Pub Date : 2025-01-29DOI: 10.1016/j.wavemoti.2025.103503
Tao Xu , Zhijun Qiao
The massive Thirring model, which describes pulse propagation in Bragg grating, is systematically investigated through Darboux transformation. Based on the Darboux transformation, we study soliton molecules, breather-positons, and semirational solutions for the massive Thirring model in this paper. What we present includes the following main results: (1) the general multiple soliton molecules (SMs) interaction, namely, SMs interact with solitons (); (2) higher-order breather-positon solutions whose center region exhibit rogue waves’ patterns; and (3) semirational solutions with arbitrary th-order rogue waves and -breathers. Finally, the generating mechanisms and related dynamics of those obtained nonlinear localized waves are discussed in details.
{"title":"The massive Thirring model in Bragg grating: Soliton molecules, breather-positon and semirational solutions","authors":"Tao Xu , Zhijun Qiao","doi":"10.1016/j.wavemoti.2025.103503","DOIUrl":"10.1016/j.wavemoti.2025.103503","url":null,"abstract":"<div><div>The massive Thirring model, which describes pulse propagation in Bragg grating, is systematically investigated through Darboux transformation. Based on the Darboux transformation, we study soliton molecules, breather-positons, and semirational solutions for the massive Thirring model in this paper. What we present includes the following main results: (1) the general multiple soliton molecules (SMs) interaction, namely, <span><math><mi>M</mi></math></span> SMs interact with <span><math><mrow><mo>(</mo><mi>N</mi><mo>−</mo><mi>M</mi><mo>)</mo></mrow></math></span> solitons (<span><math><mrow><mn>0</mn><mo>≤</mo><mi>M</mi><mo>≤</mo><mi>N</mi></mrow></math></span>); (2) higher-order breather-positon solutions whose center region exhibit rogue waves’ patterns; and (3) semirational solutions with arbitrary <span><math><mi>M</mi></math></span>th-order rogue waves and <span><math><mrow><mo>(</mo><mi>N</mi><mo>−</mo><mi>M</mi><mo>)</mo></mrow></math></span>-breathers. Finally, the generating mechanisms and related dynamics of those obtained nonlinear localized waves are discussed in details.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"134 ","pages":"Article 103503"},"PeriodicalIF":2.1,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143169420","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 : 2025-01-27DOI: 10.1016/j.wavemoti.2025.103498
Junrong Liu , Wen-Xiu Ma
The development of sharing-bicycle systems is accompanied by serious phenomena such as indiscriminate parking of shared bikes. This study aims to explore causes of parking behaviour problems in a sharing-bicycle system. Based on user demand and the characteristics of the shared bicycle system, we establish the evolutionary equations for the two variables, the density of user groups on the road, and the density of parked shared bicycles on the road, and study conditions satisfied by a shock wave solution. The results of the model’s shock wave solution, time-invariant solution, and travelling wave solution allow us to reveal the phenomenon of aggregation of sharing-bicycles on the sidewalk due to the architecture of a sharing-bicycle system, as well as the fluctuation of the variables that still exists in a stable system. The results have a wide range of potential impacts on sharing-bicycle system operators. In terms of operation strategy, operators can predict the gathering situation of sharing-bicycle system at different times and places according to our model, so as to optimize vehicle scheduling and parking management and reduce the phenomenon of disorderly parking. In addition, in terms of cost control, operators can use resources more effectively and reduce operating costs through more accurate forecasting and scheduling. Our research findings, when combined the basic technologies of modern sharing-bicycle system (such as mobile payment and location technology), promise to significantly enhance system optimization, control, and management, thereby fostering the sustainable growth of the sharing-bicycle industry.
