The effect of waves on rubble-mound structures

For thousands of years breakwaters have been built at or near the coast to protect harbors or coastlines from wave attack. One of the earliest known harbor protection schemes was devised in about 2000 B.C. for the Port of Pharos on the open coast of Egypt; it had a rubble-mound breakwater approximately 8500 ft long composed of large blocks of stone with smaller stone filling the spaces between blocks (Savile 1940). Until the development of experimental laboratory techniques to investigate the effect of waves on breakwaters, these structures were designed primarily from experience gained from other similar structures. It is the purpose of this review to discuss various aspects of the hydrodynamics of wave attack on such structures and the relation of certain analytic considerations and experimental results to the design of a rubble-mound. A breakwater built as a rubble-mound is constructed by placing material of various sizes layer by layer (or unit by unit) until the desired cross-section shape is achieved. Generally, the units are not structurally connected, so that the integrity of the rubble-mound depends on features such as the weight of the material, the interlocking nature of the material, and the cross section of the structure. Usually the structure is built with material graded from smaller sizes in the core to larger material armoring the face against wave attack. The armor layer may be composed of quarry-stone, if it is available in the required sizes and is economically feasible to use. When these conditions are not met, specially designed concrete units for armoring the face of the rubble-mound have been developed that tend to interlock better than rock when properly placed; hence, it may be possible to use armor units lighter than the required quarry-stone. Over the years numerous geometric shapes have been developed for such armor units, with each shape generally introduced in an attempt to improve on the interlocking characteristics of its predecessors. To mention only a few, various names used for different units are: tribars, tetrapods, quadripods, and dolosse. A brief description of two of these is presented; for a more detailed discussion of shape along with drawings of the units the interested reader is directed to CERC (1966) and Hudson(1974). Tribars, which consist basically of three circular cylinders connected by a yoke of three cylinders, are usually placed in a uniform geometric pattern on the face of the rubble-mound. Dolosse are shaped like the letter "H" with the vertical legs rotated 90° to each other, and are generally placed randomly on a rubble-mound face. It is the effective interlocking of dolosse that leads to the use of random placement techniques. Obviously an important aspect in the design of a rubble-mound is its stability under wave attack. This subject is discussed in detail, along with descriptions of the basis for certain design approaches currently used. The support of these design criteria as well as their limitations are discussed with reference to available experimental data. Three other aspects of the effect of waves on rubble-mounds are treated in this review: wave run-up, transmission, and overtopping. Run-up is defined as the vertical height above still water level to which waves incident upon a structure can be expected to travel up the face of the structure. Wave run-up is important in defining both the amount of wave energy transmitted over and through permeable rubble-mounds and also the quantity of water that may be expected to overtop the structure. In each of the following sections the discussion is directed toward understanding the fluid-mechanic aspects of the various problems and the features and the shortcomings of analytical and experimental models used in connection with the design of breakwaters constructed as rubble-mounds

Laboratory design-studies of the effect of waves on a proposed island site for a combined nuclear power and desalting plant

