Pub Date : 2025-10-31DOI: 10.1016/j.wavemoti.2025.103668
K.A. Lurie
The paper examines the propagation of unilateral waves through an assembly of two materials with different space- and time-dependent properties. The assembly is immovable and characterized by a checkerboard material geometry in space and time. For a special range of material and structural parameters, the checkerboard geometry secures spatiotemporal focusing of traveling waves into progressively compressing pulses accumulating their wave energy along the way.
{"title":"The mechanism of energy accumulation in dynamic pulses traveling through checkerboard material assembly in space-time","authors":"K.A. Lurie","doi":"10.1016/j.wavemoti.2025.103668","DOIUrl":"10.1016/j.wavemoti.2025.103668","url":null,"abstract":"<div><div>The paper examines the propagation of unilateral waves through an assembly of two materials with different space- and time-dependent properties. The assembly is immovable and characterized by a checkerboard material geometry in space and time. For a special range of material and structural parameters, the checkerboard geometry secures spatiotemporal focusing of traveling waves into progressively compressing pulses accumulating their wave energy along the way.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"141 ","pages":"Article 103668"},"PeriodicalIF":2.5,"publicationDate":"2025-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145474645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-28DOI: 10.1016/j.wavemoti.2025.103669
Yaru Suo , Xingming Guo , Zhaoyang Ma
A novel star-shaped metamaterial (SSM) is proposed to achieve simultaneous vibration isolation and energy absorption capabilities. The band structure of the proposed SSM is given based on the Floquet-Bloch theorem with boundary modes of each bandgap analyzed to understand the effects of each component of the unit cell on the bandgap formation. It is found that the SSM triggers monopole, dipolar and quadrupolar resonances to form locally resonant bandgaps and exhibit equivalent negative parametric characteristics. The SSM can generate the lowest bandgap frequency of 53.149 Hz and bandgaps (lower-frequency and broader bandgaps) are highly sensitive to geometric properties angle based on parametric analysis. Additionally, vibration isolation and energy absorption performance can be enhanced by introducing a gradient parameter with angle into the SSM structure. The design of the gradient structure breaks local symmetry, opening the Dirac points to generate a new bandgap. Furthermore, uniaxial compression induces different buckling deformation, enabling the gradient structure to achieve superior energy absorption performance under the same loading conditions. This study proposes a dual-functional SSM that integrates vibration isolation and energy absorption, providing a potential pathway for multifunctional metamaterial design.
{"title":"Dual-Functional Star-shaped Metamaterial for Simultaneous Vibration Isolation and Energy Absorption","authors":"Yaru Suo , Xingming Guo , Zhaoyang Ma","doi":"10.1016/j.wavemoti.2025.103669","DOIUrl":"10.1016/j.wavemoti.2025.103669","url":null,"abstract":"<div><div>A novel star-shaped metamaterial (SSM) is proposed to achieve simultaneous vibration isolation and energy absorption capabilities. The band structure of the proposed SSM is given based on the Floquet-Bloch theorem with boundary modes of each bandgap analyzed to understand the effects of each component of the unit cell on the bandgap formation. It is found that the SSM triggers monopole, dipolar and quadrupolar resonances to form locally resonant bandgaps and exhibit equivalent negative parametric characteristics. The SSM can generate the lowest bandgap frequency of 53.149 Hz and bandgaps (lower-frequency and broader bandgaps) are highly sensitive to geometric properties angle <span><math><mi>θ</mi></math></span> based on parametric analysis. Additionally, vibration isolation and energy absorption performance can be enhanced by introducing a gradient parameter with angle <span><math><mi>θ</mi></math></span> into the SSM structure. The design of the gradient structure breaks local symmetry, opening the Dirac points to generate a new bandgap. Furthermore, uniaxial compression induces different buckling deformation, enabling the gradient structure to achieve superior energy absorption performance under the same loading conditions. This study proposes a dual-functional SSM that integrates vibration isolation and energy absorption, providing a potential pathway for multifunctional metamaterial design.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"141 ","pages":"Article 103669"},"PeriodicalIF":2.5,"publicationDate":"2025-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145474644","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-24DOI: 10.1016/j.wavemoti.2025.103667
S. Bahena-Jimenez , E. Bautista , A. Mora , F. Mendez
The interaction between non-uniform marine currents and linear water waves and its effect on the liquefaction depth of the poroelastic soil is studied. The system is divided into an upper water layer, a middle soil liquefied region, and a lower non-liquefied soil. The wave–current interaction is analyzed by adopting the Rayleigh stability theory. The non-uniform current is assumed to have a vertical non-uniform profile, treated as a piecewise linear approximation. The dynamic response of the soil is analytically determined for the solid skeleton displacement, , and the pore pressure, , by applying the u-p approximation to the governing equations. The effects of the marine current direction, relative to the wave propagation, on the magnitude of soil liquefaction are studied. It is identified that the most significant values of the liquefaction depth occur for marine currents with linear profiles traveling in an opposite direction to the wave propagation; on the contrary, for currents traveling in the same direction as the wave propagation, the liquefaction depth increases for currents with non-uniform profiles. Furthermore, the influence of soil parameters such as permeability, compressibility, and shear modulus are also analyzed. As a first approximation, the present analysis may help understand the behavior of the liquefaction depth magnitude induced by the wave-non-uniform marine current interaction.