{"title":"Evolutionary equations of a sharing-bicycle system and their solutions","authors":"Junrong Liu , Wen-Xiu Ma","doi":"10.1016/j.wavemoti.2025.103498","DOIUrl":"10.1016/j.wavemoti.2025.103498","url":null,"abstract":"<div><div>The development of sharing-bicycle systems is accompanied by serious phenomena such as indiscriminate parking of shared bikes. This study aims to explore causes of parking behaviour problems in a sharing-bicycle system. Based on user demand and the characteristics of the shared bicycle system, we establish the evolutionary equations for the two variables, the density of user groups on the road, and the density of parked shared bicycles on the road, and study conditions satisfied by a shock wave solution. The results of the model’s shock wave solution, time-invariant solution, and travelling wave solution allow us to reveal the phenomenon of aggregation of sharing-bicycles on the sidewalk due to the architecture of a sharing-bicycle system, as well as the fluctuation of the variables that still exists in a stable system. The results have a wide range of potential impacts on sharing-bicycle system operators. In terms of operation strategy, operators can predict the gathering situation of sharing-bicycle system at different times and places according to our model, so as to optimize vehicle scheduling and parking management and reduce the phenomenon of disorderly parking. In addition, in terms of cost control, operators can use resources more effectively and reduce operating costs through more accurate forecasting and scheduling. Our research findings, when combined the basic technologies of modern sharing-bicycle system (such as mobile payment and location technology), promise to significantly enhance system optimization, control, and management, thereby fostering the sustainable growth of the sharing-bicycle industry.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"134 ","pages":"Article 103498"},"PeriodicalIF":2.1,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143169415","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 : 2025-01-27DOI: 10.1016/j.wavemoti.2025.103501
Magdy A. Sirwah
The study examines the sloshing behavior of two superposed viscoelastic fluid layers governed by Walter’s liquid ‘B” model within a rectangular tank, subjected to horizontal vibrations. Our investigation is extending to take into account the influence of a flexible plate floating on the top fluid layer, where a modified membrane equation is used to model the stress balance on the surface. Additionally, an insoluble surfactant exists at the liquid–liquid interface within the flow system. The problem’s mathematical model is linked with the linearized Navier–Stokes equation for viscoelastic fluids, along with boundary conditions, which are solved using Laplace transform. Durbin’s numerical inverse Laplace transform scheme is used to numerically calculate solutions of the governing equations in the time domain. Graphical representations of the numerical results are included to investigate the free surface profiles, sloshing forces and moments skeletons and evolution of surface concentration under horizontal excitations, examining their behavior in relation to uniform thickness and structural rigidity of the floating elastic plate; Marangoni number and the relaxation times coefficients of the fluids. The results showed that both the thickness and structural rigidity of the floating elastic enhances the wave stability of both free surfaces of liquids, and it also causes a significant decrease in the forces acting on the walls of the container, which constitutes a safety factor to maintain the integrity of the container. On the other hand, increasing the viscoelastic parameters stimulates the sloshing waves and increases the compressive forces on the walls of the container.
{"title":"Sloshing characteristics of viscoelastic liquids in a rectangular container with a floating flexible plate","authors":"Magdy A. Sirwah","doi":"10.1016/j.wavemoti.2025.103501","DOIUrl":"10.1016/j.wavemoti.2025.103501","url":null,"abstract":"<div><div>The study examines the sloshing behavior of two superposed viscoelastic fluid layers governed by Walter’s liquid ‘B” model within a rectangular tank, subjected to horizontal vibrations. Our investigation is extending to take into account the influence of a flexible plate floating on the top fluid layer, where a modified membrane equation is used to model the stress balance on the surface. Additionally, an insoluble surfactant exists at the liquid–liquid interface within the flow system. The problem’s mathematical model is linked with the linearized Navier–Stokes equation for viscoelastic fluids, along with boundary conditions, which are solved using Laplace transform. Durbin’s numerical inverse Laplace transform scheme is used to numerically calculate solutions of the governing equations in the time domain. Graphical representations of the numerical results are included to investigate the free surface profiles, sloshing forces and moments skeletons and evolution of surface concentration under horizontal excitations, examining their behavior in relation to uniform thickness and structural rigidity of the floating elastic plate; Marangoni number and the relaxation times coefficients of the fluids. The results showed that both the thickness and structural rigidity of the floating elastic enhances the wave stability of both free surfaces of liquids, and it also causes a significant decrease in the forces acting on the walls of the container, which constitutes a safety factor to maintain the integrity of the container. On the other hand, increasing the viscoelastic parameters stimulates the sloshing waves and increases the compressive forces on the walls of the container.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"134 ","pages":"Article 103501"},"PeriodicalIF":2.1,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143169422","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 : 2025-01-25DOI: 10.1016/j.wavemoti.2025.103504
Wenjie Xiao, Can Wang, Jiang Xu
In highway guardrail systems, the buried section of pipes with soil filling on the interior results in discrepancies during guided wave inspection. This study investigates the propagation characteristics of L (0, 2) mode guided waves in the pipes, particularly focusing on the effects of soil cover conditions on wave behavior. Using modal analysis within the COMSOL, we simulated the dispersion curves and displacement distribution structures of guided waves in different modes. The L (0, 2) mode was selected for its relatively stable wave speed and minimal radial displacement, making it suitable for the study of guided wave propagation characteristics under various soil cover conditions. A finite element simulation model was developed to account for guided wave propagation in steel pipes with different soil cover conditions. This study observed diminished reflection echoes at the transition from the exposed to the soil-covered pipeline section, concomitant with a minor reduction in wave velocity within the soil-covered regions. Specifically, the L (0, 2) mode guided waves exhibited alterations in both wave velocity and reflection coefficients across varying soil cover conditions. The velocity decrement was approximated to 1.5 % with external soil cover and escalated to about 3.5 % with combined internal and external soil cover. Experimental validation substantiated the propagation characteristics of L (0, 2) mode guided waves in steel pipes under soil cover conditions. The findings provide a theoretical foundation for the detection of burial length in guardrail steel pipes.
