Pub Date : 2024-10-16DOI: 10.1016/j.wavemoti.2024.103422
Didier Felbacq, Anthony Gourdin, Emmanuel Rousseau
The scattering of scalar waves by a set of scatterers is considered. It is proven that the scattered field can be represented as an integral supported by any smooth surface enclosing the scatterers. This is a generalization of the series expansion over spherical harmonics and spherical Bessel functions for spherical geometries. More precisely, given a set of scatterers, the field scattered by any subset can be expressed as an integral over any smooth surface enclosing the given subset alone. It is then possible to solve the multiple scattering problem by using this integral representation instead of an expansion over spherical harmonics. This result is used to develop an extension of the Fast Multipole Method in order to deal with subsets that are not enclosed within non-intersecting balls.
{"title":"A single layer representation of the scattered field for multiple scattering problems","authors":"Didier Felbacq, Anthony Gourdin, Emmanuel Rousseau","doi":"10.1016/j.wavemoti.2024.103422","DOIUrl":"10.1016/j.wavemoti.2024.103422","url":null,"abstract":"<div><div>The scattering of scalar waves by a set of scatterers is considered. It is proven that the scattered field can be represented as an integral supported by any smooth surface enclosing the scatterers. This is a generalization of the series expansion over spherical harmonics and spherical Bessel functions for spherical geometries. More precisely, given a set of scatterers, the field scattered by any subset can be expressed as an integral over any smooth surface enclosing the given subset alone. It is then possible to solve the multiple scattering problem by using this integral representation instead of an expansion over spherical harmonics. This result is used to develop an extension of the Fast Multipole Method in order to deal with subsets that are not enclosed within non-intersecting balls.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"132 ","pages":"Article 103422"},"PeriodicalIF":2.1,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The global solvability in time and the potential for blow-up of solutions to non-integrable focusing nonlinear Schrödinger equations with nonzero boundary conditions at infinity present challenges that are less explored and understood compared to the case of zero boundary conditions. In this work, we address these questions by establishing estimates on the lifespan of solutions to non-integrable equations involving a general class of nonlinearities. These estimates depend on the size of the initial data, the growth of the nonlinearity, and relevant quantities associated with the amplitude of the background. The estimates provide quantified upper bounds for the minimum guaranteed lifespan of solutions. Qualitatively, for small initial data and background, these upper bounds suggest long survival times consistent with global existence of solutions. On the other hand, for larger initial data and background, the estimates indicate the potential for the intriguing phenomenon of instantaneous collapse in finite time. These qualitative theoretical results are illustrated via numerical simulations. Furthermore, importantly, the numerical findings motivate the proof of improved theoretical upper bounds that provide excellent quantitative agreement with the order of the numerically identified lifespan of solutions.
{"title":"On the lifespan of nonzero background solutions to a class of focusing nonlinear Schrödinger equations","authors":"Dirk Hennig , Nikos I. Karachalios , Dionyssios Mantzavinos , Dimitrios Mitsotakis","doi":"10.1016/j.wavemoti.2024.103419","DOIUrl":"10.1016/j.wavemoti.2024.103419","url":null,"abstract":"<div><div>The global solvability in time and the potential for blow-up of solutions to non-integrable focusing nonlinear Schrödinger equations with nonzero boundary conditions at infinity present challenges that are less explored and understood compared to the case of zero boundary conditions. In this work, we address these questions by establishing estimates on the lifespan of solutions to non-integrable equations involving a general class of nonlinearities. These estimates depend on the size of the initial data, the growth of the nonlinearity, and relevant quantities associated with the amplitude of the background. The estimates provide quantified upper bounds for the minimum guaranteed lifespan of solutions. Qualitatively, for small initial data and background, these upper bounds suggest long survival times consistent with global existence of solutions. On the other hand, for larger initial data and background, the estimates indicate the potential for the intriguing phenomenon of instantaneous collapse in finite time. These qualitative theoretical results are illustrated via numerical simulations. Furthermore, importantly, the numerical findings motivate the proof of improved theoretical upper bounds that provide excellent quantitative agreement with the order of the numerically identified lifespan of solutions.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"132 ","pages":"Article 103419"},"PeriodicalIF":2.1,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-11DOI: 10.1016/j.wavemoti.2024.103421
Ben Wilks , Michael H. Meylan , Fabien Montiel , Sarah Wakes
The generalised eigenfunction expansion method (GEM) and the singularity expansion method (SEM) are applied to solve the canonical problem of wave scattering on an infinite stretched string in the time domain. The GEM, which is shown to be equivalent to d’Alembert’s formula when no scatterer is present, is also derived in the case of a point-mass scatterer coupled to a spring. The discrete GEM, which generalises the discrete Fourier transform, is shown to reduce to matrix multiplication. The SEM, which is derived from the Fourier transform and the residue theorem, is also applied to solve the problem of scattering by the mass–spring system. The GEM and SEM are also used to solve the problem of wave scattering by a mass positioned a fixed distance from an anchor point, which supports more complicated resonant behaviour.