{"title":"Hydrodynamics interaction between water waves of small amplitude and non-uniform marine currents in the liquefaction depth of poroelastic soils","authors":"S. Bahena-Jimenez , E. Bautista , A. Mora , F. Mendez","doi":"10.1016/j.wavemoti.2025.103667","DOIUrl":"10.1016/j.wavemoti.2025.103667","url":null,"abstract":"<div><div>The interaction between non-uniform marine currents and linear water waves and its effect on the liquefaction depth of the poroelastic soil is studied. The system is divided into an upper water layer, a middle soil liquefied region, and a lower non-liquefied soil. The wave–current interaction is analyzed by adopting the Rayleigh stability theory. The non-uniform current is assumed to have a vertical non-uniform profile, treated as a piecewise linear approximation. The dynamic response of the soil is analytically determined for the solid skeleton displacement, <span><math><mi>u</mi></math></span>, and the pore pressure, <span><math><mi>p</mi></math></span>, by applying the <em>u-p</em> approximation to the governing equations. The effects of the marine current direction, relative to the wave propagation, on the magnitude of soil liquefaction are studied. It is identified that the most significant values of the liquefaction depth occur for marine currents with linear profiles traveling in an opposite direction to the wave propagation; on the contrary, for currents traveling in the same direction as the wave propagation, the liquefaction depth increases for currents with non-uniform profiles. Furthermore, the influence of soil parameters such as permeability, compressibility, and shear modulus are also analyzed. As a first approximation, the present analysis may help understand the behavior of the liquefaction depth magnitude induced by the wave-non-uniform marine current interaction.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"141 ","pages":"Article 103667"},"PeriodicalIF":2.5,"publicationDate":"2025-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145425344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-23DOI: 10.1016/j.wavemoti.2025.103654
Deqin Qiu , Wei Liu , Yongshuai Zhang
This manuscript revisits the Darboux–Bäcklund transformation of the Tzitzéica equation, a classical geometric equation introduced by Romanian researcher Tzitzéica who inspired affine differential geometry. The construction of the first-order Darboux–Bäcklund transformation is re-examined. By applying Bianchi’s permutability, the second-order Bäcklund transformation (or nonlinear superposition formula) is derived. The two-fold and -fold Darboux transformations of the Tzitzéica equation are expressed by the compact determinants. These transformations require specific constraints on additional eigenfunctions and spectral parameters. Applying the generated Darboux–Bäcklund formulas, the 1- and 2-order soliton solutions for the Tzitzéica equation are constructed. The decomposition of the 2-soliton solution for the Tzitzéica equation and the constant ‘phase shift’ and approximate trajectories are obtained. Notably, the second-order complex-valued solutions exhibit diverse dynamical behaviors (e.g., breathers, solitons, and periodic waves) by choosing different values of free parameters.
