Wave Transmission Coefficients Research Articles

Investigation of hydrodynamic characteristics of an oyster reef under regular waves

Oyster reef living shorelines are popular solutions to mitigate coastal hazards while providing ecosystem services, and their hydrodynamic characteristics deserve further examination. This paper reports an experimental and numerical study of the hydrodynamic behavior of a bagged oyster shell (BOS) reef under regular waves. The dependence of the pore pressure within the reef and the hydrodynamic coefficients on the reef height, length, porosity, and wave parameters are investigated. The results show that the normalized maximum pore pressure ps_m∗ decreases from the seaside of the BOS reef to its leeside and decreases with increasing dimensionless reef length. With increasing wave steepness, ps_m∗ fluctuates with an overall increasing trend. With increasing BOS reef porosity, ps_m∗ decreases at seaside locations and increases at leeside locations; simultaneously, the wave reflection coefficient Kr and the wave dissipation coefficient Kd decrease, and the wave transmission coefficient Kt increases. With increasing wave steepness for a given wave period, Kr and Kt tend to increase, but Kd exhibits the opposite trend. As the dimensionless reef height and length increase, Kt decreases and Kd increases. Multivariate nonlinear regression and genetic programming-based symbolic regression methods are individually used to derive two formulas for predicting the wave transmission coefficient, with the formula from the latter method being found to give a higher prediction accuracy.

Reduction in wave shoaling over a linear transition bottom using a porous medium

Wave shoaling, which involves an increase in wave amplitude due to changes in water depth, can damage shorelines. To mitigate this damage, we propose using porous structures such as mangrove forests. In this study, we use a mathematical model to examine how mangroves, acting as a porous breakwater, can reduce wave shoaling amplitude. Shallow water equations are used as the governing equations and are modified to account for the presence of porous media. To measure the wave reduction generated by the porous media, the wave transmission coefficient is estimated using analytical and numerical approaches. The separation of variables method and the staggered finite volume method are utilized for each approach, respectively. The numerical results are then validated against the previously obtained analytical solutions. We then vary the friction and porosity parameters, influenced by the presence and extent of porous media, to evaluate their effectiveness in reducing wave shoaling.

Physical modelling study on wave damping induced by an idealized floating kelp farm

A physical modelling study was carried out to investigate random wave damping promoted by an idealized floating kelp farm. The experimental conditions spanned intermediate water depths and both linear and nonlinear water waves. Unlike previous studies of wave damping promoted by vegetation, the floating kelp farm was placed close to the water surface with a ratio between vegetation height and water depth close to 0.25. The wave transmission coefficient induced by the floating kelp farm ranged between 0.56 and 0.96. This coefficient decreased for longer floating kelp farms and it was a function of the ratio between kelp farm length and incident wavelength and of the relative wave depth. Spectral analysis showed that wave damping was not frequency-dependent for wave frequencies close to the peak frequency. The wave transmission coefficients of a floating kelp farm with about 100 culture lines and with an extension of approximately 200 m were similar to those of submerged detached breakwaters with a relative crest freeboard smaller than -0.4. Furthermore, the bulk drag coefficient of near-surface idealized floating kelp farms can be modelled as a function of the Keulegan-Carpenter number. This study highlights the potential viability of nature-based solutions such as floating kelp farms for coastal protection.

Effect of open-area ratios on wave attenuation over a submerged reef breakwater: An experimental study

The reef-type submerged breakwater (RSB) has been implemented around the world to provide coastal protection and natural shelter and habitat for marine species at the same time. A series of laboratory experiments are conducted in a wave flume to study wave propagation and transmission over RSBs with the four open-area ratios of 0.047, 0.131, 0.257, and 0.560. The experimental results demonstrate that the RSB significantly alters the wave propagation characteristics. The RSBs with the open-area ratio of 0.047 and 0.131 reduce the wave height to ∼70%. The RSBs with the open-area ratio of 0.047 and 0.131 perform better in attenuating than those with the open-area ratio of 0.257, and 0.560. As the open-area ratio decreases, the transmission coefficient decreases, while the dissipation coefficient increases. An empirical formula is proposed to calculate the wave transmission coefficient as a function of the RSB open-area ratio and wave steepness under regular waves. A cubic empirical formula with one unknown is also proposed to relate the distance from RSB stoss face to wave breaking point and the open-area ratio. The present study is expected to optimize RSB design for coastal protection.

