Incident Wave Height Research Articles

Wave transformation across impermeable and porous artificial reefs

Porous artificial reefs can function as nature-based solutions for coastal protection, due to their ability to dissipate wave energy while providing habitat for marine species. However, due to the lack of quantitative understanding of wave interactions with porous artificial reefs, there is uncertainty in how to optimize design for coastal protection applications. To address this gap, physical modelling experiments were conducted in a wave flume to investigate wave transformation across both porous and impermeable artificial reefs exposed to a range of regular wave conditions and submergence depths. The results highlight how key changes to wave kinematics (e.g., wave celerity, wave breaking) and wave energy (through reflection, dissipation and transmission) differ considerably between impermeable and porous artificial reefs. These differences in wave kinematic properties and energy balances across each reef can be well characterized by consideration of the effective crest depth (i.e., the total height of water at a point on the reef, including that in the voids) that accounts for the porosity of the reef structure, rather than the actual depth of the reef crest. The ratio of the effective crest depth to the incident wave height, termed the ‘relative effective crest depth’, was used to develop robust formulations to accurately predict wave reflection and transmission coefficients across both reefs over the range of wave and water depth conditions. The new formulations were also compared to other datasets reported in the literature, and were found to provide accurate predictions of both wave reflection and transmission for the broad range of submerged porous coastal structures considered (including artificial reefs and submerged breakwaters).

Modeling investigation of wave-induced longshore current distribution patterns on barred beaches

A three-dimensional coupled wave-current model was employed to investigate the wave-induced longshore currents on barred beaches. The modeling system was developed by coupling the finite-volume community ocean model (FVCOM) and the simulating waves nearshore (SWAN) model to fully describe wave-current interactions in the nearshore region. The three-dimensional radiation stress, surface rollers and wave-enhanced turbulent mixing were incorporated as the major wave effects on currents. The model was first evaluated against data collected from multiple sets of laboratory experiments. Diagnostic simulations demonstrated that the contributions of the wave rollers and wave-induced mixing, in addition to the radiation stress, were important for ensuring accurate calculations. Then, the longshore current patterns on barred beaches were investigated through simulations of a series of test cases under controlled conditions. The cross-shore distribution of wave-induced longshore currents, which predominantly occurred within the barred beach surf zone, usually exhibited bimodal characteristics. The maximum peak longshore current velocity was positively correlated with the incident wave height and period. As the bar height and width increased, the first velocity peak of the longshore current strengthened, while the second peak weakened. In most cases, the maximum longshore current velocity on a barred beach coincided with the first peak, which could occur anywhere from the bar-trough region to the bar-crest region, depending on the wave and bar heights. This finding could be used to clarify the cross-shore location discrepancies in the maximum peak longshore current velocity reported in previously published studies.

Effects of multi motion responses and incident-wave height on the gap resonances in a moonpool

The hydrodynamic characteristics of a free-floating moonpool encountering the gap resonances are investigated based on the constrained interpolation profile method in numerical wave tank. This paper mainly concentrates on the influences of the moonpool's motion responses and the incident-wave height on the gap resonances in the free-floating moonpool. Numerical results demonstrated that the heave response significantly changes the frequency and the magnitude of the linear gap resonance, while the roll motion influences more on the vertical wave loads and the wave responses in the fluid field. The heave and roll response of the free-floating moonpool are generally independent. Moreover, the magnitudes of the nonlinear gap resonances have the tendency of catching up and exceeding the linear gap resonance as the incident-wave height increasing for the free-floating moonpool, which is the consequence of the higher-order harmonics driven by the nonlinear processes and the linear secondary resonant region induced by the heave response. Based on the wavelet transform, it could be observed that the amplified harmonic component usually takes more time to be fully developed than other harmonic components during the development of its corresponding nonlinear gap resonance.

On the behavior of higher harmonics in the evolution of nonlinear water waves in the presence of abrupt depth transitions

The presence of abrupt depth transitions might trigger strong nonlinear effects on propagating water waves near coastal regions. In this study, the dynamics of nonlinear monochromatic waves over a submerged step representing the abrupt depth transitions are investigated both experimentally and numerically. Within the framework of the free-surface Euler equations, a fully nonlinear potential flow model based on a conformal mapping method is established to investigate the higher harmonics. The numerical method has been well validated with experimental measurements. To analyze the wave nonlinearity at the transitions, the higher harmonics are extracted both in the spatial and time domains. It is shown that abrupt depth transitions enhance the higher harmonic amplitudes in the shallower regions on the step. The effects of the incident wave frequency and height are studied. It is found that the higher harmonics induced by the abrupt depth transitions become more significant with increasing wave steepness. An analysis of the evolution of the skewness and kurtosis demonstrates the high asymmetry of the surface elevation on the upstream junction. The asymmetry shows clear nonlinear effect from the higher harmonics.