There were four major objectives to this investigation: 1) the determination of the degree of stability of the island face when constructed of armor units of various weights; 2) the run-up for a two-dimensional wave system impinging on the island face; 3) the run-up envelope on the four sides of the island in a three-dimensional model; and 4) the wave patterns caused by the effect of the island on its wave environment. Models having three different length scales were tested in the wave tank (1:50, 1:45, and 1:40) and these models are referred to as the two-dimensional models. One model was tested in the wave basin at an undistorted scale of 1:150 and it is referred to in this report as the three-dimensional model. The first two-dimensional model was built to a scale of 1:50 and essentially corresponded to the original design proposed by Omar Lillevang, Consulting Engineer to the Bechtel Corporation. The prototype tribar weight, equivalent to the model tribar used, was 18.9 tons. This structure was stable; however, it was overtopped by waves. With an increase in the crest elevation from +30 ft. to +40 ft. some overtopping was still experienced. The second model was built at an increased scale, 1:40. At the same time the composite slope which existed in the original design was changed so that the island face had a continuous slope of 3 horizontal to 1 vertical with the crest of the defense at elevation +40 ft. This particular model scale was chosen so that, according to the literature, the tribars would be at a condition of incipient failure for high waves. Since the same armor units were used in this model as were used in the 1:50 scale model, the increase in model scale reduced the equivalent weight of the tribars to 9.7 tons and the maximum weight of the armor rock "B" from 10 tons to 5.1 tons. The prototype structure which corresponds to this model was found to be unstable, as expected. It was observed in testing that a critical feature of the construction which contributes to the stability of the structure is the degree to which the cap-rock section is interlocked with the tribar section. The modification made to the slope of the island face and the increased crest elevation eliminated the problem of overtopping, and the maximum run-up for a 14-sec. wave was to elevation +38 ft. Since the model having a 1:40 length scale was unstable and that with a scale of 1:50 was stable, a third model was constructed with a model scale between these two values, a scale of 1:45. The equivalent prototype tribar weight and the maximum weight of the "B" rock for this third model, still using the same model armor units, were increased to 13.8 tons and 7.3 tons respectively by this change. The slope of the wave defense and the crest elevation were the same for this structure as they were in the 1:40 scale model, i. e., a continuous slope of the island face of 3 horizontal to 1 vertical and a crest elevation of +40 ft. This model was satisfactory both with respect to stability and to run-up. Run-up measurements were made for waves of various heights at wave periods of 16 sec., 14 sec., and 12 sec. The maximum run-up was to elevations +39 ft., +35 ft., and +31 ft. respectively for these three wave periods. The three-dimensional model of the ocean bottom and the island was built to an undistorted scale of 1:150 with the island constructed the same as the 1:45 scale two-dimensional model. In these tests in the large wave basin the wave direction was varied as well as the wave period and wave height. The run-up envelopes obtained showed that, for comparable wave heights, the worst condition of run-up was for normally incident waves impinging on the seaward face of the island. The run-up measured for the normally incident direction was usually approximately 10% less than the run-up in the two-dimensional model for the same wave periods and wave heights. For the case of oblique wave incidence the maximum run-up was at the island corner first attacked by the wave with the run-up decreasing with distance from this corner, and this run-up was comparable to the maximum run-up experienced at normal wave incidence. However, the maximum average run up for the oblique case was significantly less than that experienced in the case of normal wave incidence. The run-up on the shoreward face of the island for all wave directions was of the order of 1/10th of that experienced on the seaward face. Detailed observations of the wave pattern in the lee of the island indicated that there were regions near the beach where the currents were in a direction opposite to the observed general current. From overhead photographs it was found that generally this occurred in regions where the waves which diffract from around the sides of the island intersect. Measurements were made of the maximum elevation of the water surface in the region of the causeway for the case of oblique wave incidence

A Lagrangian model for wave-induced harbour oscillations

A set of equations in the Lagrangian description are derived for the propagation of long gravity waves in two horizontal directions for the purpose of determining the response of harbours with sloping boundaries to long waves. The equations include terms to account for weakly nonlinear and dispersive processes. A finite element formulation for these equations is developed which treats the propagation of transient waves in regions of arbitrary shape with vertical or sloping boundaries. Open boundaries are treated by specifying the wave elevation along the boundary or by applying a radiation boundary condition to absorb the waves leaving the computational domain. Nonlinear aspects of the interaction of long gravity waves with sloping boundaries and frequency dispersion due to non-hydrostatic effects are investigated. Results from the model are then compared with laboratory experiments of the response to long-wave excitation of a narrow rectangular harbour with a depth that decreases linearly from the entrance to the shore line

Bow Wave Dynamics

Experimental studies of air entrainment by breaking waves are essential for advancing the understanding of these flows and creating valid models. The present study used experimental simulations of a ship bow wave to examine its dynamics and air entrainment processes. The simulated waves were created by a deflecting plate mounted at an angle in a supercritical free-surface flow in a flume. Measurements of the bow wave geometry at two scales and also for a bow wave created by a wedge in a towing tank are presented. Contact line and bow wave profile measurements from the different experiments are compared and demonstrate the similarity of the flume simulations to the towing tank experiments. The bow wave profile data from the towing tank experiments were used to investigate the scaling of the wave with the flow and the dependence on geometric parameters. In addition, surface disturbances observed on the plunging wave are documented herein because of the role they play in air entrainment. The air entrainment itself is explored in Waniewski et al (2001)