{"title":"Research on propagation characteristics of L (0, 2) mode guided waves in the pipe with soil cover conditions","authors":"Wenjie Xiao, Can Wang, Jiang Xu","doi":"10.1016/j.wavemoti.2025.103504","DOIUrl":"10.1016/j.wavemoti.2025.103504","url":null,"abstract":"<div><div>In highway guardrail systems, the buried section of pipes with soil filling on the interior results in discrepancies during guided wave inspection. This study investigates the propagation characteristics of L (0, 2) mode guided waves in the pipes, particularly focusing on the effects of soil cover conditions on wave behavior. Using modal analysis within the COMSOL, we simulated the dispersion curves and displacement distribution structures of guided waves in different modes. The L (0, 2) mode was selected for its relatively stable wave speed and minimal radial displacement, making it suitable for the study of guided wave propagation characteristics under various soil cover conditions. A finite element simulation model was developed to account for guided wave propagation in steel pipes with different soil cover conditions. This study observed diminished reflection echoes at the transition from the exposed to the soil-covered pipeline section, concomitant with a minor reduction in wave velocity within the soil-covered regions. Specifically, the L (0, 2) mode guided waves exhibited alterations in both wave velocity and reflection coefficients across varying soil cover conditions. The velocity decrement was approximated to 1.5 % with external soil cover and escalated to about 3.5 % with combined internal and external soil cover. Experimental validation substantiated the propagation characteristics of L (0, 2) mode guided waves in steel pipes under soil cover conditions. The findings provide a theoretical foundation for the detection of burial length in guardrail steel pipes.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"134 ","pages":"Article 103504"},"PeriodicalIF":2.1,"publicationDate":"2025-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143169416","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 : 2025-01-25DOI: 10.1016/j.wavemoti.2025.103499
Hemanta Dikshit , Anoop Akkoorath Mana , Venkata R. Sonti
The sound radiation from a finite, simply-supported rectangular unbaffled plate submerged and vibrating in water is considered. The objective is to obtain a closed form expression for the coupled resonance frequencies of this water-loaded plate. The sound pressure at an arbitrary point in the surrounding fluid medium is expressed as an integral of the product of the pressure jump and the derivative of the Green’s function over the plate surface. Using Euler’s equation in the plane of the plate, a linear system of equations is obtained for the displacement field. The solution procedure involves a certain parameter known as the modal coupling coefficient. This coupling coefficient differs from that of the analogous problem of sound radiation by a baffled plate in that a square root term appears in the numerator. The improper double integral in the coupling coefficient is approximated analytically using the contour integration technique. It is in the nature of panel radiation that due to water loading, several types of modal interactions happen depending upon the frequency of excitation. For underwater applications, keeping 10 kHz as the upper limit of the excitation frequency, approximate analytical expressions for the modal coupling coefficient are derived specifically for the corner–corner and the edge–edge type interactions. Next, a small fluid loading parameter is introduced into the coupled equation of motion for the free vibration problem through the residual contribution of the coupling coefficient. Then, the perturbation method is used to obtain the closed form expression for the coupled resonance frequencies. Using this closed form expression, the coupled natural frequencies are computed for a standard size panel and compared with those obtained from the numerical calculations. A good match is observed between the two results. Along the way, a concerted effort is made to provide bounds on the error in the modal coupling coefficient caused by the various approximations. The closed form natural frequency expression is valid for a range of panel sizes, aspect ratios and thicknesses.