应用广义特征函数展开法（GEM）和奇异性展开法（SEM）求解了时域中无限拉伸弦上波散射的典型问题。在没有散射体存在的情况下，GEM 与达朗贝尔公式等价；在点质量散射体与弹簧耦合的情况下，也推导出了 GEM。离散 GEM 是对离散傅立叶变换的概括，证明它可以简化为矩阵乘法。由傅立叶变换和残差定理推导出的 SEM 也被用于解决质量-弹簧系统的散射问题。此外，GEM 和 SEM 还被用于解决与锚点保持固定距离的质量的波散射问题，它支持更复杂的共振行为。
{"title":"Generalised eigenfunction expansion and singularity expansion methods for canonical time-domain wave scattering problems","authors":"Ben Wilks , Michael H. Meylan , Fabien Montiel , Sarah Wakes","doi":"10.1016/j.wavemoti.2024.103421","DOIUrl":"10.1016/j.wavemoti.2024.103421","url":null,"abstract":"<div><div>The generalised eigenfunction expansion method (GEM) and the singularity expansion method (SEM) are applied to solve the canonical problem of wave scattering on an infinite stretched string in the time domain. The GEM, which is shown to be equivalent to d’Alembert’s formula when no scatterer is present, is also derived in the case of a point-mass scatterer coupled to a spring. The discrete GEM, which generalises the discrete Fourier transform, is shown to reduce to matrix multiplication. The SEM, which is derived from the Fourier transform and the residue theorem, is also applied to solve the problem of scattering by the mass–spring system. The GEM and SEM are also used to solve the problem of wave scattering by a mass positioned a fixed distance from an anchor point, which supports more complicated resonant behaviour.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"132 ","pages":"Article 103421"},"PeriodicalIF":2.1,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531505","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-06DOI: 10.1016/j.wavemoti.2024.103420
E.I. Shifrin, I.M. Lebedev
A problem of calculating of natural frequencies of a Timoshenko beam weakened by a finite number of transverse open cracks is considered. The problem is solved for both known crack models. In one model every crack is simulated by a single, massless rotational spring. In the other model every crack is simulated by two massless springs (one extensional and another one rotational). An effective method for calculation of the natural frequencies of a vibrating beam with cracks, which was previously successfully applied to Euler-Bernoulli beams, is extended to the case of Timoshenko beam. The developed method makes it possible to significantly reduce the order of the determinant, the zeros of which are natural frequencies. Numerical examples are considered. The results are compared with the known where it is possible.
{"title":"Natural frequencies of a Timoshenko beam with cracks","authors":"E.I. Shifrin, I.M. Lebedev","doi":"10.1016/j.wavemoti.2024.103420","DOIUrl":"10.1016/j.wavemoti.2024.103420","url":null,"abstract":"<div><div>A problem of calculating of natural frequencies of a Timoshenko beam weakened by a finite number of transverse open cracks is considered. The problem is solved for both known crack models. In one model every crack is simulated by a single, massless rotational spring. In the other model every crack is simulated by two massless springs (one extensional and another one rotational). An effective method for calculation of the natural frequencies of a vibrating beam with cracks, which was previously successfully applied to Euler-Bernoulli beams, is extended to the case of Timoshenko beam. The developed method makes it possible to significantly reduce the order of the determinant, the zeros of which are natural frequencies. Numerical examples are considered. The results are compared with the known where it is possible.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"131 ","pages":"Article 103420"},"PeriodicalIF":2.1,"publicationDate":"2024-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142433958","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 : 2024-09-29DOI: 10.1016/j.wavemoti.2024.103417
Jian Chang, Zhaqilao
In this paper, we construct the rogue wave solutions on the background of the Jacobian elliptic functions for a higher-order nonlinear Schrödinger–Maxwell–Bloch system. The Jacobian elliptic function traveling wave solutions as the seed solutions are considered. Through the approach of the nonlinearization of the Lax pair and Darboux transformation method, the rogue waves and the line rogue waves on the Jacobian elliptic functions dn and cn background are obtained, respectively.