{"title":"Darboux–Bäcklund transformation of the Tzitzéica equation: Novel solitons and breathers","authors":"Deqin Qiu , Wei Liu , Yongshuai Zhang","doi":"10.1016/j.wavemoti.2025.103654","DOIUrl":"10.1016/j.wavemoti.2025.103654","url":null,"abstract":"<div><div>This manuscript revisits the Darboux–Bäcklund transformation of the Tzitzéica equation, a classical geometric equation introduced by Romanian researcher Tzitzéica who inspired affine differential geometry. The construction of the first-order Darboux–Bäcklund transformation is re-examined. By applying Bianchi’s permutability, the second-order Bäcklund transformation (or nonlinear superposition formula) is derived. The two-fold and <span><math><mi>n</mi></math></span>-fold Darboux transformations of the Tzitzéica equation are expressed by the compact determinants. These transformations require specific constraints on additional eigenfunctions and spectral parameters. Applying the generated Darboux–Bäcklund formulas, the 1- and 2-order soliton solutions for the Tzitzéica equation are constructed. The decomposition of the 2-soliton solution for the Tzitzéica equation and the constant ‘phase shift’ and approximate trajectories are obtained. Notably, the second-order complex-valued solutions exhibit diverse dynamical behaviors (<em>e.g</em>., breathers, solitons, and periodic waves) by choosing different values of free parameters.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"141 ","pages":"Article 103654"},"PeriodicalIF":2.5,"publicationDate":"2025-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145365193","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-21DOI: 10.1016/j.wavemoti.2025.103665
Dede Tarwidi , Sri Redjeki Pudjaprasetya , Didit Adytia
In this study, an embedded wave generation technique is developed in a two-layer non-hydrostatic model (NH-2L). The wave generation is implemented by formulating the suitable source function and embedding it as a source term within the mass conservation equation. A straightforward, step-by-step method for constructing wave generation through embedded sources is described. The numerical model is subsequently tested through various test cases that encompass wave generation, including both regular and irregular waves. The results of wave generation are evaluated against analytical solutions and existing experimental data. The wave generation method can accurately generate monochromatic waves in both intermediate and deep water regions under absorbing boundary conditions. The simulation results for regular and irregular waves are in agreement with those obtained by laboratory experiments, demonstrating that the embedded wave generation technique implemented in the two-layer non-hydrostatic model can be used to study wave transformation in coastal regions.
{"title":"Embedded wave generation technique for two-layer non-hydrostatic models","authors":"Dede Tarwidi , Sri Redjeki Pudjaprasetya , Didit Adytia","doi":"10.1016/j.wavemoti.2025.103665","DOIUrl":"10.1016/j.wavemoti.2025.103665","url":null,"abstract":"<div><div>In this study, an embedded wave generation technique is developed in a two-layer non-hydrostatic model (NH-2L). The wave generation is implemented by formulating the suitable source function and embedding it as a source term within the mass conservation equation. A straightforward, step-by-step method for constructing wave generation through embedded sources is described. The numerical model is subsequently tested through various test cases that encompass wave generation, including both regular and irregular waves. The results of wave generation are evaluated against analytical solutions and existing experimental data. The wave generation method can accurately generate monochromatic waves in both intermediate and deep water regions under absorbing boundary conditions. The simulation results for regular and irregular waves are in agreement with those obtained by laboratory experiments, demonstrating that the embedded wave generation technique implemented in the two-layer non-hydrostatic model can be used to study wave transformation in coastal regions.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"141 ","pages":"Article 103665"},"PeriodicalIF":2.5,"publicationDate":"2025-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145365194","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we derive the non-degenerate and degenerate one- and two-soliton solutions to the semi-discrete vector nonlinear Schrödinger system, which can describe the mean-field waves within the Bose–Einstein condensate system, via Hirota’s bilinear method. The plots with different hump structures for two components are shown under the appropriate restrictions of parameters. Non-degenerate one-soliton solutions that have the double-hump structure and degenerate one-soliton solutions that have the single-hump structure are presented together. Non-degenerate two-soliton solutions can be classified as completely and partially non-degenerate solitons, corresponding to a variety of hump structures for two components. We also show some snapshots of these solitons at different moments. Moreover, a bound state for two-soliton solutions is depicted.
