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In this paper, a two-dimensional time-domain numerical flume has been established to model and investigate nonlinear interactions between nonlinear surface waves and a submerged inclined thin plate. The model solves the Laplace equation and the fully nonlinear free surface boundary conditions within the framework of potential flow theory based on the high-order boundary element method. The mixed Euler–Lagrangian method is applied to update the water surface at each time step, and the fourth-order Runge–Kutta method for time stepping. A so-called four-point method was employed to separate the second-order harmonic free and bounded wave that has the same wave frequency but different wave celerity in front of and behind the submerged plate. It is found that the amplitude of the second-order harmonic free wave increases with the inclination angle of the submerged plate, and the level/amount of the increase is larger for a larger wave steepness. In addition, the amplitudes of both the second-order reflected and transmitted waves are found to increase with the wave steepness, and their empirical relationships are derived for potential use in practical engineering.

The paper presents the results of the research focused on linear and nonlinear wave generation and propagation in a deepwater towing tank equipped with a single flap-type wavemaker of variable draft. The problem of wave generation and propagation has been theoretically formulated and solved by applying an analytical method; linear and nonlinear solutions were obtained. The linear solution has been verified experimentally. The laboratory experiments confirmed that a linear model can be applied to predict the generation and propagation of water waves of low steepness. However, according to the analysis, the discrepancies between wave profiles predicted by applying the linear and nonlinear models rapidly increases with increasing wave steepness. Additionally, the secondary phenomena which occur in the towing tank, including: disintegration of wave profile, wave reflections from the beach and wave damping, were analyzed. Knowledge on the nonlinear processes and phenomena is essential for modeling the environmental conditions during tests carried out to secure the safety of the naval and offshore constructions. The theoretical formulation was derived and the solution was obtained by the Institute of Hydroengineering of the Polish Academy of Sciences IBW PAN while the experimental research was carried out in Ship Hydromechanics Division of the Ship Design and Research Centre CTO S.A.

The problem of impact pressure distribution on a monopole structure excited by irregular breaking waves is investigated. The analysis is performed by applying a numerical model that combines potential flow model with a Navier-Stokes/VOF solution. The temporal pressure distribution is analysed for two breaking wave cases characterized by the significant difference in the steepness of the wave front. The peak impact pressures are observed in the region below the overturning wave jet where the pressure increases rapidly resulting in a peak value of the slamming coefficient equal to Cs=2π. The vertical load distribution provided by the derived model is more realistic than a rectangular shape distribution applied in engineering practice. This is because the vertical load distribution strongly depends on breaking wave shape and it is difficult to uniquely approximate such a load distribution by a rectangle.

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.

In this study, multi-tracker optimization algorithm (MTOA), particle swarm optimization (PSO), and differential evolution (DE) algorithms were integrated with support vector regression (SVR) to predict energy dissipation downstream of labyrinth weirs (Δ E). In order to evaluate the performance of these methods, the results are compared with corresponding outcome obtained by applying two other methods, namely, multilayer perceptron neural network (MLPNN) and multiple linear regressions methods (MLR). The input parameters comprise the discharge, the upstream flow depth, the crest length of a single cycle of the labyrinth weir, the width of a single cycle of the labyrinth weir, the apex width, the number of labyrinth weir cycles, the sidewall angle, and the height of weir. The results indicate that the meta-heuristic algorithms substantially improve the performance of SVR. The results show that the integrative methods, SVR-MTOA, SVR-PSO, and SVR-DE, are more accurate than the MLPNN and the MLR. In average, the integrative methods provide 39.63% more accurate results than the MLPNN and 79.34% more accurate results than the MLR. The average RMSE and R2 for the integrative methods are 0.0054 m and 0.977, respectively. Among all integrative methods, the SVR-MTOA yields the best results, with RMSE = 0.0044 m and R2 = 0.986. [ABSTRACT FROM AUTHOR]

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.