{"title":"Rogue waves on the periodic background for a higher-order nonlinear Schrödinger–Maxwell–Bloch system","authors":"Jian Chang, Zhaqilao","doi":"10.1016/j.wavemoti.2024.103417","DOIUrl":"10.1016/j.wavemoti.2024.103417","url":null,"abstract":"<div><div>In this paper, we construct the rogue wave solutions on the background of the Jacobian elliptic functions for a higher-order nonlinear Schrödinger–Maxwell–Bloch system. The Jacobian elliptic function traveling wave solutions as the seed solutions are considered. Through the approach of the nonlinearization of the Lax pair and Darboux transformation method, the rogue waves and the line rogue waves on the Jacobian elliptic functions dn and cn background are obtained, respectively.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"131 ","pages":"Article 103417"},"PeriodicalIF":2.1,"publicationDate":"2024-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142420738","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 : 2024-09-19DOI: 10.1016/j.wavemoti.2024.103411
José M. Carcione , Jing Ba
The analogy between electromagnetism and gravitation was achieved by linearizing the tensorial gravitational equations of general relativity and converting them into a vector form corresponding to Maxwell’s electromagnetic equations. On this basis, we use the equivalence with viscoelasticity and propose a theory of gravitational waves. We add a damping term to the differential equations, which is equivalent to Ohm’s law in electromagnetism and Maxwell’s viscosity in viscoelasticity, to describe the attenuation of the waves. The differential equations in viscoelasticity are those of cross-plane shear waves, commonly referred to as SH waves. A plane-wave analysis gives the phase velocity, the energy velocity, the quality factor and the attenuation factor of the field as well as the energy balance. To obtain these properties, we use the analogy with viscoelasticity; the properties of electromagnetic and gravitational waves are similar to those of shear waves. The presence of attenuation means that the transient field is generally a composition of inhomogeneous (non-uniform) plane waves, where the propagation and attenuation vectors do not point in the same direction and the phase velocity vector and the energy flux (energy velocity) are not collinear. The polarization of cross-plane field is linear and perpendicular to the propagation-attenuation plane, while the polarization of the field within the plane is elliptical. Transient wave fields in the space–time domain are analyzed with the Green function (in homogeneous media) and with a grid method (in heterogeneous media) based on the Fourier pseudospectral method for calculating the spatial derivatives and a Runge–Kutta scheme of order 4 for the time stepping. In the examples, wave propagation at the Sun–Earth and Earth–Moon distances using quadrupole sources is considered in comparison to viscoelastic waves. The Green and grid solutions are compared to test the latter algorithm. Finally, an example of propagation in heterogeneous media is presented.
通过将广义相对论的张量引力方程线性化，并将其转换为与麦克斯韦电磁方程相对应的矢量形式，实现了电磁学与引力之间的类比。在此基础上，我们利用与粘弹性的等价关系，提出了引力波理论。我们在微分方程中加入了一个阻尼项，相当于电磁学中的欧姆定律和粘弹性中的麦克斯韦粘度，用来描述波的衰减。粘弹性中的微分方程是跨平面剪切波的微分方程，通常称为 SH 波。平面波分析给出了相速度、能量速度、场的品质因数和衰减系数以及能量平衡。为了获得这些特性，我们使用了粘弹性的类比方法；电磁波和引力波的特性与剪切波相似。衰减的存在意味着瞬态场通常由不均匀（非均匀）平面波组成，其中传播矢量和衰减矢量不指向同一方向，相位速度矢量和能量通量（能量速度）也不平行。跨平面场的极化是线性的，垂直于传播-衰减平面，而平面内场的极化是椭圆形的。分析时空域中的瞬态波场时，使用了格林函数（在均质介质中）和网格法（在异质介质中），网格法基于计算空间导数的傅立叶伪谱法和计算时间步进的 4 阶 Runge-Kutta 方案。在示例中，考虑了使用四极源在太阳-地球和地球-月球距离上的波传播，并与粘弹性波进行了比较。比较了格林解法和网格解法，以测试后一种算法。最后，介绍了一个在异质介质中传播的例子。
{"title":"On the viscoelastic-electromagnetic-gravitational analogy","authors":"José M. Carcione , Jing Ba","doi":"10.1016/j.wavemoti.2024.103411","DOIUrl":"10.1016/j.wavemoti.2024.103411","url":null,"abstract":"<div><div>The analogy between electromagnetism and gravitation was achieved by linearizing the tensorial gravitational equations of general relativity and converting them into a vector form corresponding to Maxwell’s electromagnetic equations. On this basis, we use the equivalence with viscoelasticity and propose a theory of gravitational waves. We add a damping term to the differential equations, which is equivalent to Ohm’s law in electromagnetism and Maxwell’s viscosity in viscoelasticity, to describe the attenuation of the waves. The differential