{"title":"Non-degenerate and degenerate soliton solutions to the semi-discrete vector nonlinear Schrödinger system","authors":"Yang-Yang Du , Yan-Nan Zhao , Hui-Qin Hao , Rui Guo , Jian-Wen Zhang","doi":"10.1016/j.wavemoti.2025.103657","DOIUrl":"10.1016/j.wavemoti.2025.103657","url":null,"abstract":"<div><div>In this paper, we derive the non-degenerate and degenerate one- and two-soliton solutions to the semi-discrete vector nonlinear Schrödinger system, which can describe the mean-field waves within the Bose–Einstein condensate system, via Hirota’s bilinear method. The plots with different hump structures for two components are shown under the appropriate restrictions of parameters. Non-degenerate one-soliton solutions that have the double-hump structure and degenerate one-soliton solutions that have the single-hump structure are presented together. Non-degenerate two-soliton solutions can be classified as completely and partially non-degenerate solitons, corresponding to a variety of hump structures for two components. We also show some snapshots of these solitons at different moments. Moreover, a bound state for two-soliton solutions is depicted.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"141 ","pages":"Article 103657"},"PeriodicalIF":2.5,"publicationDate":"2025-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145334792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-13DOI: 10.1016/j.wavemoti.2025.103658
Tugce Sezer, Semra Ahmetolan, Ayse Peker-Dobie, Ali Demirci
This work examines the propagation of Rayleigh surface waves in an elastic half-space covered by a layer with spatially varying surface corrugation. The mathematical model is established within the framework of two-dimensional linear elasticity, considering general roughness profiles for both the upper free surface and the interface of the layer. A perturbation method is employed to derive analytical expressions for the displacement fields, and dispersion relations are obtained by enforcing the relevant boundary and continuity conditions. The influence of surface corrugation parameters on phase velocity and wave propagation is examined numerically for periodic roughness profiles using selected real material models. The results demonstrate that both the amplitude and geometric characteristics of the surface irregularities have a pronounced impact on the dispersion behaviour of Rayleigh waves. These findings provide new insights into wave propagation in layered elastic media with irregular boundaries and may inform future applications in wave-based sensing, nondestructive evaluation, and acoustic material design.
{"title":"Effects of surface roughness on generalised Rayleigh waves in elastic waveguides","authors":"Tugce Sezer, Semra Ahmetolan, Ayse Peker-Dobie, Ali Demirci","doi":"10.1016/j.wavemoti.2025.103658","DOIUrl":"10.1016/j.wavemoti.2025.103658","url":null,"abstract":"<div><div>This work examines the propagation of Rayleigh surface waves in an elastic half-space covered by a layer with spatially varying surface corrugation. The mathematical model is established within the framework of two-dimensional linear elasticity, considering general roughness profiles for both the upper free surface and the interface of the layer. A perturbation method is employed to derive analytical expressions for the displacement fields, and dispersion relations are obtained by enforcing the relevant boundary and continuity conditions. The influence of surface corrugation parameters on phase velocity and wave propagation is examined numerically for periodic roughness profiles using selected real material models. The results demonstrate that both the amplitude and geometric characteristics of the surface irregularities have a pronounced impact on the dispersion behaviour of Rayleigh waves. These findings provide new insights into wave propagation in layered elastic media with irregular boundaries and may inform future applications in wave-based sensing, nondestructive evaluation, and acoustic material design.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"141 ","pages":"Article 103658"},"PeriodicalIF":2.5,"publicationDate":"2025-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145334791","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-13DOI: 10.1016/j.wavemoti.2025.103656
Zhonglong Zhao , Lihan Zhang , Yong Chen
To explain the formation mechanism of extreme events such as ocean rogue waves and light pulse train excitation, under investigation in this paper is the (2＋1)-dimensional Fokas system, which is considered as the propagation model of nonlinear waves in optical fibers. By applying the complex conjugate condition to the N-soliton solutions, the breather solutions are gained. Breathers can be transformed into nonlinear waves, which is known as state transition. By controlling the wave number ratio, five types of transformed waves are studied, including quasi-soliton, W-typed quasi-periodic wave, M-typed soliton, oscillation M-shaped soliton and multi-peak soliton. The Riemannian circle is introduced to present the gradient relationship of transformed nonlinear waves. When the phase shift produced by the elastic collision of two-soliton or two-breather is large but limited, the two V-shaped structures of two-soliton or two-breather have significantly separated, accompanied by the formation of a branch connecting the two V-shaped solitons. Two quasi-resonant interactions, namely weakly quasi-resonance and strongly quasi-resonance are investigated. Based on the asymptotic analysis method, the properties of the resonant branch are analyzed in detail, including the trajectory, amplitude and velocity. Moreover, the intermediate resonant branch is a new branch generated due to the increase of phase shift, which exhibits temporal invariance and spatial locality. By introducing the small parameter , the length of the intermediate resonant branch is studied. These results are not only foundational for understanding nonlinear wave dynamics in the Fokas system but also offer critical insights into extreme event formation across disciplines. They explain rogue wave generation in fluids, light pulse anomalies in optical fibers and wave behaviors in shallow water theory. The findings bridge mathematical integrability and physical phenomena, providing a universal framework for analyzing localized wave transitions and resonant interactions in high-dimensional nonlinear systems.
