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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.

A theoretical approach was applied to study the vibration of simple-supported submerged horizontal plate. The derived analytical solution was used to determine natural frequencies for a horizontal plate vibrating in fluid. The investigations were conducted for a very wide range of material density and elasticity modulus covering all materials used in engineering practice. Analysis shows that plate vibration frequency decreases with increasing plate width and draft, and decreases with decreasing plate thickness. Moreover, the results show that a substantial effect on vibration of submerged plate has mass of water above plate. The results also show that plate vibration frequency decreases with increasing plate material density and decreases with decreasing elasticity modulus. The dominant factors affecting the vibration of the submerged plate are the plate width, the plate thickness, and elasticity modulus. For moderate and low values of elasticity modulus, vibration frequency is becoming lower than frequency of water waves. This is very important because wave frequencies overlap with the natural plate vibration frequencies, which may lead to resonance and failure of a structure. The problem is that the overlap of plate vibration frequencies and wave frequencies occurs for very wide range of wave and plate parameters. Laboratory experiments confirm theoretical results. [ABSTRACT FROM AUTHOR]

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 semi-analytical solution to an advection–diffusion equation is coupled with a nonlinear wavemaker model to investigate the effect of strong nonlinearity on wave-induced mixing. The comparisons with weakly nonlinear model predictions reveal that in the case of waves of higher steepness, enhanced mixing affects the subsurface layer of the water column. A fully nonlinear model captures the neglected higher-order terms from a weakly nonlinear solution and provides a reliable estimation of the time-mean velocity field. The corrected wave-induced mass-transport velocity leads to improved estimates of subsurface mixing intensity and ocean surface temperature. [ABSTRACT FROM AUTHOR]

In this study novel integrative machine learning models embedded with the firefly algorithm (FA) were developed and employed to predict energy dissipation on block ramps. The used models include multi-layer perceptron neural network (MLPNN), adaptive neuro-fuzzy inference system (ANFIS), group method of data handling (GMDH), support vector regression (SVR), linear equation (LE), and nonlinear regression equation (NE). The investigation focused on the evaluation of the performance of standard and integrative models in different runs. The performances of machine learning models and the nonlinear equation are higher than the linear equation. The results also show that FA increases the performance of all applied models. Moreover, the results indicate that the ANFIS-FA is the most stable integrative model in comparison to the other embedded methods and reveal that GMDH and SVR are the most stable technique among all applied models. The results also show that the accuracy of the LE-FA technique is relatively low, RMSE=0.091. The most accurate results provide SVR-FA, RMSE=0.034. [ABSTRACT FROM AUTHOR]

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.

A numerical model is derived to investigate the effect of breaking wave shape on impact load on a monopile structure. The derived model combines potential flow model with a Navier-Stokes/VOF solution. The analysis indicates that the breaking wave impact on a monopile structure results in an extremely rapid increase of pressure to high amplitudes. The peak impact pressure occurs in the region below the overturning wave jet. The breaking wave impact leads to extremely high slamming forces. It is observed that the slamming coefficient corresponding to the peak impact force approaches 2π. The area directly affected by the impact force is much higher than the impact area considered in engineering practice. Moreover, the analysis shows that the vertical load distribution is far more realistic than a rectangular shape distribution commonly applied in engineering practice. The results also show that the parameters of the rectangular shape distribution applied in engineering practice are complex function of the breaking wave shape and cannot be uniquely defined beforehand. This is because the vertical load distribution strongly depends on breaking wave shape and it is difficult to uniquely approximate such a complex load distribution by a rectangle. The derived results are compared with experimental data from laboratory experiments on irregular breaking wave loads on a monopile structure. Numerical results are in reasonable agreement with experimental data. [ABSTRACT FROM AUTHOR]

Abstract An efficient semi-analytical solution to the problem of nonlinear water waves propagating at a constant depth is derived using parallel computing techniques. The approach is based on the assumptions of an irrotational flow of an inviscid and incompressible fluid. Velocity potential and free-surface displacement functions are represented in a form based on Fourier series satisfying a formulated initial boundary-value problem by a proper selection of time-dependent coefficients. The eigenfunction expansions are resolved by means of a Fast Fourier Transform technique and a higher-order time-stepping procedure to provide an efficient spectral collocation method of computation of wave-induced free-surface flows. The application of the Fourier transform qualifies the semi-analytical algorithm for efficient parallelization. Hence, the numerical model performance is improved using the computing capabilities of a GPU. The derived semi-analytical approach is easy to implement and may be straightforwardly extended to cover the generation of waves in a flume or a basin. The ability of the model to reproduce nonlinear phenomena is demonstrated in simulations of two- and three-dimensional instabilities of a modulated Stokes wave. The model can be used to solve standard as well as complex wave problems in large computational domains considerably faster than its CPU-based counterpart. [ABSTRACT FROM AUTHOR]

