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With the recent development from grey infrastructures to green infrastructures, artificial reefs become more popular in coastal protection projects. To investigate the responses of beach profile evolution to the presence of an artificial reef, a non-hydrostatic model is established. Both hydrodynamic and morphodynamic evolution for the beach with and without an artificial reef are compared under regular wave conditions. In addition, the protected beach profile evolution by an artificial reef is discussed under irregular wave conditions. Three key parameters in non-hydrostatic simulation are considered for sensitivity analysis, including maximum wave steepness criterium (maxbrsteep), water depth factor (depthscale), and equilibrium sediment concentration factor (sedcal). The numerical results under regular wave conditions indicate that the artificial reef enhances wave attenuation by inducing wave breaking. In addition, the artificial reef reduces local flow velocity and offshore sediment transport by 51%, therefore decrease the total erosion by 53%. Over the artificial reef, wave skewness and asymmetry go through a drastic change. Under irregular wave conditions, short waves contribute to the wave energy mainly and reflection-induced standing wave effects decline considerably. It demonstrates that the artificial reef can protect the beach from regular and irregular waves by reducing erosion and offshore transport of suspended sediments. Moreover, in the wave breaking area, the increase of maximum wave steepness criterium may give arise to the wave height. The morphological evolution is more sensitive to water depth factor than equilibrium sediment concentration factor, because the former is a controlling factor for beach profile characteristics while the latter forms the sandbar varying irregularly in shape. [ABSTRACT FROM AUTHOR]

Wind effects on the evolution of a breaking wave group due to dispersive focusing are investigated using a two-phase flow Navier–Stokes solver. The Navier–Stokes equations are solved for both air and water, with the air–water interface captured by the Volume of Fluid method and the turbulence by the Smagorinsky subgrid-scale stress model. The two-phase model is first validated with the experimental measurements with and without following wind action. The following wind delays the breaking and shifts the breaking location downstream, and vice versa for the opposing wind. The wind-induced drift current is mainly responsible for these shifts of breaking time and location. The shift of breaking location and time is approximately linearly proportional to the wind speed (wind induced drift current) under weak winds, but the shift saturates under strong winds. The direct wind forcing, on the other hand, plays an increasingly larger role in the wave breaking process in the presence of stronger wind. It was found that the strong following wind forcing enhances the initiation of wave breaking, while the strong opposing wind forcing may change breaking type or suppress wave breaking of large intensity, such as plunging breaking. Accordingly, the wave shape at breaking onset is altered considerably under strong winds. The following wind increases the maximum wave height and wave skewness slightly. However, the opposing wind may also increase the maximum wave height initially because of the wind drift current induced upwave refocusing of the wave group. Eventually, stronger opposing wind decreases the wave height and wave skewness. [ABSTRACT FROM AUTHOR]

The theoretical model for group-forced infragravity (IG) waves in shallow water is not well established for nonbreaking conditions. In the present study, analytical solutions of the group-forced IG waves at O(β1) (β1 = hx/(Δkh), hx = bottom slope, Δk = group wavenumber, h = depth) in intermediate water and at O ⁡ (β 1 − 1 ) in shallow water are derived separately. In case of off-resonance [β1μ−1 = O(β1), where μ = 1 − c g 2 / (g h) is the resonant departure parameter, cg = group speed] in intermediate water, additional IG waves in quadrature with the wave group forcing (hereinafter, the nonequilibrium response or component) are induced at O(β1) relative to the equilibrium bound IG wave solution of Longuet–Higgins and Stewart (1962) in phase with the wave group. The present theory indicates that the nonequilibrium response is mainly attributed to the spatial variation of the equilibrium bound IG wave amplitude instead of group-forcing. In case of near-resonance [β1μ−1 = O(1)] in shallow water; however, both the equilibrium and nonequilibrium components are ~ O ⁡ (β 1 − 1 ) at the leading order. Based on the nearly-resonant solution, the shallow water limit of the local shoaling rate of bound IG waves over a plane sloping beach is derived to be ~h−1 for the first time. The theoretical predictions compare favorably with the laboratory experiment by Van Noorloos (2003) and the present numerical model results generated using SWASH. Based on the proposed solution, the group-forced IG waves over a symmetric shoal are investigated. In case of off-resonance, the solution predicts a roughly symmetric reversible spatial evolution of the IG wave amplitude, while in cases of near to full resonance the IG wave is significantly amplified over the shoal with asymmetric irreversible spatial evolution. [ABSTRACT FROM AUTHOR]

