The characteristics of nonlinear and supernonlinear Alfvén waves propagating in a multicomponent plasma composed of a double spectral electron distribution and positive and negative ions were investigated.The Sag...The characteristics of nonlinear and supernonlinear Alfvén waves propagating in a multicomponent plasma composed of a double spectral electron distribution and positive and negative ions were investigated.The Sagdeev technique was employed,and an energy equation was derived.Our findings show that the proposed system reveals the existence of a double-layer solution,periodic,supersoliton,and superperiodic waves.The phase portrait and potential analysis related to these waves were investigated to study the main features of existing waves.It was also found that decreasing the electron temperature helps the superperiodic structure to be excited in our plasma model.Our results help interpret the nonlinear and supernonlinear features of the recorded Alfvén waves propagating in the ionosphere D-region.展开更多
A composite model, which is the combination of Boussinesq equations and Volume of Fluid (VOF) method, has been developed for 2-D time-domain computations of nonlinear waves in a large region. The whole computational r...A composite model, which is the combination of Boussinesq equations and Volume of Fluid (VOF) method, has been developed for 2-D time-domain computations of nonlinear waves in a large region. The whole computational region Omega is divided into two subregions. In the near-field around a structure, Omega(2), the flow is governed by 2-D Reynolds Averaged Navier-Stokes equations with a turbulence closure model of k-epsilon equations and numerically solved by the improved VOF method; whereas in the subregion Omega(1) (Omega(1) = Omega - Omega(2)) the flow is governed by one-D Boussinesq equations and numerically solved with the predictor-corrector algorithm. The velocity and the wave surface elevation are matched on the common boundary of the two subregions. Numerical tests have been conducted for the case of wave propagation and interaction with a wave barrier. It is shown that the composite model can help perform efficient computation of nonlinear waves in a large region with the complicated flow fields near structures taken into account.展开更多
A 3-D time-domain numerical coupled model is developed to obtain an efficient method for nonlinear waves acting on a box-shaped ship fixed in a harbor. The domain is divided into the inner domain and the outer domain....A 3-D time-domain numerical coupled model is developed to obtain an efficient method for nonlinear waves acting on a box-shaped ship fixed in a harbor. The domain is divided into the inner domain and the outer domain. The inner domain is the area beneath the ship and the flow is described by the simplified Euler equations. The remaining area is the outer domain and the flow is defined by the higher-order Boussinesq equations in order to consider the nonlinearity of the wave motions. Along the interface boundaries between the inner domain and the outer domain, the volume flux is assumed to be continuous and the wave pressures are equal. Relevant physical experiment is conducted to validate the present mode/and it is shown that the numerical results agree with the experimental data. Compared the coupled model with the flow in the inner domain governed by the Laplace equation, the present coupled model is more efficient and its solution procedure is simpler, which is particularly useful for the study on the effect of the nonlinear waves acting on a fixed box-shaped ship in a large harbor.展开更多
Recently, inwardly propagating waves （called antiwaves, AWs） in nonlinear oscillatory systems have attracted much attention. An interesting negative refraction phenomenon has been observed in a bidomain system where...Recently, inwardly propagating waves （called antiwaves, AWs） in nonlinear oscillatory systems have attracted much attention. An interesting negative refraction phenomenon has been observed in a bidomain system where one medium supports forwardly propagating waves （normal waves, NWs） and the other AWs. In this paper we find that negative refraction （NR） in nonlinear media has an asymmetric property, i.e., NR can be observed only by applying wave source with proper frequency to one medium, but not the other. Moreover, NR appears always when the incident waves are dense and the refractional waves are sparse. This asymmetry is a particular feature for nonlinear NR, which can neither be observed in linear refraction processes （both positive and negative refractions） nor in nonlinear positive refraction. The mechanism underlying the asymmetry of nonlinear NR are fully understood based on the competition of nonlinear waves.展开更多