{"title":"A closed form expression for the resonance frequencies of an unbaffled simply-supported rectangular water-loaded plate","authors":"Hemanta Dikshit , Anoop Akkoorath Mana , Venkata R. Sonti","doi":"10.1016/j.wavemoti.2025.103499","DOIUrl":"10.1016/j.wavemoti.2025.103499","url":null,"abstract":"<div><div>The sound radiation from a finite, simply-supported rectangular unbaffled plate submerged and vibrating in water is considered. The objective is to obtain a closed form expression for the coupled resonance frequencies of this water-loaded plate. The sound pressure at an arbitrary point in the surrounding fluid medium is expressed as an integral of the product of the pressure jump and the derivative of the Green’s function over the plate surface. Using Euler’s equation in the plane of the plate, a linear system of equations is obtained for the displacement field. The solution procedure involves a certain parameter known as the modal coupling coefficient. This coupling coefficient differs from that of the analogous problem of sound radiation by a baffled plate in that a square root term appears in the numerator. The improper double integral in the coupling coefficient is approximated analytically using the contour integration technique. It is in the nature of panel radiation that due to water loading, several types of modal interactions happen depending upon the frequency of excitation. For underwater applications, keeping 10 kHz as the upper limit of the excitation frequency, approximate analytical expressions for the modal coupling coefficient are derived specifically for the corner–corner and the edge–edge type interactions. Next, a small fluid loading parameter is introduced into the coupled equation of motion for the free vibration problem through the residual contribution of the coupling coefficient. Then, the perturbation method is used to obtain the closed form expression for the coupled resonance frequencies. Using this closed form expression, the coupled natural frequencies are computed for a standard size panel and compared with those obtained from the numerical calculations. A good match is observed between the two results. Along the way, a concerted effort is made to provide bounds on the error in the modal coupling coefficient caused by the various approximations. The closed form natural frequency expression is valid for a range of panel sizes, aspect ratios and thicknesses.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"134 ","pages":"Article 103499"},"PeriodicalIF":2.1,"publicationDate":"2025-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143169421","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 : 2025-01-23DOI: 10.1016/j.wavemoti.2025.103496
E.C. Boadi , E.G. Charalampidis , P.G. Kevrekidis , N.J. Ossi , B. Prinari
The focus of this work is on a class of solutions of the defocusing Ablowitz–Ladik lattice on an arbitrarily large background which are discrete analogs of the Kuznetsov–Ma (KM) breathers of the focusing nonlinear Schrödinger equation. One such solution was obtained in 2019 as a byproduct of the Inverse Scattering Transform, and it was observed that the solution could be regular for certain choices of the soliton parameters, but its regularity was not analyzed in detail. This work provides a systematic investigation of the conditions on the background and on the spectral parameters that guarantee the KM solution to be non-singular on the lattice for all times. Furthermore, a novel KM-type breather solution is presented which is also regular on the lattice under the same conditions. We also employ Darboux transformations to obtain a multi-KM breather solution, and show that parameters choices exist for which a double KM breather solution is regular on the lattice. We analyze the features of these solutions, including their frequency which, when tending to 0, renders them proximal to rogue waveforms. Finally, numerical results on the stability and spatio-temporal dynamics of the single KM breathers are presented, showcasing the potential destabilization of the obtained states due to the modulational instability of their background.
