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Here, for non-breaking short surface waves, we have experimentally determined the value of the turbulent eddy viscosity ν T or its ratio ν T * ≡ ν T / ν , where ν is the water kinematic viscosity. The non-breaking wave-generated turbulent eddy viscosity ν T was found to depend on the ratio of the wave period, T, to the microscale Kolmogorov time scale, τ η . Our observations were consistent with ν T * = 1.46 · (T / τ η) − 2.6 when (T / τ η) < 0.9 . That implied that the ν T * ∝ ϵ − 1.3 , where ϵ is the background turbulent energy dissipation rate. The near-surface turbulent flow associated with non-breaking waves was characterized by a short inertial subrange. The background turbulence appears to modulate the amount of energy the non-breaking waves dissipate locally and, consequently, the wave's decay rate. Our results imply that the background turbulent flow acts as a lubricant, permitting waves to propagate further when traveling over a more energetic turbulent background flow. Our results have implications for the modeling of oceanic wave propagation or the air–sea exchange processes. [ABSTRACT FROM AUTHOR]

Here, for non-breaking short surface waves, we have experimentally determined the value of the turbulent eddy viscosity νT or its ratio νT*≡νT/ν, where ν is the water kinematic viscosity. The non-breaking wave-generated turbulent eddy viscosity νT was found to depend on the ratio of the wave period, T, to the microscale Kolmogorov time scale, τη. Our observations were consistent with νT*=1.46·(T/τη)−2.6 when (T/τη)<0.9. That implied that the νT*∝ϵ−1.3, where ϵ is the background turbulent energy dissipation rate. The near-surface turbulent flow associated with non-breaking waves was characterized by a short inertial subrange. The background turbulence appears to modulate the amount of energy the non-breaking waves dissipate locally and, consequently, the wave’s decay rate. Our results imply that the background turbulent flow acts as a lubricant, permitting waves to propagate further when traveling over a more energetic turbulent background flow. Our results have implications for the modeling of oceanic wave propagation or the air–sea exchange processes.

The numerical modeling of sediment transport under wave impact is challenging because of the complex nature of the triple wave–structure–sediment interaction. This study presents three-dimensional numerical modeling of sediment scouring due to non-breaking wave impact on a vertical seawall. The Navier–Stokes–Exner equations are approximated to calculate the full evolution of flow fields and morphodynamic responses. The bed erosion model is based on the van Rijn formulation with a mass-conservative sand-slide algorithm. The numerical solution is obtained by using a projection method and a fully implicit second-order unstructured finite-volume method in a σ-coordinate computational domain. This coordinate system is employed to accurately represent the free-surface elevation and sediment/water interface evolution. Experimental results of the velocity field, surface wave motion, and scour hole formation hole are used to compare and demonstrate the proposed numerical method’s capabilities to model the seawall scour.

Abstract This paper aims at investigating the intensity of the load applied by non-breaking waves on the recurved parapet wall of vertical breakwaters. For this purpose, 2-D experiments were carried out on a simple vertical breakwater physical model with four different geometries of the parapet (with an "exit angle" of recurve of 0°, 45°, 60° and 90°), under both regular and irregular waves. The tests showed the presence of loads of a quasi-static nature and loads with a typical church roof impulsive behaviour, depending on the (non breaking) wave characteristics and on the shape of the parapet. This impulsive force resulted significantly larger than the quasi-static load of the pure vertical wall case. The maximum measured total force under regular waves was compared with the one obtained by a numerical model based on IHFOAM. For irregular waves with H s equal to 80% of the freeboard, the maximum measured horizontal load on a 90° recurved wall is equivalent to the force applied by a constant pressure of order 5 ρ gH s. It was found, by analysing waves near the leading edge of a wave-group, that history effects are important, i.e., in certain circumstances, a high wave preceded by lower waves generated a larger force than if it had been preceded by waves of the same height. For regular tests, the largest impulsive forces occurred basically at the beginning of the tests, during the initial transient ramp-up period. The irregular wave overtopping was also measured, showing good agreement with the existing predictive formulae and confirming the significant reduction of mean discharge with increasing exit angle and overhanging extension of the parapet. Highlights • Four geometries of the parapet were tested, with exit angle 0°, 45°, 60°, and 90°. • Regular (RW) and irregular waves (IW) were generated. • Under IW, impulsive loads (IL) were 5 times larger for 90° parapet than for 0°. • Under RW, IL were smaller than under IW, except for the initial transient phase. • The measured loads were predicted with satisfaction by numerical simulations. • The overtopping was in good agreement with the existing predictive formulae. [ABSTRACT FROM AUTHOR]

