Wave Transmission Coefficients Research Articles

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.

Numerical Study on Wave Dissipation and Mooring Force of a Horizontal Multi-Cylinder Floating Breakwater

A three-dimensional numerical model was established based on ANSYS-AQWA (R19.0) software for the purpose of analyzing the hydrodynamic characteristics of a floating breakwater. This study examines three distinct floating breakwaters with different cross-sectional designs in order to evaluate their respective wave dissipation capabilities. It is suggested that the horizontal multi-cylinder floating breakwater exhibits a superior ability to dissipate waves when compared to both the single-cylinder and square pontoon configurations and can be deemed the most advantageous shielding strategy for potential engineering applications. Subsequently, this study examines the effects of influential parameters, including a large cylinder diameter, a small cylinder diameter, the angular position of the small cylinder, and the height and period of the incident wave, on the wave transmission coefficient. An empirical formula for the wave transmission coefficient was derived based on the numerical results. Additionally, the effects of influential parameters, including wind speed, current velocity, incident wave height and period, and water depth, on the maximum total mooring force were investigated. Furthermore, an empirical formula for the maximum total mooring force is proposed for practical implementation in engineering.

Wave interaction with multiple adjacent floating solar panels with arbitrary constraints

The problem of wave interaction with multiple adjacent floating solar panels with arbitrary types and numbers of constraints is considered. All the solar panels are assumed to be homogeneous, with the same physical properties, as well as modeled by using the Kirchhoff-Love plate theory. The motion of the fluid is described by the linear velocity potential theory. The domain decomposition method is employed to obtain the solutions. In particular, the entire fluid domain is divided into two types, the one below the free surface, and the other below elastic plates. The velocity potential in the free surface domain is expressed into a series of eigenfunctions. By contrast, the boundary integral equation and the Green function are employed to construct the velocity potential of fluid beneath the entire elastic cover, with unknowns distributed along two interfaces and jumps of physical parameters of the plates. All these unknowns are solved from the system of linear equations, which is established from the matching conditions of velocity potentials and edge conditions. This approach is confirmed with much higher computational efficiency compared with the one only involving eigenfunction expansion for the fluid beneath each plate. Extensive results and discussions are provided for the reflection and transmission coefficients of water waves, maximum deflection, and principal strain of the elastic plates; especially, the influence of different types and numbers of edge constraints are investigated in detail.

Investigating the wave attenuation capabilities of rectangular pile head breakwater: A physical modelling approach

The study provides a comprehensive examination of single row Rectangular Pile Head Breakwaters (RPHB), encompassing both non-perforated and perforated variations. In the non-perforated RPHB category, the investigation delves into the effects of pile head height and width, and wave climate. For perforated RPHB structures, the study analyses the influence of percentage of perforations, perforation size, and depth of water. Further, the research includes a comparative assessment between non-perforated and perforated RPHB structures. Additionally, the research conducts a comparative analysis with similar structures. In the case of non-perforated RPHB, the configuration with relative pile head diameter (D/d) of 2.4 and relative pile head height (Y/Hmax) of 1.5 stood out as the most effective model. Similarly, the perforated RPHB demonstrated its maximum wave attenuation potential with percentage of perforations (P) of 24% with relative size of perforations (S/D) of 0.25. This optimal configuration achieved a minimal wave transmission coefficient (Kt) of 0.53, reflection coefficient (Kr) of 0.33, and energy dissipation coefficient (Kd) of 0.79 at a relative water depth (h/H) 0.865. Notably, the introduction of perforations on the RPHB structure led to an improvement in wave attenuation performance by 4–8%, resulting in lower reflection and higher energy dissipation. Comparatively, the RPHB structure outperformed the Enlarged (cylindrical) Pile Head Breakwater (EPHB) and Conical Pile Head Breakwater (CPHB) structures in terms of wave attenuation, exhibiting higher reflection and superior energy dissipation characteristics. The consistent outcome of these investigations reveals that the RPHB exhibits superior hydrodynamic performance characteristics and design suitability, making it a promising choice for breakwater applications.

Transmission across a ribbon containing a square [formula omitted] impurity

We study the spectrum and transmission coefficient of plane waves propagating along square ribbons of varying widths, containing a square-shaped, PT-symmetric impurity region. We start with a zero-width ribbon (1D chain) and place a PT symmetric dimer. The spectrum is computed numerically and the instability gain is computed as a function of the gain/loss dimer strength. The transmission coefficient is obtained in closed form and examined as a function of wavevector and the gain/loss parameter. Next, we study a ribbon in a narrow ladder configuration containing a square PT impurity. As before, we compute the instability gain numerically and the transmission coefficient in closed form for the two possible input modes. Finally, we repeat the calculations for a wider ladder ribbon containing a Lieb-like impurity in a PT configuration. For all cases and transmission channels, we obtain transmission divergences in wavevector-gain/loss parameter space, whose number increases with the width of the ribbon.

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).

