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A three-dimensional numerical solution was developed to determine the wave field in a narrow channel with side porous caves. The solution was achieved by applying the boundary element method. The model was applied to determine the effect of the geometry of caves and the physical and hydraulic properties of the porous material in the caves on the wave field in the channel. The results show that the cave geometry and the physical and hydraulic properties of porous material in the cave have a significant effect on the wave field in a channel. Wave transmission down the channel usually decreases with increasing cave length and cave width and decreases with increasing porosity. Moreover, wave transmission usually decreases with increasing wave-damping properties for porous material of low damping properties and increases with increasing wave-damping properties for porous material of high damping properties. A reduction of wave transmission down the channel, often substantial, can usually be achieved by increasing the porosity and increasing the wave-damping properties of the porous material. The results and additional analysis show that a reasonable wave transmission level can be achieved even for fairly short porous caves and that the model can be applied to select an optimal cave system for any prespecified conditions. Theoretical results are found to be in reasonable agreement with experimental data. CE Database subject headings: Channels, waterways; Damping; Numerical models; Porous media; Hydraulic properties.

A 3D numerical solution was derived to determine the wave field in a physical wave tank equipped with a porous wave absorber of variable width and draft. The solution was achieved by applying the boundary element method. The model was applied to analyze the effect of the geometry and material of wave absorbers on wave reflection to eventually equip a wave tank with a proper wave absorber. The results show that absorber geometry has a complex, often surprising and nonintuitive effect on wave reflection. A more pronounced effect on wave reflection possesses physical and hydraulic properties of the material used to build a wave absorber. A reduction of wave reflection can usually be achieved by increasing absorber length and simultaneously decreasing its slope, and often a reduction of wave reflection can be achieved by increasing absorber draft or width. Moreover, a reduction of wave reflection, often substantial, can be achieved by increasing porosity and the damping coefficient. The results and additional analysis show that a reasonable wave reflection level can already be achieved for fairly short absorbers, and the model can be applied to select an optimal wave absorber for any prespecified conditions. Theoretical results are in reasonable agreement with experimental data. CE Database keywords: Numerical models; Wave generation; Absorbers; Wave tanks.

A solution to the diffraction problem for second-order surface waves by a horizontal rectangular cylinder founded on a rubble base is presented. The solution was obtained by the method of matched eigenfunction expansions. Wave load on a cylinder was found by analytical integration of pressure over the wetted surface of a cylinder. The results show that the cylinder width has a significant effect on second-order vertical force and surprisingly little effect on second-order horizontal force, while the cylinder draft has a significant effect on second-order horizontal force and surprisingly little effect on second-order vertical force. Moreover, the results show surprisingly little effect of rubble base damping properties on second-order wave load. The solution reveals significant second-order load on a founded cylinder. The second-order load components may exceed by many times the corresponding first-order quantities. This phenomenon occurs within the commonly accepted range of the applicability of a second-order wave theory.

The effect of permeability on the stability of homogeneous and multilayered rubble bases is investigated. The approach consists of theoretical modeling of the interaction of water waves with a caisson-type breakwater and its rubble foundation, and then employing predicted flow fields in a stability model to determine the required stone size. The permeability is shown to have significant effect on the stability. The results indicate that the stability increases with increasing the rubble-base permeability at intermediate water depths, and increases with decreasing the rubble-base permeability in shallow water. The armor-layer permeability has little effect on the stability at intermediate water depths, but in shallow water the permeability of the armor layer has little effect on the stability only for rubble bases of low core permeability. The significant effect of permeability on the stability implies a need for including permeability effects in hydraulic modeling. An analysis or scaling of experimental data without taking the effect of permeability into account may lead to confusing conclusions or just incorrect results, which is demonstrated on the basis of the laboratory results commonly applied in design.

An analysis of the stability of multilayered rubble bases is conducted applying an approach that is based on numerical modeling. The approach consists of theoretical modeling of the interaction of water waves with a caisson-type breakwater and its rubble base and then employing the predicted flow field in a stability model to determine the required stone size. The flow in the rubble is described by the linearized Forchheimer equation of motion in a coarse granular medium. The boundary element method is applied to solve the problem of the interaction of water waves with the caisson and its rubble base, and to calculate the velocity field. The rubble base stability is determined as a function of the waves and the geometry of rubble base. It is shown that the stability increases with decreasing incident wave height, rubble base height, and bench width. Preliminary results also indicate the necessity of including permeability in the stability analysis. The theoretical results are in reasonable agreement with available experimental data.

Wave loads correct to the second order are presented for a sinusoidally moving planar wavemaker. The loads are calculated from eigenseries that are valid for a generic planar wavemaker. The second-order time-dependent and time-independent horizontal forces and moments are presented for four planar wavemaker geometries. The contributions of the second-order loads for waves of moderate steepness are approximately 15% in deep water and up to 50% or more in intermediate or shallow water. The second-order loads depend on the wavemaker geometry and on the location of the wavemaker hinge. The theoretical loads are in reasonable agreement with experimental data for a large-scale hinged wavemaker.

A solution to the diffraction problem for second-order surface waves by a semisubmerged horizontal cylinder of rectangular cross section is presented. The boundary-value problem is solved by the method of matched eigenfunction expansions. Wave loads are calculated by integrating pressures over the wetted surface of the cylinder. Horizontal and vertical forces and the moment about the heel of the cylinder are presented for four cylinder geometries. The results reveal that second-order components may become the significant contributions to the loads in deep water and may exceed the corresponding first-order quantities even for waves of moderate steepnesses. Theoretical results are confirmed by experimental data.

A theoretical approach is applied to describe the diffraction of water waves by a structure in a channel of arbitrary configuration. The solution was achieved by applying the three-dimensional (3D) boundary element method and is valid for a structure of arbitrary shape. The derived model was applied to analyze the effect of the structure geometry and the configuration of the channel on diffracted wave field and on generalized wave-load components. The results show that the wave field in the channel and wave loads on a structure strongly depend on wavelength and the geometry of the structure. The far-field wave amplitudes and wave load components oscillate with increasing wave number, and for selected wave frequencies, the incoming waves are fully transmitted and forces on the structure simultaneously vanish. This result is of practical importance. The oscillations depend primarily on the length of the structure and are associated with the formation of partially standing waves in the subdomain along the structure, which affect wave reflection in the main channel and wave loads on the structure. The effect of the draft and width of the structure on the oscillations is very limited. However, the draft and width of a structure has a substantial effect on the magnitude of wave reflection and transmission, especially for narrow channels. Moreover, the draft and width of a structure has a substantial effect on wave-load components. The analysis of the results indicates that it is difficult to simplify a theoretical description because, even for a channel of a constant depth and ideal vertical walls, once a structure is present in the channel, the problem needs to be described by 3D formulation, which complicates the solution. Theoretical results are in reasonable agreement with experimental data. [ABSTRACT FROM AUTHOR]