Experimental observation on wave propagation and geomorphological evolution in a sandbar-lagoon system

The sandbar-lagoon coast, one of the most productive and valuable ecosystems, has been strongly exposed to severe degradation. Excessive erosions aggravate the fragility of sandbar-lagoon systems. In order to seek adaptable solutions for ecological restoration, it is essential to study the hydrodynamic and morphodynamic characteristics. In this study, a series of flume experiments are conducted to investigate the wave propagation and geomorphological evolution in a typical sandbar-lagoon system. The time-series of swell and infragravity waves are obtained by a simple time-domain separation method, where wave reflection coefficient, skewness and asymmetry are calculated separately. The following conclusions can be drawn. To quantitatively assess the experimental results, a critical parameter ζ is introduced involving the incident wave height, the water depth and the sandbar freeboard. There is a linear relationship between wave attenuation and ζ. Further, a linear dependence on the maximum erosion thickness of foredune is achieved, and the maximum erosion thickness of sandbar increases with the increasing incident wave height by a superb linear correlation. Additionally, the shape transition of foredune scarp is significantly correlated with the dramatic change of the water level rise in the lagoon and the infragravity wave reflection. These findings promote better understanding for the morphodynamics of typical sandbar-lagoon systems and provide fundamental and scientific evidences on further coastal engineering.

Effects of roll motion on linear and nonlinear gap resonances in a moonpool excited by various incident-wave heights

The linear and nonlinear gap resonances in a free-rolling moonpool are investigated using a two-dimensional in-house code based on the constrained interpolation profile method. This study primarily focuses on the effects of roll motion on hydrodynamic characteristics, taking into account both the linear gap resonance and the nonlinear process-driven gap resonances. The analysis of the incident-wave height is conducted to illustrate the relationship between higher-order harmonics and nonlinear gap resonances. Numerical results demonstrate that the resonant frequency is insensitive to the roll motion. However, the roll response plays an important role in influencing the vertical wave loads on the barges and affecting the energy conversion pattern in the fluid field. According to the analysis of the incident-wave height parameter, the magnitudes of resonance at the linear and nonlinear resonant points are approximately in sub-linear and superlinear relationships with the incident-wave height, respectively. Moreover, the vortex shedding modes around the entrance of the free-rolling moonpool gradually transit from being dominated by the pairs of vortices to being dominated by the single vortex as the gap resonance changes from linear to quartic.

Wave Amplification inside an Open Circular Caisson for Wave Energy Conversion in Waters with Medium Energy Density

Wave energy is one of important marine renewable energy resources. Many studies have been devoted to harnessing the energy for human use. Though they are almost everywhere in the sea, waves can be much more significant in some sea areas than others. For example, the wave energy density in Asian waters is usually much less than that in European west coasts.
 To make the wave energy harvesting more viable in Asian waters with medium wave energy density, we propose to employ an open caisson to amplify the wave locally and to combine it with a wave energy converter to tap the amplified wave energy. In this study, we focus on the effect of incident wave height on the amplification factor which is defined as the ratio of the wave height inside the caisson to that of the incident wave. Shown in Figure 1, the caisson is mounted vertically on the horizontal seabed in the open sea. At the edge of the opening, it has two guides on the two sides of the opening. They are identical in geometry and part of a solid cylinder. The purpose of the two guides is to enhance the wave amplification inside the caisson.
 The study was conducted primarily by CFD computations and partially verified by experiments. In computations, the finite volume method was employed to discretize the Navier-Stokes equations. A multi-block grid was generated for computational purposes. The volume-of-fluid (VOF) method was used to capture the free surface. The nonlinear iterations were conducted with the PISO method. And the implicit time marching scheme was adopted in the time direction. It is interesting to find that the amplified wave height in the caisson is not linearly related to the incident wave height. Furthermore, the amplification factor is also a function of the incident wave period. The wave period at which the peak value of the amplification factor appears is insensitive to the wave height. The amplification factor is usually greater than unity for a wide range of incident wave period.