Highlights • The physical mechanism of wave scattering around the cylinder are presented and the effects of wave steepness and wave diffraction on wave run-up are discussed. • The present Navier–Stokes model is able to reproduce the wave field and deal with high non-linearities and large deformation of the free-surface around the cylinder with reasonable accuracy. • The numerical simulations are used to describe some nonlinear features in the wave run-up profiles at the given wave probes around the cylinder. Abstract In wave-structure interaction, wave run-up is an important phenomenon that needs to be considered in the design of offshore structures. A thorough understanding of the physics of the nonlinear flow phenomena is necessary for the better insight into the run-up phenomenon. The present work, primarily, is focused on the hydrodynamic simulation of wave run-up and mainly seeks to evaluate the importance of wave scattering types identified by Swanet al. (2005) and lateral progressive edge waves on nonlinear wave amplification around a single fixed cylinder. The analysis is performed numerically using Navier-Stokes solver based on OpenFOAM over a range of wave steepnesses and wavelengths. In order to study wave-cylinder interaction, a numerical wave tank is utilized which includes IHFOAM toolbox for wave generation. For the simulations, the cylinder is assumed vertical and surface piercing with a circular cross-section and the incident wave is considered fifth-order Stokes, regular and non-breaking in deep water. The obtained numerical results that are mainly analyzed in this study include local surface elevation, the scattered wave field around the cylinder and the wave forces. A grid-space and time step refinement study are carried out to evaluate the performance and accuracy of numerical wave tank. The numerical results are compared with experimental data provided by ITTC (OEC), (2013) and a good agreement was obtained which indicates that OpenFOAM is very capable of accurate modeling of nonlinear wave interaction with offshore structures. The harmonic analysis for both short and long wave cases indicates that the scattered wave field around the cylinder involves high harmonics wave run-up. It is confirmed that even the wave-structure interaction caused by the linear incident wave, can lead to weakly nonlinear wave amplification around the cylinder. In the case of long waves cases, the harmonic loading involves at-least third harmonics due to the occurrence of the second wave run-up at the front part of the cylinder. [ABSTRACT FROM AUTHOR]

A numerical model was developed to simulate the evolution of a mound placed in the offshore (i.e., outside the zone of wave breaking), exposed to varying non-breaking waves and water levels. The net sediment transport rate is assumed to be mainly dominated by bed load transport, where wave asymmetry plays an important role. The net transport over a wave cycle is expressed with reference to an equilibrium profile, which ensures model reliability and robustness. In order to validate the model, data collected at two field sites, Cocoa Beach and Perdido Key Beach in Florida, USA, were employed. The numerical results show good agreement with the measured data from the two sites in terms of the profile evolution. It demonstrates that the model has the capability to simulate the evolution of mounds placed in the offshore. In addition, several scenarios with different mound volume and location designs were investigated to indicate potential uses for the model. The results illustrate how the mound evolution is influenced by the volume and location of the mound placement.