{"title":"On the discrete Kuznetsov–Ma solutions for the defocusing Ablowitz–Ladik equation with large background amplitude","authors":"E.C. Boadi , E.G. Charalampidis , P.G. Kevrekidis , N.J. Ossi , B. Prinari","doi":"10.1016/j.wavemoti.2025.103496","DOIUrl":"10.1016/j.wavemoti.2025.103496","url":null,"abstract":"<div><div>The focus of this work is on a class of solutions of the defocusing Ablowitz–Ladik lattice on an arbitrarily large background which are discrete analogs of the Kuznetsov–Ma (KM) breathers of the focusing nonlinear Schrödinger equation. One such solution was obtained in 2019 as a byproduct of the Inverse Scattering Transform, and it was observed that the solution could be regular for certain choices of the soliton parameters, but its regularity was not analyzed in detail. This work provides a systematic investigation of the conditions on the background and on the spectral parameters that guarantee the KM solution to be non-singular on the lattice for all times. Furthermore, a novel KM-type breather solution is presented which is also regular on the lattice under the same conditions. We also employ Darboux transformations to obtain a multi-KM breather solution, and show that parameters choices exist for which a double KM breather solution is regular on the lattice. We analyze the features of these solutions, including their frequency which, when tending to 0, renders them proximal to rogue waveforms. Finally, numerical results on the stability and spatio-temporal dynamics of the single KM breathers are presented, showcasing the potential destabilization of the obtained states due to the modulational instability of their background.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"134 ","pages":"Article 103496"},"PeriodicalIF":2.1,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143168402","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 : 2025-01-21DOI: 10.1016/j.wavemoti.2025.103497
Sylvert Paul , Sirel C. Colón Useche , Mansour Ioualalen
Short-crested water waves (SCWs) are the genuine three-dimensional (3D) ocean waves. They host the phenomenon of harmonic resonances (HRs). The existence of HRs depends on their timescales, on whether or not they actually have time to develop. They are associated to superharmonic instabilities that are due to nonlinear quartet interactions. The low order HR(2,6) was chosen to match previous studies. Their multi-branch solutions and their normal forms are computed. Then, their conditions of occurrence, growth rate (inverse timescale) and persistence are discussed. It is shown that at incidence angles for which HR (2,6) occurs, its associated growth may be larger than, or at least of the same order as, those of the well-known modulational and 3D ‘horse-shoe’ pattern instabilities, which are the primary processes involved in a surface water wave field. Thus HRs seem likely to appear in a SCW field although other processes, that could inhibit their growth, are suggested.
{"title":"Time scales of a low order harmonic resonance of short-crested gravity waves on deep water","authors":"Sylvert Paul , Sirel C. Colón Useche , Mansour Ioualalen","doi":"10.1016/j.wavemoti.2025.103497","DOIUrl":"10.1016/j.wavemoti.2025.103497","url":null,"abstract":"<div><div>Short-crested water waves (SCWs) are the genuine three-dimensional (3D) ocean waves. They host the phenomenon of harmonic resonances (HRs). The existence of HRs depends on their timescales, on whether or not they actually have time to develop. They are associated to superharmonic instabilities that are due to nonlinear quartet interactions. The low order HR(2,6) was chosen to match previous studies. Their multi-branch solutions and their normal forms are computed. Then, their conditions of occurrence, growth rate (inverse timescale) and persistence are discussed. It is shown that at incidence angles for which HR (2,6) occurs, its associated growth may be larger than, or at least of the same order as, those of the well-known modulational and 3D ‘horse-shoe’ pattern instabilities, which are the primary processes involved in a surface water wave field. Thus HRs seem likely to appear in a SCW field although other processes, that could inhibit their growth, are suggested.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"134 ","pages":"Article 103497"},"PeriodicalIF":2.1,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143169414","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 : 2025-01-21DOI: 10.1016/j.wavemoti.2025.103502
Xun Yuan , Yiqing Shu , Fuchun Zhang , Penglai Guo , Weicheng Chen , Kai Fang , Yingfang Zhang , Xiaoji Zhou , Jianqing Li
Currently state-of-the-art approximate analytical solutions for the scattering of sound by a vortex are primarily based on the Plane-Wave Point Vortex (PWPV) model. In this model, the velocity of the point vortex flow field decays slowly over an infinite range, which leads to the scattered integral is ill-posed; the flow field velocity approaches infinity at the vortex core, which leads to the forward singularity. To address these two issues, based on the Plane-Wave Taylor Vortex (PWTV) model, we develop an approximate analytical solution for the scattering of sound by a vortex. In our model, the velocity of Taylor vortex flow field decays rapidly within a finite range, which can ensure the scattered integral is well-posed; the flow field velocity approaches zero at the vortex core, which can eliminate the forward singularity. We divide a Taylor vortex into a rigid vortex and a linear circular shear flow to make the scattering equation solvable. We reconstruct the composition of scattered waves and analyze the important impacts of diffraction on them. Next, after analyzing the reasons of the generation of side-lobes, we propose to replace Bessel diffraction term with the Gaussian function, which can eliminate side-lobes, thus to enhance the accuracy of the approximate solution. It is shown that the proposed approximate analytical solution is highly consistent with the numerical solution, which indicates this analytical solution can advance theoretical research on the scattering of sound by a vortex.