Wave transmission coefficient reduction by wooden fences

In this study, we investigate the efficiency of wooden fences in reducing wave amplitude using a modified version of the Linear Shallow Water Equations. The resulting model is solved analytically and numerically to obtain the wave transmission coefficient. We apply a staggered finite volume method to obtain the numerical solution of the model, which is subsequently validated through comparison with the analytical solution of the equations and experimental data from a previous study. The validated scheme is then employed to simulate the wave attenuation of wooden fences. We anticipate that this method will prove valuable in the construction of coastal defense systems, particularly for the protection of mangroves.

Sum-frequency triad interactions among surface waves propagating through an ice sheet

We study nonlinear resonant wave–wave interactions which occur when ocean waves propagate into a thin floating ice sheet. Using multiple-scale perturbation analysis, we obtain theoretical predictions of the wave amplitude evolution as a function of distance travelled past the ice edge for a semi-infinite ice sheet. The theoretical predictions are supported by a high-order spectral (HOS) method capable of simulating nonlinear interactions in both open water and the ice sheet. Using the HOS method, the amplitude evolution predictions are extended to multiple (coupled) triad interactions and a single ice sheet of finite length. We relate the amplitude evolution to mechanisms with strong frequency dependence – ice bending strain, related to ice breakup, as well as wave reflection and transmission. We show that, due to sum-frequency interactions, the maximum strain in the ice sheet can be more than twice that predicted by linearised theory. For an ice sheet of finite length, we show that nonlinear wave reflection and transmission coefficients depend on a parameter in terms of wave steepness and ice length, and can have values significantly different than those from linear theory. In particular, we show that nonlinear sum-frequency interactions can appreciably decrease the total wave energy transmitted past the ice sheet. This work has implications for understanding the occurrence of ice breakup, wave attenuation due to scattering in the marginal ice zone and the resulting ice floe size distribution.

Experimental Study on Wave Transmission Coefficient of Double Cylindrical Floating Breakwater in a Wave Basin

Floating breakwater is a better alternative than the conventional method. It is an effective coastal engineering unit used to protect coastal regions such as harbours and marinas from erosive waves. It has many other applications such as offshore renewable energy generation, infrastructure preservation, temporary structure, and provides a controlled environment for aquaculture activities. The floating breakwater such as the double cylindrical floating breakwater (DCFB) is claimed to have effective wave attenuation characteristics. A lab scale investigation was done by placing the DCFB in a controlled wave basin in with wave generator to generate wave and wave gauge to quantify the wave transmission coefficient. The wave transmission coefficient represents the effectiveness of the breakwater system in attenuating incoming waves, where an effective breakwater system will result in a low transmission coefficient value. In this study, the DCFB’s effectiveness in terms of wave transmission coefficient was investigated with two different configurations where the spacing between the cylinders of the DCFB units are 0.2 m and 0.6 m respectively. Results show that the configuration of DCFB units with 0.5 m cylinder spacing are more effective in absorbing incoming wave height resulting in lower transmission coefficient. Furthermore, some prospective areas had been identified for future enhancement.

Experimental and numerical study on hydrodynamic characteristics of a bottom-hinged pitching flap breakwater under regular waves

A bottom-hinged flap breakwater is proposed for the wave attenuation and coastal protection. A series of laboratory experiments and a CFD numerical model were conducted to investigate the hydrodynamic characteristics in regular waves. The hydrodynamic coefficients, dimensionless maximum point pressure and average pitching amplitude of flap were examined with the parameters of incident waves and flap property. As the incident wave steepness increased, the wave reflection coefficient Kr, wave transmission coefficient Kt, dimensionless maximum point pressure pmax/ρwgh, and average pitching amplitude of flap θa increased for a given wave period; however, the wave dissipation coefficient Kd decreased. As the flap relative height increased, Kr and θa increased for a given wave period; whereas, Kt decreased. Furthermore, as the flap density ratio increased, Kr, pmax/ρwgh, and fitted Kd increased; however, Kt and θa decreased. As the equivalent damping coefficient ratio increased, Kr and pmax/ρwgh increased; however, Kt and θa decreased. Additionally, a series of dimensionless parameters of incident waves and flap property were used to derive formulas for Kr, Kt and Kd, which were validated using the related data.

Fractional electrical impurity

We examine the localized mode and the transmission of plane waves across a capacitive impurity of strength Δ, in a 1D bi-inductive electrical transmission line where the usual discrete Laplacian is replaced by a fractional one characterized by a fractional exponent s. In the absence of the impurity, the plane wave dispersion is computed in closed form in terms of hypergeometric functions. It is observed that the bandwidth decreases steadily, as s decreases towards zero, reaching a minimum width at s = 0. The localized mode energy and spatial profiles are computed in closed form vía lattice Green functions. The profiles show a remnant of the staggered-unstaggered symmetry that is common in non-fractional chains. The width of the localized mode decreases with decreasing s, becoming completely localized at the impurity site at s = 0. The transmission coefficient of plane waves across the impurity is qualitatively similar to its non-fractional counterpart (s = 1), except at low s values ( s≪1 ). For a fixed exponent s, the transmission decreases with increasing Δ.