This paper describes 2-D numerical simulations of velocity and pressure fields generated by non-breaking waves on a vertical breakwater with a recurved parapet wall. The influence of the geometrical characteristics of the parapet is investigated. An impulsive pressure force is identified and discussed with respect to the pure vertical wall case. This force is generated by the seaward flow confinement induced by the surging wave crest. We refer to this impulsive impact as “confined-crest impact”. A large part of the vertical wall is affected by an impulsive increase in pressure caused by pulsating wave, compared to the case where the parapet is completely vertical. The maximum values of the impulsive pressures are localized under the recurved parapet. The total force increase on the entire structure may be significant when compared to the pure vertical wall case. [ABSTRACT FROM AUTHOR]

A 1D numerical model of Nonlinear Shallow Water Equations (NSWEs) coupled to an advection equation for suspended sediment and a bed evolution equation is developed. The moving boundary at the shoreline is treated by a coordinate transformation method (CTM). An absorbing-generating seaward boundary condition in the transformed variables is also developed. The purely hydrodynamic component (NSWEs) is verified against analytical results. The NSWEs plus advection equation is verified quasi-analytical results. The fully-coupled model with bed change due to bed-load is verified against a single swash event and long-term numerical simulation. Excellent agreement is observed in all verifications. [ABSTRACT FROM AUTHOR]

In this paper a three-dimensional circulation model has been applied to determine the spatial distribution of the temperature and mixed-layer depth (MLD) of a medium-sized shallow lake. In order to reproduce the vertical thermal structure of the lake, the impact of waves has been incorporated using several recently published schemes. These schemes approximate the additional mixing due to the orbital motion of waves, the turbulent kinetic energy produced by waves, or both. The reference solver is the Reynolds-Averaged Navier-Stokes equations with two-equation Mellor-Yamada 2.5 turbulence closure. The wave field is characterized by bulk parameters, e.g. significant wave height. The sensitivity to the choice of the wave mixing scheme is analyzed by means of an academic test case. The accuracy of the scheme is explored through data collected in Lake Balaton. The modeled temperature profiles and MLDs match measurements much better when the effect of non-breaking surface waves is included. [ABSTRACT FROM AUTHOR]

Scour may act as a threat to coastal structures stability and reduce their functionality. Thus, protection against scour can guarantee these structures’ intended performance, which can be achieved by the accurate prediction of the maximum scour depth. Since the hydrodynamics of scour is very complex, existing formulas cannot produce good predictions. Therefore, in this paper, Genetic Programming (GP) and Artificial Neural Networks (ANNs) have been used to predict the maximum scour depth at breakwaters due to non-breaking waves ( S max / H n b ). The models have been built using the relative water depth at the toe ( h t o e / L n b ), the Shields parameter ( θ ), the non-breaking wave steepness ( H n b / L n b ), and the reflection coefficient ( C r ), where in the case of irregular waves, H nb =H rms , T nb =T peak and L nb is the wavelength associated with the peak period ( L nb =L p ). 95 experimental datasets gathered from published literature on small-scale experiments have been used to develop the GP and ANNs models. The results indicate that the developed models perform significantly better than the empirical formulas derived from the mentioned experiments. The GP model is to be preferred, because it performed marginally better than the ANNs model and also produced an accurate and physically-sound equation for the prediction of the maximum scour depth. Furthermore, the average percentage change (APC) of input parameters in the GP and ANNs models shows that the maximum scour depth dependence on the reflection coefficient is larger than that of other input parameters. [ABSTRACT FROM AUTHOR]