{"title":"An approximate analytical solution on the scattering of sound by a Taylor Vortex","authors":"Xun Yuan , Yiqing Shu , Fuchun Zhang , Penglai Guo , Weicheng Chen , Kai Fang , Yingfang Zhang , Xiaoji Zhou , Jianqing Li","doi":"10.1016/j.wavemoti.2025.103502","DOIUrl":"10.1016/j.wavemoti.2025.103502","url":null,"abstract":"<div><div>Currently state-of-the-art approximate analytical solutions for the scattering of sound by a vortex are primarily based on the Plane-Wave Point Vortex (PWPV) model. In this model, the velocity of the point vortex flow field decays slowly over an infinite range, which leads to the scattered integral is ill-posed; the flow field velocity approaches infinity at the vortex core, which leads to the forward singularity. To address these two issues, based on the Plane-Wave Taylor Vortex (PWTV) model, we develop an approximate analytical solution for the scattering of sound by a vortex. In our model, the velocity of Taylor vortex flow field decays rapidly within a finite range, which can ensure the scattered integral is well-posed; the flow field velocity approaches zero at the vortex core, which can eliminate the forward singularity. We divide a Taylor vortex into a rigid vortex and a linear circular shear flow to make the scattering equation solvable. We reconstruct the composition of scattered waves and analyze the important impacts of diffraction on them. Next, after analyzing the reasons of the generation of side-lobes, we propose to replace Bessel diffraction term with the Gaussian function, which can eliminate side-lobes, thus to enhance the accuracy of the approximate solution. It is shown that the proposed approximate analytical solution is highly consistent with the numerical solution, which indicates this analytical solution can advance theoretical research on the scattering of sound by a vortex.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"134 ","pages":"Article 103502"},"PeriodicalIF":2.1,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143169417","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 : 2025-01-18DOI: 10.1016/j.wavemoti.2025.103495
R. Kusdiantara , H. Susanto , A.R. Champneys
We investigate time-independent solutions of a discrete optical cavity model featuring saturable Kerr nonlinearity, a discrete version of the Lugiato–Lefever equation. This model supports continuous wave (uniform) and localized (discrete soliton) solutions. Stationary bright solitons arise through the interaction of dark and bright uniform states, forming a homoclinic snaking bifurcation diagram within the Pomeau pinning region. As the system approaches the anti-continuum limit (weak coupling), this snaking bifurcation widens and transitions into -shaped isolas. We propose a one-active-site approximation that effectively captures the system’s behavior in this regime. The approximation also provides insight into the stability properties of soliton states. Numerical continuation and spectral analysis confirm the accuracy of this semianalytical method, showing excellent agreement with the full model.
{"title":"From snaking to isolas: A one-active-site approximation in discrete optical cavities","authors":"R. Kusdiantara , H. Susanto , A.R. Champneys","doi":"10.1016/j.wavemoti.2025.103495","DOIUrl":"10.1016/j.wavemoti.2025.103495","url":null,"abstract":"<div><div>We investigate time-independent solutions of a discrete optical cavity model featuring saturable Kerr nonlinearity, a discrete version of the Lugiato–Lefever equation. This model supports continuous wave (uniform) and localized (discrete soliton) solutions. Stationary bright solitons arise through the interaction of dark and bright uniform states, forming a homoclinic snaking bifurcation diagram within the Pomeau pinning region. As the system approaches the anti-continuum limit (weak coupling), this snaking bifurcation widens and transitions into <span><math><mo>⊂</mo></math></span>-shaped isolas. We propose a one-active-site approximation that effectively captures the system’s behavior in this regime. The approximation also provides insight into the stability properties of soliton states. Numerical continuation and spectral analysis confirm the accuracy of this semianalytical method, showing excellent agreement with the full model.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"134 ","pages":"Article 103495"},"PeriodicalIF":2.1,"publicationDate":"2025-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143168400","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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