Optimal design and placement of a combined trench and submerged breakwater system on the coastal area of Aceh

Tsunami waves are currently one of the most devastating water hazards that threaten regions or countries near the subduction zones, including Indonesia. In this research, a novel coastal protection system combining a submerged breakwater and a trench is proposed to mitigate tsunami occurrences. The model is developed based on the Shallow Water Equations, which are then solved analytically using the Separation Variables Method, and numerically using the Staggered Finite Volume Method. The wave transmission coefficient, which indicates the wave reduction rate generated by the system, is expected to be the outcome of both approaches. The numerical scheme is validated against the analytical solutions to verify its accuracy in estimating wave reduction by the system. Further, an optimization technique is integrated into the model to obtain the optimal size and position of each structure (submerged breakwater and trench) on the real bathymetry of Aceh's coast, which has been impacted by a deadly tsunami occurrence before. The results of this study are expected to be useful in the future development of coastal protection systems against tsunami waves, especially in Indonesia.

Reflection and Transmission of Plane Waves at the Interface of Fluid and Porous Media with Seismoelectric Effect

Abstract The relationship between energy flux reflection and transmission coefficient of seismoelectric plane waves in plane layered media and incident angle and frequency is studied. Pride equations is adopted to describe the coupling phenomenon between elastic waves and electromagnetic fields in subsurface fluid-saturated porous media. The Helmholtz decomposition is used to derive the energy flux expression for seismoelectric plane waves propagating in fluid-saturated porous media. It shows that the impermeable interface conditions have a great influence on the reflection and transmission coefficient of seismoelectirc waves. The transmission coefficient of slow longitudinal waves under impermeable interface is much smaller than that of permeable interface conditions Reflection coefficient of longitudinal wave, transmission coefficients of the fast longitudinal waves and transverse waves are all larger under impermeable interface conditions than that of permeable cases. And the reflection coefficient of electromagnetic wave under impermeable interface conditions is almost one order of magnitude smaller than that permeable case.

Establishing patterns of change in the coefficients of reflection, transmission, and dissipation of wave energy depending on parameters of a permeable vertical wall

The object of research is permeable vertical walls (breakwaters) with different degrees of permeability. This paper reports the results of experimental research into the interaction of gravity waves with models of permeable vertical walls (breakwaters), which were formed from cylindrical piles of circular cross-section. With the help of visual and instrumental studies, the features of interaction of surface gravity waves with permeable vertical walls of different permeability have been identified. The degree of wave transformation by these walls was also determined in the form of reflection, transmission, and dissipation coefficients of wave energy. It was established that with a decrease in the permeability of the vertical wall and an increase in the steepness of the initial wave and a decrease in its period, the height of the reflected wave increased. The pattern of the transmitted wave height had the opposite trend. It was determined that the wave reflection coefficient increased with a decrease in the permeability of the vertical wall and the steepness of the initial wave. The wave transmission coefficient had the opposite trend, namely, it increased with increasing wall permeability and with decreasing steepness of the initial wave. The gravity wave energy dissipation coefficient decreased with increasing vertical wall permeability, but for waves with a significant steepness hi/λ>0.038, a decrease in the wave energy dissipation coefficient was observed for walls with low permeability and the appearance of extreme values of this coefficient. Thus, features in the interaction of surface gravity waves with permeable vertical walls (breakwaters) of different permeability have been researched and the degree of wave transformation by these walls has been determined, which could make it possible to effectively design and operate permeable vertical walls as coastal protection structures

Influence of structure characteristics on wave transmission and shoreline response at a low-crested segmented breakwater in Little Egg Harbor Township, NJ