A theoretical model is developed to study the kinematics of water particles and mass transport of wave-induced flow generated in a closed flume. A semi-analytical pseudo-spectral solution to the problem of mechanically generated nonlinear water waves propagating at a constant depth is derived under the potential flow assumptions. Velocity potential and free-surface displacement functions are represented in a form based on Fourier series. The eigenfunction expansions are resolved by means of a Fast Fourier Transform technique and a higher order time-stepping procedure. The derived nonlinear solution of the wavemaker problem is based on Taylor series representation of the free-surface and wavemaker boundary conditions expanded up to an arbitrary truncation order. This technique is employed to study the evolution of a velocity field and particle trajectories under regular gravity waves generated in a wave flume. The instantaneous velocity fields are integrated in time to calculate the particle trajectories and time-averaged spatial distribution of Lagrangian and Eulerian mean velocities. The theoretical results are compared with the available experimental data. A good agreement is observed, which confirms the applicability of the presented theory to the problems of transport processes associated with the propagation of water waves and their generation in the flume. [ABSTRACT FROM AUTHOR]

The problem of a solitary wave attack on a vertical seawall is investigated by applying two approaches. The first is a semi-analytical method in which the Euler equations of motion are solved under the assumption of a potential flow by employing an approach based on the fast Fourier transform technique and a numerical time-stepping scheme. The second approach employed to analyse the problem considered is the smoothed particle hydrodynamics (SPH) method, in which the equations are solved in the Lagrangian coordinates. The two methods are used to simulate solitary wave propagation in water of uniform depth, followed by a wave impact on a vertical wall. The simulations focus on the determination of the maximum run-up of the wave on the wall, the calculation of pressures exerted by water on the structure, and the evaluation of water velocities in the vicinity of the structure. The predictions of the two approaches are compared to identify wave regimes for which both methods give satisfactory results. The results of numerical simulations have shown that both proposed methods predict practically the same free-surface profiles for waves of small and moderate amplitudes. For higher waves, some discrepancies between the results of the two methods occur. The two models results have been also compared with empirical data known from the literature, showing good agreement with experimental measurements in terms of the maximum wave run-up and the wave crest residence time at a wall. [ABSTRACT FROM AUTHOR]

An original method is proposed to extract drift velocity induced by waves propagating in a wave flume. The particle image velocimetry technique is employed to measure velocity fields under regular gravity waves propagating at a constant depth. Based on the measurements, the Eulerian mean current velocity is determined. The instantaneous velocity fields are integrated to calculate particle trajectories and the Lagrangian time-averaged vertical distribution of mass-transport velocity. The Stokes drift velocity is determined by subtracting the Eulerian mean current from the Lagrangian mass-transport velocity. The results are in good agreement with theoretical second-order irrotational solution and confirm applicability of the weakly nonlinear solution for calculating transport processes associated with propagating ocean waves. [ABSTRACT FROM AUTHOR]

Freak waves are unique phenomena that appear unexpectedly on the ocean surface. These waves are not only a danger to fishermen and yachtsmen, but are also capable of damaging large vessels and offshore and coastal structures. The available field measurements that provide insight into the origin and physics of freak waves are very limited. The main objective of the present study was to analyze a unique set of wave data comprising 19,025 wind-wave records from the southern Baltic Sea to provide information on the occurrence, parameters, and prevailing conditions of the formation of freak waves. The complex nature of freak waves was investigated by obtaining spectral and statistical parameters of freak-wave-prone sea states using a wide set of tools. The study revealed a large number of freak-type waves, including waves over 12 m high. The study indicates that these hazardous waves may even exceed 20 m during severe storms in the Baltic Sea. Multi-point wind-wave measurements are needed to provide more information about the physics of freak waves and to eventually develop a prediction or warning system to avoid casualties. [ABSTRACT FROM AUTHOR]

Theoretical investigations supported by a series of original laboratory experiments are conducted to study a wave-induced vertical mixing process. The derived semi-analytical solution is very efficient and is applied to predict the effects of water waves on the temperature changes and the evolution of temperature profiles. The results indicate that waves increase a mixing process. The rate of change of the temperature is higher when waves contributed to mixing process and this process increases with increasing the wavelength to water depth ratio. The analysis indicates that for typical ocean waves the contribution of water waves to mixing may be several orders of magnitude higher than a corresponding contribution arising from the classical diffusion process. This implies a need to conduct more theoretical studies and experimental investigation on the effect of water waves on mixing processes. A series of original laboratory experiments were conducted in the insulated wave flume to verify the derived model. The comparisons show a reasonable agreement between predicted and measured temperature profiles. A reasonable agreement between theoretical results and experimental data is observed for the whole considered range of initial temperature distributions. The comparisons indicate that the model is applicable even to cases when gradients in temperature distributions over water depth are fairly high. [ABSTRACT FROM AUTHOR]

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]

Mixing induced by nonbreaking surface waves was investigated in a wave tank by measuring the thermal destratification rate of the water column. One experiment without waves and four experiments with waves of amplitudes ranging from 1.0 to 1.5 cm and wavelength from 30 to 75 cm were conducted. Water temperature variations at depths from 4 to 12 cm below the surface were measured. In the layer from 4 to 7 cm, the originally dense isothermal lines disperse soon after the waves are generated, whereas the vertical gradient from 9 to 12 cm is maintained for a relatively long time. The time span, during which the water temperature becomes well mixed, changes from about 20 h for the case with no waves to tens of minutes for the case with waves, and it decreases with increasing wave amplitude and wavelength. A one-dimensional diffusion numerical model with wave-induced mixing parameterization shows consistent results with the measurement. The study demonstrates that the mixing induced by nonbreaking waves may add an important contribution to the vertical mixing process in the upper ocean and suggests a way to parameterize wave-induced mixing in numerical ocean models. [ABSTRACT FROM AUTHOR]