Void Fraction Measurment Beneath a Stationary Breaking Wave

Impedance based techniques have been used to quantify air entrainment by a stationary breaking wave at the bow of a ship. The present paper describes an impedance based void fraction meter which was developed to make measurements in this high speed, unsteady, multiphase flow, and details of its calibration are provided. In addition, air entrainment data from an experimental simulation of a bow wave are presented. The local, time averaged void fraction was mapped for flow cross sections beneath the plunging wave jet, revealing the location of the clouds of bubbles formed by that jet impacting the incoming water surface. Size distribution functions for the bubbles within the bubble clouds are also presented. The results are correlated with the wave structure described in Waniewski et al. (1997)

Wave-induced oscillations of small moored vessels

The general objective of this research is to investigate the motion of small boats moored to fixed or floating platforms in a standing wave environment. The study is directed toward an understanding of the problems of mooring small craft in marinas and toward providing information that will assist in the planning and operation of marinas. This report deals with the first phase of the experimental study concerning the surge motions of a simply moored body in a standing wave system. The body is a rectangular parallelpiped moored to a fixed support by means of a linear spring. In general it can be stated that the inviscid theory proposed by Wilson (5) and Kilner (7) adequately describes the surge motion of this body for standing waves ranging from shallow-water to deep-water waves and for ratios of body length to wave length from 0.1 to 1.5. Agreement between the experimental data and the theoretical response curves is better for certain ranges of the ratio of the natural period of the body to the wave period than for others. This is attributed to the effect of wave generation by the body on its motion. The response curves become more selective with respect to frequency as the distance of the body from a reflecting surface increases. Therefore, coupling this with viscous effects it is possible to reduce the effect of resonance considerably simply by choosing the proper body location in its standing wave environment for a particular natural frequency. The coefficient of virtual mass of the body in surge (ratio of width to length, 1:4) determined from simple free oscillations was found to correlate best with the ratio of draft to beam. For a variation of draft to beam from 0.25 to 0.95 the coefficient of virtual mass varied from approximately 1.1 to 1.25. This study emphasizes the need for more field information on the characteristics of small craft, such as the elastic characteristics of the mooring system, natural frequencies of moored boats, and the relative importance of viscous effects upon boat motions

Runup and rundown generated by three-dimensional sliding masses

To study the waves and runup/rundown generated by a sliding mass, a numerical simulation model, based on the large-eddy-simulation (LES) approach, was developed. The Smagorinsky subgrid scale model was employed to provide turbulence dissipation and the volume of fluid (VOF) method was used to track the free surface and shoreline movements. A numerical algorithm for describing the motion of the sliding mass was also implemented. To validate the numerical model, we conducted a set of large-scale experiments in a wave tank of 104m long, 3.7m wide and 4.6m deep with a plane slope (1:2) located at one end of the tank. A freely sliding wedge with two orientations and a hemisphere were used to represent landslides. Their initial positions ranged from totally aerial to fully submerged, and the slide mass was also varied over a wide range. The slides were instrumented to provide position and velocity time histories. The time-histories of water surface and the runup at a number of locations were measured. Comparisons between the numerical results and experimental data are presented only for wedge shape slides. Very good agreement is shown for the time histories of runup and generated waves. The detailed three-dimensional complex flow patterns, free surface and shoreline deformations are further illustrated by the numerical results. The maximum runup heights are presented as a function of the initial elevation and the specific weight of the slide. The effects of the wave tank width on the maximum runup are also discussed

Integration of the Head and Forelimb in Bipedal Hominids

Integration, a fundamental property of organisms, occurs via multiple mechanisms and for diverse reasons. Although there has been substantial work on the genetic and epigenetic mechanisms by which developmental integration occurs, we have less of an understanding of the evolutionary relationships between functional and developmental integration. In this respect, human evolution provides an interesting test case. In quadrupedal mammals, there is considerable functional integration among and between the limbs, but little functional integration between the limbs and the skull. The evolution of bipedalism in hominids, however, provided new opportunities for novel forms of integration by emancipating the forelimbs from any major role in locomotion. Here we consider how the forelimb and head become increasingly integrated in the genus Homo because of the biomechanical challenges of running. While the arm and the head interact little during walking, we have found that, during running, the stance side arm acts as a counterbalance to the head, stabilizing it against impulsive pitching forces generated by the heel strike transient. Moreover, the functional properties of this linkage may have driven several developmental changes in the proportions of the arm and the anatomy of the shoulder girdle during human evolution. Thus, evolutionary changes in arm and head morphology during human evolution may be more integrated than previously considered.AnthropologyHuman Evolutionary Biolog