lengths, agree well with the empirical ones, for ocean-wave data as well as for laboratory wind-wave data.