• OpenFOAM-based numerical depth-varying wave-current flume is validated against analytical solution and experiment. • Adding vertical shear to uniform current enhances/weakens harmonic wave energy and triad interaction in following/opposing current. • The following current shear may contribute to premature wave breaking at a lower sea state than that with or without uniform current. • Wave steepness at which the current shear starts to affect the crest elevation is greater in deeper water than in shallower water. A Navier-Stokes solver in OpenFOAM® is combined with the Volume of Fluid (VOF) surface capturing method to investigate the wave interaction with depth-varying currents in intermediate and shallow waters. A special attention is paid to the separate effect of vertical current shear on near resonant triad wave interactions. It was found that in the presence of following vertical current shear, the wave exhibits a sharper crest and flatter trough, and the opposite is true in the presence of opposing vertical current shear. Our model results indicate that the wave steepness at which the current shear starts to affect the crest elevation is greater in deeper water than in shallower water. We found that adding vertical current shear to the uniform current further enhances the relative harmonic wave energy and the extent of triad interaction in the following current while weakens them in the opposing current. As a result, following and opposing current shear may cause wave to break at a lower and higher sea state respectively. Due to the increased wave nonlinearity in the presence of a following current shear, a linear superposition of the individual wave and current velocities is no longer adequate to represent the total horizontal velocity close to the free surface. [ABSTRACT FROM AUTHOR]

Abstract: In this study we investigate how the wave energy deficit in the lee of an array of overtopping type wave energy converting devices (WECs), redistributes with distance from the array due to the natural variability of the wave climate and wave structure interactions. Wave directional spreading has previously been identified as the dominant mechanism that disperses the wave energy deficit, reducing the maximum wave height reduction with increasing distance from the array. In addition to this when waves pass by objects such as an overtopping type WEC device, diffracted waves re-distribute the incident wave energy and create a complex interference pattern. The effect of wave energy redistribution from diffraction on the wave energy shadow in the near and far field is less obvious. In this study, we present an approximate analytical solution that describes the diffracted and transmitted wave field about a single row array of overtopping type WECs, under random wave conditions. This is achieved with multiple superpositions of the analytical solutions for monochromatic unidirectional waves about a semi-infinite breakwater, extended to account for partial reflection and transmission. The solution is used to investigate the sensitivity of the far field wave energy shadow to the array configuration, level of energy extraction, incident wave climate, and diffraction. Our results suggest that diffraction spreads part of the wave energy passing through the array, away from the direct shadow region of the array. This, in part, counteracts the dispersion of the wave energy deficit from directional spreading. [Copyright &y& Elsevier]

Abstract: This paper presents the results of an investigation of the transformation of wave skewness and asymmetry as waves propagate obliquely over low-crested breakwaters, (LCBs), based on an analysis of measurements collected in the DELOS project. Considering the effect of the local Ursell number on wave asymmetries, a set of practical empirical formulae were established using least squares regression for both smooth and rubble mound LCBs. Predictions are in good agreement with measurements. Wave skewness on both sides of LCBs is linearly correlated for rubble mound LCBs but weakly correlated for smooth LCBs. While wave asymmetry on both sides of LCBs has a weakly quadratic correlation. The effect of the relative freeboard on the relationships of wave asymmetries between both sides is significant for rubble mound LCBs, but the same does not hold for smooth LCBs. With the presence of LCBs, wave skewness retains a positive sign on both sides but asymmetry changes from negative on the incident side to positive on the transmission side. Bispectral analysis shows that positive skewness and negative asymmetry arises from self–self and sum interactions but positive asymmetry is due to difference interactions between frequencies. The findings provide improved understanding of changes in wave skewness and asymmetry in the vicinity of structures, which may help mitigate scour and improve the stability of breakwaters. [Copyright &y& Elsevier]