Experimental study on the morphodynamic evolution of sandbar-lagoon system with emergent vegetation

A mobile-bed sandbar-lagoon model was employed in a series of flume experiments to investigate the influence of vegetation with different densities over the sandbar on wave attenuation and bed profile evolution. Nineteen flume tests were carried out for the same sandbar-lagoon model under different wave conditions. Extensive analyses were conducted on the profile evolution and the wave parameters along the profile of the sandbar-lagoon system. Based on the weighted vegetation density by the canopy width, a new empirical relationship was established between wave attenuation and vegetation density, water depth and sandbar freeboard. It was found that wave attenuation increases with the sandbar freeboard and the weighted vegetation density, and decreases with incident wave height. The collision (s-shaped scarp) and overwash (upward concave scarp) types of fore-dune morphological evolution were observed in the experiments. The maximum erosion thickness of dune follows a quadratic polynomial relationship with vegetation density, indicating that too sparse vegetation cover may lead to more erosion. It follows that an optimal vegetation density may lead to the least wave reflection due to the quadratic polynomial relationship. However, when the maximum erosion thickness of fore-dune is small, the quadratic polynomial relationship become linear. Furthermore, the experimental results indicate that wave height, water depth, sandbar freeboard and vegetation density are all important contributing factors to the morphodynamic evolution of sandbar-lagoon system with emergent vegetation. These relationships promote the development of wave-vegetation-sediment mechanics and provide a scientific guide to carry out coastal ecological restoration projects especially in the sandbar-lagoon system.

PROGRESSION OF MEAN DAMAGE ON A MOUND BREAKWATER IN ITS SERVICE LIFE

Because of the expected sea level rise, most of the human properties located on the coast have to be protected during the present century. One of the engineering alternatives is to build rock sloping coastal structures. Currently, their design has to include procedures for aging and deteriorating to forecast their maintenance and reparation costs during its service life. The objective of the present research is to reformulate the rate of mean damage proposed by Melby and Kobayashi (1998) to predict the progression of mean damage, S, on a given mound breakwater typology under sequences of storms with varying wave conditions and water levels. The proposal is based on the interplay of water depth, h, incident significant wave height, Hs and mean wave period, Tm at the toe of the slope, and the impinging number of waves, Nw (Losada et al. (2021)).

The influence of vegetated marshes on wave transformation in sheltered estuaries

Assessing the influence of marshes on mitigating flooding along estuarine shorelines under the pressures of sea level rise requires understanding wave transformation across the marsh. A numerical model was applied to investigate how vegetated marshes influence wave transformation. XBeach non-hydrostatic (XB-NH) was calibrated and validated with high frequency pressure data from the marsh at China Camp State Park in San Pablo Bay, California (USA). The model was used to examine how marsh and hydrodynamic characteristics change the potential for marshes to mitigate wave driven flooding. Model results demonstrate that hydrodynamics, vegetation, and marsh width influence wave transformation most, while marsh morphology parameters such as elevation and slope had least effect. Results suggest that in the range of settings explored here (incident wave heights ranging from 0.5 to 3 m and water levels ranging from current mean higher high water to 3 m above current mean higher high water), in comparison to wave propagation over an unvegetated mudflat, marsh vegetation reduces runup by a median of 40 cm and wave height by a median of 35 cm. Results illustrate how marshes can be strategically utilized to provide flood reduction benefits.

Hydrodynamics of LIMPET type OWC device under Stokes second-order waves

This research aims to investigate the hydrodynamic performance and efficiency of the LIMPET oscillating water column (OWC) device. A two-dimensional numerical wave tank (NWT) is used in a fully nonlinear Reynolds averaged Navier–Stokes equations (RANS) model with the k−ω turbulence model for the Stokes second-order incident waves. A volume of fluid (VOF) method is utilized to capture the free surface elevation. The numerical simulation shows qualitative velocity vector and streamline profiles inside the chamber of the LIMPET OWC device across a whole pressure fluctuation cycle. It is found that the fluid particles with smaller velocity magnitudes are distributed throughout all directions, whereas the fluid particles with larger velocity magnitudes are aligned in one direction close to the orifice of the OWC device. Higher incident wave heights promote the additional vortex generation at the lower tip of the front wall of the device chamber. The specific dissipation rate is considerably higher as incident wave heights become higher, which demonstrates that the wave energy dissipation is higher for higher incident wave heights. The power produced by the LIMPET OWC device is higher for the incident waves having higher incident wave heights. In contrast, the efficiency of the OWC device depends on various parameters like incident wave height, water depth to wavelength ratio, pneumatic damping coefficients, etc.