Coastal structures may cease to function properly due to seabed scouring. Hence, prediction of the maximum scour depth is of great importance for the protection of these structures. Since scour is the result of a complicated interaction between structure, sediment, and incoming waves, empirical equations are not as accurate as machine learning schemes, which are being widely employed for the coastal engineering modeling. In this paper, which can be regarded as an extension of Pourzangbar et al. (2016), two soft computing methods, a support vector regression (SVR), and a model tree algorithm (M5′), have been implemented to predict the maximum scour depth due to non-breaking waves. The models predict the relative scour depth ( S max /H 0 ) on the basis of the following variables: relative water depth at the toe of the breakwater ( h toe /L 0 ), Shields parameter ( θ ), non-breaking wave steepness ( H 0 /L 0 ), and reflection coefficient ( Cr ). 95 laboratory data points, extracted from dedicated experimental studies, have been used for developing the models, whose performances have been assessed on the basis of statistical parameters. The results suggest that all of the developed models predict the maximum scour depth with high precision, the M5′ model performed marginally better than the SVR model and also allowed to define a set of transparent and physically sound relationships. Such relationships, which are in good agreement with the existing empirical findings, show that the relative scour depth is mainly affected by wave reflection. [ABSTRACT FROM AUTHOR]

This paper presents experimental measurements of beaching times for buoyant microplastic particles released, both in the pre-breaking region and within the surf zone. The beaching times are used to quantify cross-shore Lagrangian transport velocities of the microplastics. Prior to breaking the particles travel onshore with a velocity close to the Lagrangian fluid particle velocity, regardless of particle characteristics. In the surf zone the Lagrangian velocities of the microplastics increase and become closer to the wave celerity. Furthermore, it is demonstrated that particles having low Dean numbers (dimensionless fall velocity) are transported at higher mean velocities, as they have a larger tendency to be at the free-surface relative to particles with higher Dean numbers. An empirical relation is formulated for predicting the cross-shore Lagrangian transport velocities of buoyant microplastic particles, valid for both non-breaking and breaking irregular waves. The expression matches the present experiments well, in addition to two prior studies. [Display omitted] • Experiments show that buoyant microplastic particles are transported onshore by waves until they are eventually beached. • Prior to breaking the microplastic transport velocity is near that of the fluid, regardless of particle characteristics. • In the surf zone the Lagrangian particle transport velocities increase, becoming closer to the breaking wave celerity. • Beneath breaking waves particles with high (low) rise velocities have larger (smaller) Lagrangian transport velocities. • An equation predicting wave-induced transport velocity of buoyant microplastics across the coastal profile is provided. [ABSTRACT FROM AUTHOR]

Abstract: Empirical formulas have been developed to calculate the fractional bed-load and suspended-load transport rates and near-bed suspended-load concentration under non-breaking waves and currents for coastal applications. The formulas relate the bed-load transport rate to the grain shear stress, the suspended-load transport rate to the energy of the flow system, and the near-bed suspended-load concentration to the bed-load transport rate, velocity and layer thickness. Adequate methods are adopted to determine the bed shear stress due to coexisted waves and currents. The hiding and exposure mechanism in nonuniform bed material is considered through a correction factor that is related to the hiding and exposure probabilities and in turn the size composition of bed material. The developed formulas have been tested using a large database of single-sized sediment transport and several sets of multiple-sized sediment transport data collected from literature, and compared with several existing formulas. The developed formulas can provide reasonably good predictions for the test cases. [Copyright &y& Elsevier]

Abstract: Using a detailed set of hydrodynamic and suspended-sediment observations, we developed data-driven algorithms based on Boosted Regression Trees and Artificial Neural Networks to predict suspended-sediment reference (near-bed) concentration using water depth, wave-orbital semi-excursion, wave period and bed-sediment grainsize as inputs. With one exception, the response of the data-driven algorithms was physically sound; the exception was the response to water depth. Outside of the range covered by the data, predictor performance could not be assessed and is not necessarily reliable. Boosted Regression Trees provide the best predictor of suspended-sediment reference concentration and have a clear explanatory power. Artificial Neural Networks provide slightly poorer predictions. Although the response of the latter is more difficult to interpret, they can be more easily included in numerical models simulating larger (in space) and longer (in time) morphodynamic behavior. Within the range of variability provided by the measurements, these algorithms outperform conventional process-based predictors. [Copyright &y& Elsevier]