Graveling Point Beach, a public beach within Little Egg Harbor Township, New Jer- sey, has been experiencing long-term erosion. To address the issue, a living shoreline project consisting of four low-crested rubble-mound breakwaters and a beach nour- ishment was constructed beginning in fall 2022 (structures) and finishing in spring 2023 (beach nourishment). A variety of field methods were used to investigate the influence of the breakwater system on wave transmission and beach fill evolution. The observations are then compared to common empirical estimations. A median wave transmission coefficient of 0.4 was measured for incident waves with a median height and peak period of 9 cm and 2 sec, respectively. The observed transmission coefficient was higher than that predicted by models such as Briganti et al. (2003) and Van der Meer and Daemen (1994) suggesting other processes such as diffraction may be influencing the results. Structure from Motion (SfM) was used to generate a series of Digital Elevation Models (DEMs) which show salients forming behind the structures. The resulting salient growth was compared to the model of Suh and Dalrymple (1987), which was shown to overpredict the amplitude of the salient at Graveling Point. However, the expected relationship of breakwaters with increased offshore distance having shorter salient lengths was generally observed. The equation was refit using the field data at Graveling Point and laboratory data with similar wave heights and periods from Suh and Dalrymple to derive a modified model that may be more appropriate in low-energy environments

Effects of Fallen Posidonia Oceanica Seagrass Leaves on Wave Energy at Sandy Beaches

Posidonia Oceanica (PO) is an endemic marine plant in the Mediterranean Sea. In an experimental study conducted in the Eastern Mediterranean, the effects of natural PO leaves on reducing the height of incident waves impacting a beach were measured. The transmission coefficient (Kt) was found to vary between 0.73 and 0.94, which is equivalent to a wave height decay of 6–27%. The results show that in their natural environment, free-floating dead PO leaves dissipate incoming wave energy and have the capacity to protect beaches against erosion. Further analysis in separate frequency bands showed that waves with periods between 4.5–6.2 s were more sensitive to PO leaves in terms of energy dissipation. The transmission coefficient for medium-period waves, calculated using the medium-frequency part of the wave spectrum, delivered a maximum transmission coefficient of 0.5, corresponding to a 50% decay in wave height due to PO leaves.

Numerical modeling of wave interaction with a porous floating structure consisting of uniform spheres

Porous materials are increasingly being used in the design of floating structures in coastal and ocean engineering, but there is a lack of numerical tools that can aid in the design of a movable floating porous structure. To close this gap, the existing volume-averaged numerical model for flow interacting with a fixed porous body was extended to floating scenarios by (1) using the relative velocity in the porous friction force, (2) calculating rigid body motion using volume integral of porous body force, and (3) modifying a dynamic mesh algorithm for a mobile porous body. As a demonstration, the developed model was applied to a porous floating structure consisting of cubically packed uniform spheres. Two sets of model applications were involved. The first set considered three-dimensional flow around a fixed porous block placed beneath the free surface. The measured total force on the block under wave or steady flows was predicted accurately with an error less than 10%. The second set involved a two-dimensional wave interacting with a floating porous block representing a breakwater. For free-floating conditions, the model can accurately predict the dynamic response of the structure, including the time varying movement of its rigid body and the mean drift. For mooring-restrained conditions, the mooring force and wave transmission coefficients were also predicted well with an error less than 20%. The proposed numerical approach can be applied to other floating structures with a rigid volumetric porous body. Future research is also required to study the microscopic pore flows, upon which more detailed parameterization of the porous media can be derived.