{"title":"State transition and branch structure dynamics of localized waves for the (2+1)-dimensional Fokas system in optical fibers","authors":"Zhonglong Zhao , Lihan Zhang , Yong Chen","doi":"10.1016/j.wavemoti.2025.103656","DOIUrl":"10.1016/j.wavemoti.2025.103656","url":null,"abstract":"<div><div>To explain the formation mechanism of extreme events such as ocean rogue waves and light pulse train excitation, under investigation in this paper is the (2＋1)-dimensional Fokas system, which is considered as the propagation model of nonlinear waves in optical fibers. By applying the complex conjugate condition to the N-soliton solutions, the breather solutions are gained. Breathers can be transformed into nonlinear waves, which is known as state transition. By controlling the wave number ratio, five types of transformed waves are studied, including quasi-soliton, W-typed quasi-periodic wave, M-typed soliton, oscillation M-shaped soliton and multi-peak soliton. The Riemannian circle is introduced to present the gradient relationship of transformed nonlinear waves. When the phase shift produced by the elastic collision of two-soliton or two-breather is large but limited, the two V-shaped structures of two-soliton or two-breather have significantly separated, accompanied by the formation of a branch connecting the two V-shaped solitons. Two quasi-resonant interactions, namely weakly quasi-resonance and strongly quasi-resonance are investigated. Based on the asymptotic analysis method, the properties of the resonant branch are analyzed in detail, including the trajectory, amplitude and velocity. Moreover, the intermediate resonant branch is a new branch generated due to the increase of phase shift, which exhibits temporal invariance and spatial locality. By introducing the small parameter <span><math><mi>κ</mi></math></span>, the length of the intermediate resonant branch is studied. These results are not only foundational for understanding nonlinear wave dynamics in the Fokas system but also offer critical insights into extreme event formation across disciplines. They explain rogue wave generation in fluids, light pulse anomalies in optical fibers and wave behaviors in shallow water theory. The findings bridge mathematical integrability and physical phenomena, providing a universal framework for analyzing localized wave transitions and resonant interactions in high-dimensional nonlinear systems.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"140 ","pages":"Article 103656"},"PeriodicalIF":2.5,"publicationDate":"2025-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145333125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-11DOI: 10.1016/j.wavemoti.2025.103653
Mampi Majhi , Gour Das , Rumpa Chakraborty
A semi-analytic model that indicates wave energy dissipation due to submerged porous piers with varying porosity placed over an uneven ocean bed is presented here. An infinite trench is present in the ocean bed. The oblique wave interaction with porous barriers and an infinite trench helps to reduce wave loads on shorelines by allowing water to pass through them. Presuming two-dimensional linear wave theory, the matched eigenfunction expansion method, followed by the multi-term Galerkin approximation, is considered to solve the boundary value problem. In Galerkin approximation, the basis functions are chosen in terms of orthogonal and simple polynomials multiplied by appropriate weight functions whose forms are dictated by the edge conditions of the barriers and trench edges. The sensitivity of wave reflection and transmission to structural parameters is analyzed. Due to the presence of multiple barriers and trench bottom together, Bragg resonance phenomena in the reflection curve are seen in the energy reflection coefficient, and these phenomena are depicted graphically. A new mathematical form of the energy identity has been derived, which involves a constant term and an energy loss term that occurs due to the present structure. The computed numerical results for physical quantities, viz., reflection and transmission coefficients, energy dissipation, wave force, fluid velocity, and the free surface elevation, are graphically depicted for various values of several parameters. Also, the present results are validated against using the energy identity and the results presented in the existing literature. One special case, when trench depth is finite, the energy coefficient is evaluated and explained graphically. The present study is likely to be of immense importance in the design of breakwaters as a combination of permeable barriers and trench for protecting coastal infrastructures.