• Hydrodynamic behaviour of a hull-wall system is extensively investigated over the range of hull draft ratio d/h ∈[0.4, 0.98]. • Enlightened by the low-frequency acoustic resonance in cavities, Helmholtz resonance of water waves in the gap is introduced. • Significant flow blockage phenomenon is observed as the hull approaches the bottom boundary. • Influence of wave nonlinearity on the behaviour of the Helmholtz-type hull-wall system is illustrated. Viscous and nonlinear effects on the gap resonance between a deep-draft hull and a vertical wall are investigated numerically, with particular attention to the low-frequency response, i.e., Helmholtz resonance. Viscous-flow computations indicate that the free-surface response in the gap initially increases and then decreases as the hull draft-to-depth ratio varies from 0.4 to 0.98. Conditions in which there is near complete dissipation and minimal wave reflection (i.e., K d = 0.99, K r = 0.07) are identified and the effect of wave height is evaluated. Vorticity contours are used to study the flow field between the hull and boundaries. Significant flow blockage is shown to occur when the hull approaches the bottom boundary, attenuating the gap resonance. In this case, full development of these vortices and water transport into and out of the gap is restricted, leading to increased wave reflection. Numerical simulations for various incident wave heights demonstrate that the Helmholtz resonance still results in substantial wave dissipation (i.e., K d > 0.89), which is in contrast to the behaviour observed for conventional gap problems. The findings may inform innovative designs for long wave absorbing breakwaters and Oscillating Water Column devices. [Display omitted] [ABSTRACT FROM AUTHOR]

In this paper, we use the perturbation method to develop a new mathematical derivation to describe nonlinear partial standing wave over uniformly sloping bottoms. In the Lagrangian coordinate system, the particle trajectories are obtained as a function of the nonlinear order parameter ɛ and the bottom slope α to the second order of the perturbation. The setups and mean return flow for an arbitrary bottom in the Lagrangian framework are also found as part of the solutions. The direct influences of reflection coefficient, wave steepness and bottom slope on the surface profiles of partially reflected waves are also derived. This nonlinear analytical solution is verified by reduction to the classical Stokes solution of progressive waves in both the deep water and constant depth limit. This solution allows to describe the successive deformation of partial reflected wave profiles and water particle trajectories prior to wave breaking to be described. The dynamic properties including mass transport, and Lagrangian mean level and radiation stress for nonlinear partially reflected waves on various sloping bottoms are investigated. [ABSTRACT FROM AUTHOR]

A theoretical model based on the linear potential flow theory and eigenfunction expansion-matching method is developed to analyze the interaction between water waves and multi-chamber oscillating water columns (OWCs) embedded in a caisson array. The semi-analytical solution consists of the diffraction and radiation components of periodic OWCs. The velocity singularity at the tip of the OWC chamber walls is resolved by implementing a Chebyshev polynomial expansion. The unknown expansion coefficients are determined by the continuity equations of velocity and pressure at the interface of subdomains. The semi-analytical solution is verified using the Haskind relation and the conservation law of wave energy flux. It is found that multi-chamber OWCs have higher hydrodynamic efficiency over a broader frequency bandwidth than traditional single- and dual-chamber OWCs. The maximum hydrodynamic efficiency η increases with increasing of chamber number (J), from 0.5 (J = 1) to nearly 1.0 (J = 8 and 12). It is also found that a larger incident wave angle leads to a narrower frequency bandwidth for energy capturing. Increasing the incident wave angle from π/3 to 5π/12 results in a decrease of the first cutoff frequency k c from 2.41 to 2.02, and therefore results in the energy capture bandwidth narrowing accordingly. Both constructive and destructive hydrodynamic interactions between caissons array and OWCs are observed over the tested frequency range. Interestingly, when configuration of the OWC chambers is reversed, the transmission coefficient remains unchanged. • A theoretical model for wave interaction with multi-chamber OWCs embedded in a caisson array is developed. • Multi-chamber OWCs achieve a higher hydrodynamic efficiency than the single- and dual-chamber OWCs. • Both constructive and destructive hydrodynamic interactions between OWCs and the caisson array are observed. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents an integrated investigation of physical processes generating impulsive pressures under the action of plunging breakers impinging on gravel beaches. This work is an extension of a recent investigation which suggested that wave impacts from plunging breakers acting on gravel beaches may be a key mechanism to enhance sediment mobilisation. In particular, comparisons of full scale laboratory measurements against model results from a well-validated phase/depth-resolving numerical model based on the Reynolds–Averaged Navier–Stokes (RANS) equations are presented. This represents the first attempt at comparison with such a tool against observed hydrodynamics on steep (slope~1/8) gravel beaches at prototype scale. In order to understand how impulsive pressures are generated under plunging waves, the numerical model is used to carry out a detailed investigation to examine the role of each of the acceleration terms in the momentum balance. Consistent with prior studies, numerical results show that under plunging breakers the local acceleration (∂u/∂t) alone cannot be used as a proxy for pressure gradients. However, the contribution of the third term (w∂u/∂z) of total acceleration is recognized for the first time and indicates that this term has an important role in both the induced pressure gradient and sediment mobilisation as induced by this particular type of breaking. Furthermore, results suggest that a parameterisation of the pressure gradient in terms of ∂u/∂t+u∂u/∂x, may not suffice when dealing with plunging breakers and hence there is a lack of a suitable parameterisation of this process in the present literature. Thus, for different types of breaking it may be necessary to consider a different characterisation of the pressure gradient toward the parameterisation of sediment transport inside the surf zone. [Copyright &y& Elsevier]