equations in viscoelasticity are those of cross-plane shear waves, commonly referred to as SH waves. A plane-wave analysis gives the phase velocity, the energy velocity, the quality factor and the attenuation factor of the field as well as the energy balance. To obtain these properties, we use the analogy with viscoelasticity; the properties of electromagnetic and gravitational waves are similar to those of shear waves. The presence of attenuation means that the transient field is generally a composition of inhomogeneous (non-uniform) plane waves, where the propagation and attenuation vectors do not point in the same direction and the phase velocity vector and the energy flux (energy velocity) are not collinear. The polarization of cross-plane field is linear and perpendicular to the propagation-attenuation plane, while the polarization of the field within the plane is elliptical. Transient wave fields in the space–time domain are analyzed with the Green function (in homogeneous media) and with a grid method (in heterogeneous media) based on the Fourier pseudospectral method for calculating the spatial derivatives and a Runge–Kutta scheme of order 4 for the time stepping. In the examples, wave propagation at the Sun–Earth and Earth–Moon distances using quadrupole sources is considered in comparison to viscoelastic waves. The Green and grid solutions are compared to test the latter algorithm. Finally, an example of propagation in heterogeneous media is presented.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"131 ","pages":"Article 103411"},"PeriodicalIF":2.1,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441459","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 : 2024-09-18DOI: 10.1016/j.wavemoti.2024.103415
P.M. Jordan , A. Puri
An analysis of isothermal acoustic traveling waves in a particular sub-class of Maxwell fluids, specifically, those which behave like perfect gases and wherein the shear viscosity is proportional to the square of the mass density, is presented. Exact solutions are derived and analyzed, shock thickness results are computed, and the thermodynamic consistency of the isothermal assumption is verified vis-à-vis the Mach number values considered. It is shown that, within the range where both yield dispersed shock profiles, the Maxwell case leads to significantly smaller shock thicknesses and more asymmetric solution profiles than those admitted by the corresponding Newtonian (fluid) case.
{"title":"The impact of relaxation on isothermal acoustic traveling waves: A new solvable model based on Navier–Stokes–Maxwell theory","authors":"P.M. Jordan , A. Puri","doi":"10.1016/j.wavemoti.2024.103415","DOIUrl":"10.1016/j.wavemoti.2024.103415","url":null,"abstract":"<div><div>An analysis of isothermal acoustic traveling waves in a particular sub-class of Maxwell fluids, specifically, those which behave like perfect gases and wherein the shear viscosity is proportional to the square of the mass density, is presented. Exact solutions are derived and analyzed, shock thickness results are computed, and the thermodynamic consistency of the isothermal assumption is verified vis-à-vis the Mach number values considered. It is shown that, within the range where both yield dispersed shock profiles, the Maxwell case leads to significantly smaller shock thicknesses and more asymmetric solution profiles than those admitted by the corresponding Newtonian (fluid) case.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"131 ","pages":"Article 103415"},"PeriodicalIF":2.1,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142315738","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 : 2024-09-18DOI: 10.1016/j.wavemoti.2024.103416
Guoyi Fu, Xiaoyan Chen, Shihui Zhu
This study is concerned with solitary wave solutions and the dynamic behavior of the (2+1)-dimensional nonlinear fractional Schrödinger system. By exploring the dynamic properties of the equilibrium levels to the corresponding Hamiltonian, the expressions of exact solutions of the above system are obtained, including solitary wave solutions, periodic wave solutions, singular periodic wave solutions, singular wave solutions, kink wave solutions, and anti-kink wave solutions. Moreover, the linear stability, geometric characteristics, and limiting behavior of these solutions to the nonlinear fractional Schrödinger system were investigated.