{"title":"Wave energy dissipation and Bragg scattering by multiple non-uniform porous piers placed over an infinite trench bottom","authors":"Mampi Majhi , Gour Das , Rumpa Chakraborty","doi":"10.1016/j.wavemoti.2025.103653","DOIUrl":"10.1016/j.wavemoti.2025.103653","url":null,"abstract":"<div><div>A semi-analytic model that indicates wave energy dissipation due to submerged porous piers with varying porosity placed over an uneven ocean bed is presented here. An infinite trench is present in the ocean bed. The oblique wave interaction with porous barriers and an infinite trench helps to reduce wave loads on shorelines by allowing water to pass through them. Presuming two-dimensional linear wave theory, the matched eigenfunction expansion method, followed by the multi-term Galerkin approximation, is considered to solve the boundary value problem. In Galerkin approximation, the basis functions are chosen in terms of orthogonal and simple polynomials multiplied by appropriate weight functions whose forms are dictated by the edge conditions of the barriers and trench edges. The sensitivity of wave reflection and transmission to structural parameters is analyzed. Due to the presence of multiple barriers and trench bottom together, Bragg resonance phenomena in the reflection curve are seen in the energy reflection coefficient, and these phenomena are depicted graphically. A new mathematical form of the energy identity has been derived, which involves a constant term and an energy loss term that occurs due to the present structure. The computed numerical results for physical quantities, viz., reflection and transmission coefficients, energy dissipation, wave force, fluid velocity, and the free surface elevation, are graphically depicted for various values of several parameters. Also, the present results are validated against using the energy identity and the results presented in the existing literature. One special case, when trench depth is finite, the energy coefficient is evaluated and explained graphically. The present study is likely to be of immense importance in the design of breakwaters as a combination of permeable barriers and trench for protecting coastal infrastructures.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"140 ","pages":"Article 103653"},"PeriodicalIF":2.5,"publicationDate":"2025-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145333127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-11DOI: 10.1016/j.wavemoti.2025.103655
Jordan P.A. Pitt , Luke G. Bennetts
A theoretical model is used to study the propagation of water waves into and through the marginal ice zone. The marginal ice zone is modelled as a region composed of thin floating elastic plates separated by open water gaps, with randomly chosen lengths. The impact of the marginal ice zone on incoming waves is determined using a reconstruction of the dominant wavelength and attenuation rate, and a transferred amplitude (measuring the change in amplitude at the ice edge), and these quantities are studied for different ice concentrations (the areal fraction of ice cover to open water). For all concentrations, the model is shown to predict a deterministic limit for ice covers composed of floes and gaps much smaller than wavelengths, where the wave fields are independent of the particular realisation of the ice cover and insensitive to further reduction in floe and gap lengths (called the small floe–gap limit). The obtained small floe–gap limit is replicated by using a periodic ice cover that supports damped Bloch waves. The model predicts that as concentration decreases, the wavelength increases and the transferred amplitude and attenuation rate decrease, with attenuation rate scaling with ice concentration.
{"title":"Model study of ocean wave propagation through broken sea ice covers with variable ice concentration","authors":"Jordan P.A. Pitt , Luke G. Bennetts","doi":"10.1016/j.wavemoti.2025.103655","DOIUrl":"10.1016/j.wavemoti.2025.103655","url":null,"abstract":"<div><div>A theoretical model is used to study the propagation of water waves into and through the marginal ice zone. The marginal ice zone is modelled as a region composed of thin floating elastic plates separated by open water gaps, with randomly chosen lengths. The impact of the marginal ice zone on incoming waves is determined using a reconstruction of the dominant wavelength and attenuation rate, and a transferred amplitude (measuring the change in amplitude at the ice edge), and these quantities are studied for different ice concentrations (the areal fraction of ice cover to open water). For all concentrations, the model is shown to predict a deterministic limit for ice covers composed of floes and gaps much smaller than wavelengths, where the wave fields are independent of the particular realisation of the ice cover and insensitive to further reduction in floe and gap lengths (called the small floe–gap limit). The obtained small floe–gap limit is replicated by using a periodic ice cover that supports damped Bloch waves. The model predicts that as concentration decreases, the wavelength increases and the transferred amplitude and attenuation rate decrease, with attenuation rate scaling with ice concentration.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"141 ","pages":"Article 103655"},"PeriodicalIF":2.5,"publicationDate":"2025-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145365421","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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