Laboratory Study on Wave Attenuation by Elastic Mangrove Model with Canopy

This study evaluates the effectiveness of artificial Kandelia obovata forests in wave attenuation through physical model experiments conducted in a wave flume. The experiments meticulously replicated real-world hydrodynamic conditions and mangrove movement responses using the principles of gravitational and motion similarity, with a scaled 1:10 model of Kandelia obovata. Our approach included comparative experiments against a 1:100 gradient concrete slope to isolate the effects of seabed friction and flume wall reflections. The wave height was measured using strategically placed wave gauges. The findings indicated that the artificial Kandelia obovata forests significantly attenuated waves, with a decrease in the total attenuation capacity as the water depth increased from 2.75 m to 3.28 m under both regular and irregular waves. The elastic mangrove model with a canopy effect led to a 15% increase in wave attenuation over cylindrical models. Predictive models using multivariate nonlinear regression and back propagation neural networks showed that the latter provided a superior accuracy in estimating wave transmission coefficients

A modified displacement discontinuity method for seismic wave propagation across rock masses with thin-layer joints

Seismic wave propagation across rock masses with thin-layer joints by the modified displacement discontinuity method (M-DDM) is of great importance for geophysical surveys. The M-DDM introduces a frequency-dependent effective stiffness to describe the dynamic stress-closure relationship of a thin-layer joint. We verify the accuracy of M-DDM in studying seismic wave propagation across rock masses with thin-layer joints. Subsequently, we evaluate the influence of the joint thickness and the incident wave frequency on M-DDM accuracy. We analyze the prediction error of the transmission coefficient obtained with M-DDM. The results demonstrate that the frequency-dependent effective joint stiffness increases with increasing incident wave frequency and decreases with increasing joint thickness. Compared with the traditional displacement discontinuity method (DDM), M-DDM more accurately predicts the transmission coefficients of seismic waves propagating across thin-layer joints. The transmission coefficient prediction error obtained based on M-DDM increases with increasing joint thickness and incident wave frequency and is always smaller than that obtained based on DDM. Therefore, the M-DDM can be used to effectively investigate seismic wave propagation across rock masses with thin-layer joints.

Numerical modeling of bamboo fences with various infill porosities deployed for mangrove restoration

As part of mangrove restoration initiatives eco-friendly fence has been implemented in eroded coastal areas in recent years. These fences provide the capacity to mitigate incoming wave energy and facilitate sediment deposition, thereby promoting the establishment and maintenance of mangrove habitats. Nevertheless, it is crucial to investigate the influence of the infill porosity on the wave dissipation performance of these fences, as the infill porosity can vary considerably across different restoration projects. The aim of this research is to explore the relationship between the infill porosity and wave dissipation effectiveness to identify more efficient designs for these eco-friendly restoration measures. The experiments involving wave interactions with fence models were conducted in a wave flume measuring 0.8 m in width and 25 m in length. Four wooden fences with distinct infill porosities ranging from 0.60 to 0.90 were strategically positioned to assess wave transmission, reflection, and dissipation phenomena under 18 distinct wave conditions. Additionally, the simulating waves till shore (SWASH)model was employed to calibrate critical bulk drag coefficient parameters and simulate the flow velocity distribution surrounding the fences under the experimental wave conditions. The findings indicated that a fence with a reduced infill porosity exhibits a higher wave transmission coefficient. However, this is accompanied by a higher reflection coefficient and lower wave energy dissipation within the fence. Both the infill porosity and incident wave conditions influence the flow velocity distribution characteristics in the vicinity of the fences. The area where the interaction between waves and fences is the most prominent is concentrated in the upper water layer immediately adjacent to the frontal section of the fences. Understanding the velocity distribution and hydrodynamic characteristics of the fence area aids in better determining the suitable porosity of fill materials for engineering applications.

Experimental study on the use of artificial meadows that mimic wave-vegetation interactions for coastal protection

A detailed experimental study was conducted on five artificial meadows made of structures that mimic wave-vegetation interactions. The meadows were of different lengths and leaf thicknesses under regular and random waves, such that the leaf thickness changed as the meadow length increased. Different wave heights, periods, and tidal conditions were examined. The results for regular and random waves were consistent. The meadow length had a stronger influence (30%–50%) on wave transmission than leaf thickness (5%–10%). A lower wave transmission was observed at higher wave energies due to enhanced wave-vegetation interaction, higher wave reflection, and effective energy dissipation. Compared with submerged conditions or when the top of the meadow was at still-water level, a lower wave transmission and higher wave reflection and energy dissipation were noted when the leaves emerged in the air. The longest meadow in the emerged condition reduced the wave height by more than 50% at mid meadow. Furthermore, a wave transmission coefficient of 0.3 was achieved by this model, which is desirable for the design of this wave barrier type. The model with the best overall hydrodynamic performance can be used alone or combined with existing natural vegetation for coastal protection.