Wave Characteristics over a Dual Porous Submerged Breakwater Using a Fully Nonlinear Numerical Wave Tank with a Porous Domain

This study developed a two-dimensional fully nonlinear numerical wave tank (FN-NWT) to examine the nonlinear interaction between waves and dual submerged porous structures. Using the FN-NWT, not only reflection and transmission coefficients, but also wave deformation/force depending on porosity were investigated. The FN-NWT was developed using the boundary element method (BEM), and consisted of a fluid domain and a porous medium domain. Darcy’s law or the non-Darcy (Forchheimer) flow equation were applied to the flow passing through the porous domain. The wave reflection coefficient of the porous submerged structures agreed well with the given experimental data when using Forchheimer flow boundary conditions. Excessive attenuation of the transmitted wave occurred when Darcy’s condition was employed. The difference in each coefficient due to the spacing of the submerged structure was reduced in the porous structure compared with the non-porous structure. The difference according to the incident wave height was clearly revealed in the transmission coefficient. The developed dual-domain FN-NWT can be applied to investigate the nonlinear interaction between waves and porous structures as a first-cut design tool.

Nonlinear wave propagation in a vegetated sandbar-lagoon system

The sandbar-lagoon system presents a rich variety of values. At the same time, the degradation of ecosystems and coastal erosion caused by human activities and climate change are even more severe. A series of ecological conservation and restoration projects focused on vegetation rehabilitation have been implemented. However, there is insufficient scientific evidence to guide coastal engineering in the presence of vegetation. In this paper, ten tests were presented to experimentally investigate nonlinear wave propagation in a vegetated sandbar-lagoon system. The following conclusions can be obtained. In the absence of vegetation, the low-frequency wave energy proportion gradually increases with the rise of incident wave height. Double-peaked and even multi-peaked spectra are notable throughout the propagation in tests with larger incident wave heights. Wave height decay and wave energy dissipation due to vegetation effects increase as the incident wave height increases. The dependence of the wave energy dissipation induced by vegetation on the incident wave energy (the square of wave height) presents a linear relationship. Vegetation plays an important and complex role in both sea-swell wave and infragravity wave attenuation.

An experimental study on monitoring wave profiles with LiDAR

Light Detection and Ranging (LiDAR) has become increasingly popular for on-site wave monitoring due to its high temporal and spatial resolution. However, its potential application in the laboratory has not been well studied. In this study, a LiDAR and seven wave probes were used in a wave flume with a slope, to study the ability of LiDAR monitoring wave profiles in the laboratory. The results show good agreement between the time series of free surface measured by the LiDAR and wave probes, with an average error of less than 4%. Effective sampling ratio (the ratio of the number of LiDAR signals received per second to the sampling frequency at a point), relative wave height, positions of the breaker point and incident wave height are the key factors affecting LiDAR measurement error. When the value of effective sampling ratio is less than 0.8, it has dominant influence on the error. In shallow water, relative wave height is the dominant factor. A negative linear correlation is found between the measurement error and the incident wave height. These findings provide important guidance for processing and assessment of LiDAR data.

Solitary wave attenuation characteristics of mangroves and multi-parameter prediction model

Mangroves contribute to wave attenuation and improve coastal disaster prevention. Extensive studies have been conducted to explore wave attenuation by mangroves using rigid cylinders. However, few studies have investigated interactions between solitary waves and mangroves with roots. Therefore, laboratory experiments are conducted to investigate wave dissipation along a 1:10 scale Rhizophora mangrove forest under solitary waves, and wave attenuation characteristics are analyzed to highlight the significance of the effects of mangrove roots on wave damping. A numerical model of mangrove with roots is conducted by combining cylinder and porous media, where the trunk is considered as a cylinder and roots are simulated by introducing the resistance source term and porosity effect into the momentum equation. Results show that wave parameters (still water depth and incident wave height) and a vegetation parameter (vegetation submerged projected area) are the dominant variables affecting wave attenuation. In addition, multivariate nonlinear regression, genetic programming, and back propagation (BP) neural network are employed to explore the relationship between the wave attenuation coefficient and other related dimensionless parameters. Results show that the BP model is more accurate in predicting the wave attenuation coefficient as compared with other methods and thus can predict solitary wave attenuation in mangrove forests.

