Advances in Coastal and Ocean Engineering

The following sections are included:

• PREFACE TO THE REVIEW SERIES

• PREFACE TO THE FIRST VOLUME

• CONTRIBUTORS

• CONTENTS

There are two different restoring forces involved in a water-wave problem: gravitational and surface-tension forces. Both effects are discussed from basic fluid-mechanics view points. Maintaining the analyses as rigorous as possible but still within the basis of the continuum hypothesis, the free surface is treated as the air-water (two-fluid) interface, which creates a material discontinuity in fluid properties. The jump discontinuity condition of the general form of conservation equation is derived. At a material boundary such as the air-water interface, the jump condition of conservation of mass yields the kinematic free-surface boundary condition, the jump condition of conservation of linear momentum yields the dynamic free-surface boundary condition. The no-slip boundary condition arises at a material boundary as a consequence of the jump condition for mechanical-energy conservation; note that the no-slip condition is usually an assumed condition, but our anaylsis demonstrates that it is a necessary condition for the mechanical energy consideration at the interface.

A constant magnitude of pressure along the free surface is often imposed in traditional water-wave problems for irrotational fluid motions. It is demonstrated that, if this condition is imposed, water must be considered to be inviscid. Nevertheless, the resulting potential-flow solution requires the fictitious energy input from the surroundings, i.e., air, through the free surface. Under a more rigorous free-surface condition such as vanishing stresses on the interface, irrotational flows cannot exist at the free surface and must form a boundary layer. It is also demonstrated that the existence of air and variations in surface tension due to surfactant affect significantly wave-attenuation behavior.

In a real-fluid environment, flows at the free surface must be vortical. Because of this observation, the jump condition for the vorticity equation is examined. The resulting condition requires that the tangential component of fluid acceleration must be continuous across the fluid-fluid interface, which is not trivial since fluids are allowed to deform. It is demonstrated that the jump condition for three-dimensional flows is grossly different from that of two-dimensional flows; as far as behaviors of vortical flows at the free surface are concerned, two-dimensional flow approximation is inadequate. Vorticity normal to the interface and vorticity bending caused by the interface curvature appear to play important roles in determining free-surface vortex motions. It is found that the consideration of air above the free surface is essential to characterize vortical flows correctly at the air-water interface. Even though the air may not be important for water-flow dynamics, the air condition is crucial for the creation of fluid rotation at the interface of water.

Throughout this article, the air-water interface behaviors are examined based on the basic fluid mechanics view point. This will provide clear physical interpretations of free-surface dynamics, which hopefully leads to improvement of models.

The general interaction problem between waves in coastal waters and the seabed is considered. In particular, the role of the seabed in dissipating wave energy is examined, and various dissipation mechanisms are reviewed. A portion of the wave energy is consumed in inducing and maintaining sediment motion on the sea floor. Modes and characteristics of the resulting granular flow in waves are discussed in rather general terms. Furthermore, recent advances in studying nonlinear energy transfer into the seabed and the different modes of wave-induced sediment fluidization processes in cohesive as well as cohesionless seabeds are presented. Finally, we discuss some selected issues concerning the interaction of gravity marine structures with the seabed.

This paper reviews two different approaches for deriving shallow water equations. The Hamiltonian approach is first used to obtain he Boussinesq equations in terms of the horizontal velocity on the free surface. A direct perturbation method is introduced to derive a general nonlinear shallow water equation. Various forms of Boussinesq equations are discussed. Some of these Boussinesq equations are shown to be unstable subject to short wave disturbances. The dispersion characteristics, both linear and nonlinear, of the shallow water equations are compared with those of the Stokes' wave theory. As far as the linear dispersion is concerned, an optimal form of the Boussinesq equations is identified, which is applicable even in deep water. However, if the nonlinearity is important in deep water, none of the equations discussed in this paper can provide an adequate description of nonlinear dispersion in deep water.

Cross-shore sediment transport is relevant to several coastal engineering problems, yet this process is poorly understood, in part due to the relatively short time that it has been under study. Applications range from the rapid seaward transport associated with beach and dune erosion due to episodic storm events to the extremely slow response to relative sea level rise. At any time and location in the nearshore, there are active forces which tend to displace sediment seaward and landward. One of these forces, gravity, can be quantified readily; however, the others are known only qualitatively. If the forces were held constant, the profile and cross-shore sediment transport would approach equilibrium and zero, respectively. Although equilibrium may never be achieved in nature due to the time varying forcing, a review of concepts and methodology is presented since they can be applied effectively to many coastal engineering problems. There have been accelerated efforts over the last decade to model profiles which are out of equilibrium. Two types of dynamic models are defined as "closed loop", which converge to a target profile, and "open loop", which do not necessarily approach an equilibrium. The formulation of these models includes the sediment continuity equation and a transport equation. The transport equation for the closed loop models is chosen to ensure equilibration for fixed forcing conditions, whereas various representations have been proposed for the open loop models including formulations of the bed load and/or suspended load transport dynamics. Based on published results and considerations of the dynamics, available models of the two types are examined and evaluated. Of the three published closed loop models examined, only one (SBEACH) can represent a bar. The model's performance, based on available comparisons with laboratory and field data, is considered reasonably good. However, the transport direction is independent of local beach slope, an effect that would disqualify the model from representing profile equilibration following a nourishment event, and possibly other applications. Also, because the model calibration is based on laboratory data using monochromatic waves, the bar feature is more accentuated than in nature. Previously published results including those from six open loop models tested against the same data sets are presented and reviewed. Wide ranges of behavior are exhibited by the various models with the transport differing by more than a factor of four and some transport predictions displaying instability effects. The tendency for a pronounced bar under the action of regular waves and a subdued bar for irregular waves was well predicted by most of the open loop models. It is not known whether or not these models are stable for long run times. Because of the uncertainties in convergence and transport magnitudes associated with the open loop models, it is concluded that closed loop models are more appropriate for engineering applications and that open loop models remain in the research arena.

This paper first gives an overall view of physical processes involved with rubble mound structures and a classification of these structures. Governing parameters are described as hydraulic parameters (related to waves, wave run-up and run-down, overtopping, transmission and reflection) and as structural parameters (related to waves, rock, cross-section and response of the structure). The description of hydraulic response is divided into:

• wave run-up and run-down,

• wave overtopping,

• wave transmission,

• wave reflection.

The main part of the paper describes the structural response (stability) which is divided into:

• rock armor layers,

• armor layers with concrete units,

• underlayers, filters, toe protection and head,

• low-crested structures,

• berm breakwaters.

The description of hydraulic and structural response is given in design formulas or graphs which can be used for a conceptual design of rubble mound structures.