Fast and accurate estimation of wave runup is needed for coral-reef islands, but most of the existing formulae are not applicable in this context. Tree-based models were applied to the comprehensive numerical database of Pearson et al. (J. Geophys. Res. Oceans. 122, 10099–10117) to identify the essential predictor parameters for runup in coral-reef environments and classify different runup regimes on which a set of runup formulae was developed. It was found that, wave conditions, reef roughness, and reef-flat length are generally crucial for predicting runup, while the importance of forereef and beach slopes depends on the relative reef submergence (reef submergence normalized by off-reef wave height). The forereef slope is more important than the beach slope when waves mainly break over the forereef at low relative reef submergences but less important when waves mainly break over the reef flat and the beach at middle and high relative reef submergences. The proposed formula set was validated against data from laboratory and field coral reefs, which implies that the formula set has the potential for fast prediction of runup along coral-reef islands at broad scales for flooding assessment. • Four regimes of wave runup over reef-lined beaches are identified. • An explicit runup formula set corresponding to the four regimes is derived. • The formula set is validated against data of laboratory and field coral reefs. • Beach slope is more important than forereef slope at high water levels. [ABSTRACT FROM AUTHOR]

Infragravity waves (IGWs) play a crucial role in nearshore hydrodynamics and are the primary drivers of coastal hazards such as harbor resonance and overtopping over seawalls. Field observations show that during five storm events in Fall 2013, the IGW heights at the landward side were significantly larger than those at the seaward side of an isolated shoal near Cape Canaveral, Florida, USA. The concurrent offshore incident waves were energetic with directions nearly perpendicular to the shoal. The maximum wave height-to-depth ratio was below 0.3, indicating no wave breaking. Here, we propose a semi-analytical model in combination with field observations to investigate the shoal-induced increase in the cross-shoal IGW energy flux. The model was proposed based on the theory of spatial evolution of nonlinear energy transfer from primary waves to IGWs over an idealized trapezoidal topography under nonbreaking conditions, and was calibrated using a numerical dataset of 21 test cases generated by the non-hydrostatic numerical wave model Simulating Waves till SHore (SWASH). The predicted increase in the cross-shoal IGW energy fluxes are in reasonable agreement with field observations, with 78 % data variability explained by the model. Also, the IGW energy flux increase calculated from the observed IGW height increase was found to coincide with the observed IGW energy flux increase in the cross-shoal direction. The results strongly indicate that the observed amplification of IGWs near Cape Canaveral in Fall 2013 is largely attributed to the topography-induced nonlinear energy transfers from sea-swells to IGWs. [ABSTRACT FROM AUTHOR]

This paper presents a second-order asymptotic solution in the Lagrangian description for nonlinear partial standing wave in the finite water depth. The asymptotic solution that is uniformly valid satisfies the irrotationality condition and zero pressure at the free surface. In the Lagrangian approximation, the explicit nonlinear parametric equations for the particle trajectories are obtained. In particular, the Lagrangian mean level of a particle motion for the partial standing wave is found as a part of the solution which is different from that in an Eulerian system. This solution enables the description of wave profile and particle trajectory, which can be progressive, standing or partial standing waves. The dynamic properties of nonlinear partial standing waves, including mass transport velocity, radiation stress, wave setup and pressure due to reflection are also investigated. [ABSTRACT FROM AUTHOR]