Wave Basin Experiments Of Wave-Driven Hydrodynamics Over Submerged Coastal Structures And Artificial Reefs

Submerged coastal structures, such as submerged breakwaters and artificial reefs, modify incident wave fields and alter a wide range of nearshore hydrodynamic processes. Submerged breakwaters are usually designed for a singular function of wave attenuation; whereas nature-based artificial reef structures aim to both attenuate wave energy while enhancing ecosystem services, including the creation of habitat for marine organisms and the promotion of biodiversity. However, to date the application of artificial reefs has remained more limited due to the poorer understanding of how reefs influence key nearshore processes that determine their effectiveness. Existing research on submerged breakwaters has mostly focused on quantifying the wave transmission, which is ratio between the incident wave energy onshore and offshore of the reefs (e.g., van Gent 2023). The wave transmission coefficient has conventionally served as a primary design criterion related to the effectiveness of reefs in offering coastal protection. However, a meta-analysis of the shoreline response to constructed submerged breakwaters found that in the majority of cases erosion occurred in their lee (Ranasinghe and Turner., 2006), which demonstrates our limited knowledge on how reefs modify coastal processes. Wave-reef interactions can lead to the generation of mean (wave-averaged) currents and water levels (setup). Numerical modelling studies have found that two and four-cell mean circulation patterns can develop in response to changes to the wave field caused by submerged structures (Ranasinghe et al., 2006, da Silva et al., 2022). A two-cell circulation is characterized by diverging currents behind the reefs and at the shoreline, which could lead to an erosive shoreline. In contrast, a four-cell circulation is characterized by diverging currents in the immediate lee but converging currents at the shoreline, which would result in beach accretion. While these modelling studies advanced the understanding of how reefs influence shoreline hydrodynamics, the absence of comprehensive experimental observations replicating submerged coastal structures has hindered their rigorous validation. Here we present the findings of an extensive set of 3D wave basin experiments that were designed to investigate the detailed wave-driven hydrodynamics around submerged coastal structures subject to a range of wave conditions, water levels and reef layouts.

Numerical Integration and Angular Spectrum Modeling of Resonant and Non-Resonant Wave Interaction with a Solid Plate

The angular spectrum (AS) model is widely used to calculate the pressure transmitted through, and reflected from, a fluid-immersed solid plate, using a baffled piston as source. However, narrow peaks (infinite peaks for the lossless case) in the piston aperture function and in the plane wave transmission and reflection coefficients, in addition to a highly oscillatory integrand, cause challenges in the numerical integration. To overcome the challenges related to the aperture function peak, the AS model is reformulated using integration by parts. The peaks in the transmission and reflection coefficients are identified as symmetric and antisymmetric Scholte modes, and a numerical integration method is provided enabling integration over these peaks. The AS-model is also used to obtain the full-wave diffraction correction for a pulse-train transmitted through, or reflected from, the plate, which is highly relevant in pulse-transmit or pulse-receive measurements. The diffraction effects caused by the plate are calculated by suppressing resonance effects in the plate and obtaining the corresponding plane wave pressure transmission and reflection coefficients. A hybrid Gauss-Filon adaptive numerical integration method is used to calculate the pressure. These calculations are conducted in APAS, a MATLAB program developed in the current work and provided as open-source supplementary material.

