Journal of Waterway, Port, Coastal, and Ocean Engineering

The water‐wave interaction with submerged breakwaters is examined to determine the reflection and transmission coefficients. Three types of breakwaters are considered, namely, a submerged breakwater extending from the sea bed until below the waterline, a breakwater extending from above the seawater to some distance below, and a breakwater extending all the way from the seabed with a slit at some distance from the bed. In all three cases the breakwaters are assumed to be rigid, thin, and impermeable, and subjected to linear monochromatic waves, and the fluid motion is idealized as linearized, two‐dimensional potential flow. A computationally efficient method—an eigenfunction technique with a mixed boundary condition—is used to determine the velocity potential anywhere in the region of flow. The least‐square method has been utilized in the solution for the mixed boundary condition. The accuracy of the solution is demonstrated by comparing the numerical values for the transmission coefficient with those obtained from experiments or other analytical solutions but with water depth restrictions. Numerical results in terms of both reflection and transmission coefficients are presented for each case.

The diffraction of water waves by an offshore breakwater consisting of an infinite row of equally spaced vertical screens is investigated theoretically. A Green's function approach is utilized and the use of geometric periodicity reduces the problem to that of a singular integral equation for the potential difference across a single screen element. The integral equation is then solved numerically by expressing this potential difference as a series of Chebyshev polynomials with unknown coefficients. The reflected and transmitted wave systems each consist of a finite number of propagating wave components. The accuracy of the numerical scheme is verified based on energy considerations. A reflection coefficient is defined in terms of the amplitude of the asymptotic wave traveling in a direction opposite to that of the incident wave system. Reflection coefficients are presented for a variety of angles of wave incidence and screen width‐to‐spacing ratios. These results indicate that for certain parameter combinations significant wave reflection can be obtained utilizing this type of breakwater configuration.

Boussinesq‐type equations can be used to model the nonlinear transformation of surface waves in shallow water due to the effects of shoaling, refraction, diffraction, and reflection. Different linear dispersion relations can be obtained by expressing the equations in different velocity variables. In this paper, a new form of the Boussinesq equations is derived using the velocity at an arbitrary distance from the still water level as the velocity variable instead of the commonly used depth‐averaged velocity. This significantly improves the linear dispersion properties of the Boussinesq equations, making them applicable to a wider range of water depths. A finite difference method is used to solve the equations. Numerical and experimental results are compared for the propagation of regular and irregular waves on a constant slope beach. The results demonstrate that the new form of the equations can reasonably simulate several nonlinear effects that occur in the shoaling of surface waves from deep to shallow water including the amplification of the forced lower‐ and higher‐frequency wave harmonics and the associated increase in the horizontal and vertical asymmetry of the waves.

Large‐scale experiments were conducted on the interaction of water waves and a fluid‐filled membrane cylinder. The test results can be used to address the potential effectiveness of fluid‐filled membranes as engineering structures. A circular cross section was modeled to compare to the results for a rigid circular cylinder that had a zero reflection coefficient and is not a wave barrier. The circular membrane cylinder did not have a zero reflection coefficient and the transmission and reflection characteristics show a strong period dependence. In particular, the results show that there is a range of wave periods where fluid‐filled membranes might serve as an effective breakwater. For the range of excitation periods that the membrane is effective as a wave barrier, the transmitted wave energy is reduced by a combination of rigid‐body motion, deformation, and viscous effects. For other excitation periods the membrane performs similar to a rigid cylinder.

An empirical analysis of the shoreline response to both single and multiple detached breakwaters is presented. In the analysis, equilibrium conditions are assumed. The analysis is based, in part, on previously published experimental data, which are also the basis of a previous study of equilibrium shoreline response to breakwaters. The current analysis differs from the previous analysis in several ways: (1) The effects of wave steepness and beach slope are included; (2) waves are allowed to approach from any direction in deep water; and (3) the effects of segmented breakwaters can be analyzed. Neither analysis includes the effects of grain size. The current analysis can be used to predict the formation of tombolos and salients, and to predict the maximum shoreline retreat or shoreline advance. To demonstrate the utility of the analysis, the shoreline response to the 11‐unit breakwater system at Bay Ridge, Md., is predicted. The predicted and actual shorelines are shown to be in good agreement.

In this paper, the diffraction theory originally developed for $N$ bottom‐mounted vertical circular cylinders is reviewed and generalized to be applicable to deep‐draft truncated vertical cylinders, such as the columns of a tension‐leg platform (TLP). More importantly, the complementary radiation problem for $N$ vertical circular cylinders is solved. Radiation potentials as well as added mass and wave damping for six‐degree‐of‐freedom motions are obtained in closed forms. To demonstrate the usefulness of the present method, it is applied to the computation of wave loads and hydrodynamic coefficients for four columns of the ISSC TLP and a row of 19 bottom‐mounted vertical cylinders. The present method quickly produces reasonably accurate solutions and precludes the laborious convergence test and grid generation, and hence should be a valuable tool for the preliminary design of deep‐draft multicolumn structures, especially when the number of the columns is large.