Abstract: A new database of laboratory experiments involving sand transport processes over horizontal, mobile sand beds under full-scale non-breaking wave and non-breaking wave-plus-current conditions is described. The database contains details of the flow and bed conditions, information on which quantities were measured and the value of the measured net sand transport rate for 298 experiments conducted in 7 large-scale laboratory facilities. Analysis of the coverage of the experiments and the measured net sand transport rates identified the following gaps in the range of test conditions and/or the type of measurements: (i) graded sand experiments, (ii) wave-plus-current experiments and (iii) intra-wave velocity and concentration measurements in the ripple regime. Furthermore, it highlights two areas requiring further research: (i) the differences in sand transport processes and sand transport rates between real waves and tunnel flows with nominally similar near-bed oscillatory flow conditions and (ii) the effects of acceleration skewness on transport rates. The database is a useful resource for the development and validation of sand transport models for coastal applications. [Copyright &y& Elsevier]

The numerical modeling of sediment transport under wave impact is challenging because of the complex nature of the triple wave–structure–sediment interaction. This study presents three-dimensional numerical modeling of sediment scouring due to non-breaking wave impact on a vertical seawall. The Navier–Stokes–Exner equations are approximated to calculate the full evolution of flow fields and morphodynamic responses. The bed erosion model is based on the van Rijn formulation with a mass-conservative sand-slide algorithm. The numerical solution is obtained by using a projection method and a fully implicit second-order unstructured finite-volume method in a σ -coordinate computational domain. This coordinate system is employed to accurately represent the free-surface elevation and sediment/water interface evolution. Experimental results of the velocity field, surface wave motion, and scour hole formation hole are used to compare and demonstrate the proposed numerical method's capabilities to model the seawall scour. [ABSTRACT FROM AUTHOR]

Abstract: Wave run-up, and flow visualization experiments were conducted with a 1:2 sloped sea wall model. The visualization experiments gave an overview of flow fields in reflected, non-breaking conditions. Maximum particle velocities were found to be significantly smaller than suggested in the literature. Downrush produced a fast sheet flow, extending down to the toe of the sea wall. This created a ‘reverse’ breaker during the retreat of the initially non-breaking wave, which explains the high-energy dissipation rates for non-breaking waves reported in the literature. Embankments may therefore be exposed to wave impact pressures in areas up to 1.18H 0 below MWL. [Copyright &y& Elsevier]

Abstract: The combined effects of wave kinematics, turbulent diffusion, and buoyancy on the transport of oil droplets at sea were investigated in this work using random walk techniques in a Monte Carlo framework. Six hundred oil particles were placed at the water surface and tracked for 500 wave periods. A dimensionless formulation was presented that allowed reporting distances in terms of the wave length and times in terms of the wave period. Stokes’ drift was, expectedly, the major mechanism for horizontal transport. It was also found that plumes that have large terminal rise velocities move faster forward but spread less than those that have small terminal rise velocities. The increase in wave slope (or wave steepness) caused an increase in transport and spreading of the plume. Our results supported treating the oil as completely mixed vertically in a layer near the surface. In the horizontal direction, buoyant plumes had spreading coefficients that are essentially constant after about 200 wave periods. But neutrally buoyant plumes had horizontal spreading coefficients that increased with time (for the simulation time of 500 wave periods). Techniques for generalizing the results for a wide range of wave parameters were presented. [Copyright &y& Elsevier]