{"title":"Solitary wave solutions and their limits to the fractional Schrödinger system","authors":"Guoyi Fu, Xiaoyan Chen, Shihui Zhu","doi":"10.1016/j.wavemoti.2024.103416","DOIUrl":"10.1016/j.wavemoti.2024.103416","url":null,"abstract":"<div><div>This study is concerned with solitary wave solutions and the dynamic behavior of the (2+1)-dimensional nonlinear fractional Schrödinger system. By exploring the dynamic properties of the equilibrium levels to the corresponding Hamiltonian, the expressions of exact solutions of the above system are obtained, including solitary wave solutions, periodic wave solutions, singular periodic wave solutions, singular wave solutions, kink wave solutions, and anti-kink wave solutions. Moreover, the linear stability, geometric characteristics, and limiting behavior of these solutions to the nonlinear fractional Schrödinger system were investigated.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"131 ","pages":"Article 103416"},"PeriodicalIF":2.1,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142315737","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 : 2024-09-18DOI: 10.1016/j.wavemoti.2024.103414
Kai Zhou , Sen-Yue Lou , Shou-Feng Shen
By means of the Hirota’s bilinear method and special multi-linear variable separation ansatz, new exact solutions with low dimensional arbitrary functions of some (2+1)-dimensional nonlinear evolution equations are constructed. That is, we propose a unified method for solving the mNNV-type equations and the Burger-type equations. The key factor to the success of this method is that we have constructed some simplified Hirota’s bilinear calculation formulas in the form of variable separation of arbitrary order. Appropriate multi-valued functions are used to construct coherent structures such as the bell-type, peak-type and loop-type folding waves.
{"title":"New exact solutions of some (2+1)-dimensional nonlinear evolution equations and folding waves","authors":"Kai Zhou , Sen-Yue Lou , Shou-Feng Shen","doi":"10.1016/j.wavemoti.2024.103414","DOIUrl":"10.1016/j.wavemoti.2024.103414","url":null,"abstract":"<div><p>By means of the Hirota’s bilinear method and special multi-linear variable separation ansatz, new exact solutions with low dimensional arbitrary functions of some (2+1)-dimensional nonlinear evolution equations are constructed. That is, we propose a unified method for solving the mNNV-type equations and the Burger-type equations. The key factor to the success of this method is that we have constructed some simplified Hirota’s bilinear calculation formulas in the form of variable separation of arbitrary order. Appropriate multi-valued functions are used to construct coherent structures such as the bell-type, peak-type and loop-type folding waves.</p></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"131 ","pages":"Article 103414"},"PeriodicalIF":2.1,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142274165","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 : 2024-09-14DOI: 10.1016/j.wavemoti.2024.103410
Na Liu , Xiaojun Yin , Ruigang Zhang , Quansheng Liu
Here, we present a higher dimensional model from the vorticity equation, which describes the dynamic characteristics of large scale Rossby waves by utilizing the Gardner-Morikawa coordinate transformation and the perturbation method. To reveal the influence of physical parameters on the higher dimensional model, we first give the dispersion relation of the model and the N-soliton solutions by Hirota method. Subsequently, the lump solutions are derived by using the long wave limit method. It demonstrates that the horizontal component of the Coriolis force acts as a forcing force on the nonlinear Rossby waves, and affects the amplitude of the meridional structure. Moreover, under the background of secondary zonal basic flow, for different lump solutions, the flow field will appear dipole blocking or double vortex structure. It is also indicated that the horizontal Coriolis force only causes the vortex to move in the latitudinal direction.
{"title":"A higher dimensional model of geophysical fluid with the complete Coriolis force and vortex structure","authors":"Na Liu , Xiaojun Yin , Ruigang Zhang , Quansheng Liu","doi":"10.1016/j.wavemoti.2024.103410","DOIUrl":"10.1016/j.wavemoti.2024.103410","url":null,"abstract":"<div><div>Here, we present a higher dimensional model from the vorticity equation, which describes the dynamic characteristics of large scale Rossby waves by utilizing the Gardner-Morikawa coordinate transformation and the perturbation method. To reveal the influence of physical parameters on the higher dimensional model, we first give the dispersion relation of the model and the N-soliton solutions by Hirota method. Subsequently, the lump solutions are derived by using the long wave limit method. It demonstrates that the horizontal component of the Coriolis force acts as a forcing force on the nonlinear Rossby waves, and affects the amplitude of the meridional structure. Moreover, under the background of secondary zonal basic flow, for different lump solutions, the flow field will appear dipole blocking or double vortex structure. It is also indicated that the horizontal Coriolis force only causes the vortex to move in the latitudinal direction.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"131 ","pages":"Article 103410"},"PeriodicalIF":2.1,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142319550","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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