Experimental study on an isolated oscillating water column wave energy converting device in oblique waves

The oscillating water column is the most widely used wave energy conversion technology for long-term operations, which has the potential to play a critical role in massive applications of wave energy. In this study, an isolated OWC model employing a generic cubic air chamber and an impulse turbine model was tested in a wave tank using regular and irregular wave scenarios. The wave distribution characteristics surrounding the isolated OWC model in oblique waves with various incident angles and other testing conditions were reported. As the incident waves were forward, the symmetrical wave-height distributions could be observed with enhancement and reduction zones in front of the skirt wall and in the sheltered area of the model. Furthermore, the wave distributions were asymmetrical and more complicated in oblique waves. In addition, the effects of the incident wave angle, height, period, and rotation speed of the turbine model on the staged and overall energy-harvesting performances were analyzed. The OWC model obtained the peak energy-harvesting performance, which reduced as the incident angle decreased. As the incident angle decreased to 60° and zero, the overall capture width ratio reduced to approximately two-thirds and a quarter of the value for the incident angle of 90°. Based on experimental results, the annual energy production of a prototype isolated OWC plant in a typical sea state in North China was predicted. The annual energy production of the plant in the actual sea condition was approximately two-thirds of that only in the forward wave incidence.

Experimental and numerical investigations on the solitary wave actions on a land-fixed OWC wave energy converter

The dynamic performance of a typical land-fixed oscillating water column (OWC) wave energy converter (WEC) under solitary waves (SW) is experimentally and numerically investigated. Both two-dimensional (2-D) and three-dimensional (3-D) numerical models are considered in the present study. The air orifices of the OWC chamber in 2-D and 3-D models are represented by a narrow rectangular opening and a circular opening, respectively, with the same opening ratio (i.e., the cross sectional area ratio between opening and the air chamber). It is found that the overflow of the orifice occurs when the wave height exceeds a threshold, which results in a larger wave force on the structure compared with that induced by the SW crest. The 2-D numerical model fails to predict the overflow phenomena due to the full submergence of the orifice. The overtopping and roof impacting phenomena are induced when the wave run-up exceeds the front wall height. A portion of the SW energy is released during this process. Hence, total wave forces are reduced. The effect of wave heights on force components exhibits different behaviors due to the coupling of air and water inside the chamber. Both the impacting force and overtopping discharge increase with incident wave heights.

Effects of currents on nonlinear wave transformation in a reef-lagoon-channel system

Wave nonlinearity can drive the near-bed sediment transport and nutrient delivery on coral reefs. Previous studies have primarily concentrated on the wave nonlinearity evolution for a specific cross-shore profile and have scarcely taken the effects of currents into consideration. To better understand the nonlinear wave transformation on reef coasts, the wave height distribution and wave nonlinearity evolution are analyzed based on 3D reef-lagoon-channel experiments in a wave basin. By taking the current velocity into consideration, the Glukhovskiy distribution function is improved in calculating the probability of large wave height in the sequence. Wave skewness and asymmetry on the reef and in the channel are parameterized with the Ursell number considering the Doppler effect induced by opposing or following currents. The accuracies for estimating wave skewness and asymmetry are improved by 39% and 66%, respectively. The influence of Doppler effect on wave shapes on the reef flat and in the channel varies significantly with the incident wave heights and reef submergences. Furthermore, it is also noticed that the reduction of local water depth caused by the propagation of infragravity wave troughs increases short-wave skewness at individual wave scale on the middle of reef flat, while its effect on short-wave asymmetry is not significant.

Experimental investigation of breaking regular waves slamming on offshore wind jacket structure

A series of experiments were carried out to investigate the breaking regular wave slamming on an offshore wind jacket structure in a wave flume. The breaking wave characteristics, global slamming forces and local pressure distributions are analyzed. The effects of relative location between jacket structure and breaker location, bottom slope, water depth, incident wave period and wave height on the slamming force and pressure distribution of the jacket structure are investigated. The results show that the maximum value of normalized peak pressure and location will be significantly affected by the bottom slope and water depth. Modified empirical formulas are proposed to calculate the slamming force and slamming duration for the offshore wind jacket structure.

Experimental Investigation of Wave Propagation and Overtopping over Seawalls on a Reef Flat

A series of physical model tests were performed to investigate the wave propagation, pressure, and wave overtopping processes for vertical and sloped seawalls on the reef flat. For both regular and irregular waves, the effects of incident wave height, wave period, relative distance, fore reef slope, and still-water depth on wave propagation, wave pressure distribution, and mean wave overtopping discharge were investigated. The peak pressure increased with the increase in incident wave height and decreased with the increase in relative distance and fore reef slope. The mean wave overtopping discharge over the vertical and sloped seawalls increased with the increase in incident wave height, wave period, and still-water depth, but it was significantly reduced with the increase in relative distance and fore reef slope. Modified empirical formulas are proposed for predicting the wave force and mean wave overtopping discharge over the vertical and sloped seawalls on the reef flat for both regular and irregular waves.