In this paper, an extended numerical analysis of the "confined-crest impact" (hereinafter referred as "C–CI"), induced by non-breaking waves on recurved parapet walls, is presented to better understand the physics and characteristics of this impulsive wave phenomenon, which significantly depends on the geometry of the parapet (here made by a sector of circumference) as well as on non-breaking wave steepness. A dimensional analysis of the forces has been carried out and used to analyse the results obtained by numerical CFD computations. The numerical simulations, performed for different radii of curvature, opening angles and incoming wave characteristics (changing both the wave height H and wave period T), have shown that the maximum impulsive pressure: (i) takes place on the top of the recurved parapet and decreases moving towards the S W L , where it tends to vanish; (ii) tends to decrease as the radii of curvature and the incoming wave characteristics (wave height H and period T) increase. However, this reduction in the maximum pressure, is always accompanied by an increase of the forces acting on the recurved parapet and a decrease of the wave overtopping volumes. Moreover, the maximum wave induced pressures have been examined by means of regular and irregular wave conditions in order to analyse the possibility of schematising the effects (i.e. forces) of an irregular sea state with those of a regular one, providing an equivalent force and therefore saving computational time. Based on the new results, a schematization of the pressure diagram induced by the C–CI impact has been proposed, used to extend the Goda-Takahashi pressure diagrams, valid for vertical walls in non-breaking wave conditions, including recurved walls. - The effects induced by the Confined-Crest Impact on recurved parapets in nonbreaking wave conditions are investigated in this study. - A large number of numerical tests, by varying the geometrical parameters of the recurved parapet and the wave conditions, have been carried out. - A dimensional analysis highlights the close dependence of the Confined-Crest Impact on the dimensionless parameter Hl L 2 . - Large impulsive forces induced by the Confined-Crest Impact occur in the upper part of the structure, avove the SWL. - A new method to calculate the pressure on vertical breakwaters with revurved parapets is proposed in order to provide a simple design tool. [ABSTRACT FROM AUTHOR]

Runup on a slender cylindrical column exposed to long, steep waves, at finite and great depth is quantified by high speed camera technique in wave channel. Ratio between water depth (h) and cylinder diameter (D) is h / D = 10,4.16 , 2. 5. Breaking and non-breaking wave events are made by focusing technique. The trough-to-trough period (T T T ), crest height (η 0. m ), frequency (ω = 2 π / T T T ) and reference speed (g / ω) of each wave event are defined (g denotes acceleration of gravity). Wavenumber (k) is obtained from the dispersion relation. Experimental runup maximum (R u m) is presented in terms of variable Z = [ 2 ω 2 (R u m − η 0 , m ) / g ] 1 / 2 . Measurements at finite water depth collapse along a linear relationship k η 0 , m = a + b Z where coefficients are obtained from the experiments. Results from other studies including large scale measurements fit to this curve, for h / D < 5 , k h < 2 and k D < 0.52. Results at great water depth with h / D = 10 show, beyond a threshold wave slope, a similar relationship. Growth factor (1 / b) is then much stronger. Gradual transition between results at finite depth and great water depth occurs for 5 < h / D < 10 and k h > 2.5. Measured runup velocity along the column is up to 1.8 times the reference speed at great depth (h / D = 10) and up to 1.2 times the reference speed at finite depth. Wave slope k η 0 , m is up to 0.56. • Videoimages of wave runup on a column are digitized. • The runup is presented in nondimensional form. • There is collapse of the runup data at great depth and at finite depth. • Runup velocity relative to the wave propagation speed shows another collapse of the data. • Results are suitable for offshore windfarm developments. [ABSTRACT FROM AUTHOR]

A numerical model was developed to simulate the evolution of a mound placed in the offshore (i.e., outside the zone of wave breaking), exposed to varying non-breaking waves and water levels. The net sediment transport rate is assumed to be mainly dominated by bed load transport, where wave asymmetry plays an important role. The net transport over a wave cycle is expressed with reference to an equilibrium profile, which ensures model reliability and robustness. In order to validate the model, data collected at two field sites, Cocoa Beach and Perdido Key Beach in Florida, USA, were employed. The numerical results show good agreement with the measured data from the two sites in terms of the profile evolution. It demonstrates that the model has the capability to simulate the evolution of mounds placed in the offshore. In addition, several scenarios with different mound volume and location designs were investigated to indicate potential uses for the model. The results illustrate how the mound evolution is influenced by the volume and location of the mound placement. [ABSTRACT FROM AUTHOR]