Hydrodynamics and wave transmission through a hollow triangle breakwater

Coastal protection, shoreline stabilization and mangrove forest restoration are pressing issues in such coastal regions worldwide as the Mekong Delta. A hollow triangle breakwater TC1 was developed to protect the coastline against erosion. The TC1 breakwater consists of holes arranged on the waveward and leeward sides, allowing for wave energy dissipation, water exchange, and sediment deposition to facilitate mangrove restoration. To evaluate comprehensively the working principles of the TC1, we investigate herein the wave-structure interaction under regular waves by means of an advanced computational fluid dynamics (CFD) platform, i.e. FLOW-3D. The numerical model was calibrated against experimental results with great agreement across three different water depths where the breakwater was tested. We also analyzed the velocity dynamics in the waveward and leeward sides of the breakwater and it revealed a significant difference of approximately 50% following the change in water depths from 0.66 m to 0.96 m. Furthermore, we examined the wave forces on both solid and hollow forms of TC1 structures, the wave forces on a hollow form were found to decrease by 20–30% in comparison with the forces on a solid form. In addition, the effect of liquid characteristics, i.e., density, viscosity and temperature showed slightly impact on wave transmission coefficients through the breakwater by 0.4–0.7 %.

Experimental investigation on the hydrodynamic performance of an inverted trapezoidal breakwater

ABSTRACT The wave transmission, reflection, and dissipation characteristics of conventional (trapezoidal (TBs)) and non-conventional (inverted trapezoidal (ITBs) and rectangular (RB)) breakwaters with the same volume and porosity are evaluated under different submergence ratios, wave heights, and wave periods in regular and random waves. The experimental investigation revealed that the ITB shape is the most efficient cross section for reducing wave transmission coefficient (Kt) when the breakwater is submerged or the still water level (SWL) is at the crest of the breakwater, whereas the conventional TB is the least efficient. Compared to the conventional TB, the ITB reduced Kt by 10%–20% under submerged conditions and by 20%–30% when the SWL is at the breakwater crest. Kt < 0.2 is obtained for a relative water depth d/Lp > 0.2, which is suitable for most wave damping applications in the field when the ITB crest is at the SWL or when the crest emerges.

Acoustic radiation from multilayered materials using the reciprocity principle.

Application of the reciprocity principle to evaluate the acoustic radiation from arbitrary multilayered fluid and solid materials is described. To include the effect of shear motion in surrounding media, including viscosity in a fluid, equations for the acoustic radiation from such materials under point force excitation are developed in terms of reflection and transmission coefficients for longitudinal and shear waves. Calculations for forcing on either side of the layered material and in arbitrary directions, and for any asymmetric layer arrangements, are conducted. The frequency range of the calculations is not restricted by thin-plate or thick-plate theory. The test case for the radiation from plates embedded in a viscous and attenuating fluid has been investigated in detail. The effect of viscosity and attenuation has been quantified and shown to be significant at high frequencies. Application to the problem of flow noise is also briefly discussed.

Submerged low-crested structures in front of coastal structures

Climate adaptation of coastal structures has become more important due to climate change, resulting in sea level rise and increased wave loading on coastal structures with depth-limited wave conditions. One of the climate adaptation measures to ensure that existing coastal structures continue to perform their function after unforeseen sea level rise, is to reduce the wave loading before the waves reach the existing coastal structure. This can be achieved by constructing a low-crested structure in front of the existing structure. Between the two structures, structure-induced wave set-up occurs. This structure-induced wave set-up has been studied based on wave flume tests. The effects of structure-induced wave set-up on wave transmission at the low-crested structures and the effects on wave overtopping at the emerged coastal structures were also measured and analyzed.The structure-induced wave set-up depends on the freeboard, wave steepness, and permeability of the low-crested structure. For configurations with impermeable low-crested structures, this wave-set-up does not depend on the distance between the two structures. Empirical expressions to estimate structure-induced wave set-up are derived for impermeable and permeable low-crested structures.The measurements indicate that the effect of structure-induced wave set-up on the wave transmission coefficients is negligibly small.The structure-induced wave set-up increases the wave overtopping discharges at the emerged coastal structure. This effect can be taken into account in wave overtopping estimates by reducing the freeboard with the structure-induced wave set-up.