This paper investigates the collision between two nonlinear waves with arbitrary angle in two-dimensional nonlinear lattice. By using the extended Poincarge-Lighthill-Kuo perturbation method, it obtains two Korteweg-d...This paper investigates the collision between two nonlinear waves with arbitrary angle in two-dimensional nonlinear lattice. By using the extended Poincarge-Lighthill-Kuo perturbation method, it obtains two Korteweg-de Vries equations for nonlinear waves in both the ζ and η directions, respectively, and derives the analytical phase shifts after the collision of two nonlinear waves. Finally, the solution of u（υ） up to O（ε^3） order is given.展开更多
This paper investigates the collision between two nonlinear waves with different propagation directions in two- dimensional dust crystals. Using the extended Poincare-Lighthill-Kuo perturbation method, two Korteweg-de...This paper investigates the collision between two nonlinear waves with different propagation directions in two- dimensional dust crystals. Using the extended Poincare-Lighthill-Kuo perturbation method, two Korteweg-de Vries equations for nonlinear waves in both the ξ and η directions are obtained, respectively, and the analytical phase shifts and trajectories after the collision of two nonlinear waves are derived. Finally, the effects of parameters of the lattice constant a, the arbitrary constant u0η, the forces f（r）, and the colliding angle θ on the phase shifts of both colliding nonlinear waves are examined.展开更多
A nonlinear wave equation of elastic rod taking account of finite deformation, transverse inertia and shearing strain is derived by means of the Hamilton principle in this paper. Nonlinear wave equation and truncated ...A nonlinear wave equation of elastic rod taking account of finite deformation, transverse inertia and shearing strain is derived by means of the Hamilton principle in this paper. Nonlinear wave equation and truncated nonlinear wave equation are solved by the Jacobi elliptic sine function expansion and the third kind of Jacobi elliptic function expansion method. The exact periodic solutions of these nonlinear equations are obtained, including the shock wave solution and the solitary wave solution. The necessary condition of exact periodic solutions, shock solution and solitary solution existence is discussed.展开更多
By using Hamilton-type variation principle in non-conservation system, the nonlinear equation of wave motion of a elastic thin rod was derived according to Lagrange description of finite deformation theory. The dissip...By using Hamilton-type variation principle in non-conservation system, the nonlinear equation of wave motion of a elastic thin rod was derived according to Lagrange description of finite deformation theory. The dissipation caused due to viscous effect and the dispersion introduced by transverse inertia were taken into consideration so that steady traveling wave solution can be obtained. Using multi-scale method the nonlinear equation is reduced to a KdV-Burgers equation which corresponds with saddle-spiral heteroclinic orbit on phase plane. Its solution is called the oscillating-solitary wave or saddle-spiral shock wave. If viscous effect or transverse inertia is neglected, the equation is degraded to classical KdV or Burgers equation. The former implies a propagating solitary wave with homoclinic on phase plane, the latter means shock wave and heteroclinic orbit.展开更多
Based on the high order nonlinear and dispersive wave equation with a dissipative term, a numerical model for nonlinear waves is developed, It is suitable to calculate wave propagation in water areas with an arbitrari...Based on the high order nonlinear and dispersive wave equation with a dissipative term, a numerical model for nonlinear waves is developed, It is suitable to calculate wave propagation in water areas with an arbitrarily varying bottom slope and a relative depth h/L(0)less than or equal to1. By the application of the completely implicit stagger grid and central difference algorithm, discrete governing equations are obtained. Although the central difference algorithm of second-order accuracy both in time and space domains is used to yield the difference equations, the order of truncation error in the difference equation is the same as that of the third-order derivatives of the Boussinesq equation. In this paper, the correction to the first-order derivative is made, and the accuracy of the difference equation is improved. The verifications of accuracy show that the results of the numerical model are in good agreement with those of analytical Solutions and physical models.展开更多
The generation and propagation mechanism of strong nonlinear waves in the South China Sea is an essential research area. In this study, the third-generation wave model WAVEWATCH Ⅲ is employed to simulate wave fields ...The generation and propagation mechanism of strong nonlinear waves in the South China Sea is an essential research area. In this study, the third-generation wave model WAVEWATCH Ⅲ is employed to simulate wave fields under extreme sea states. The model, integrating the ST6 source term, is validated against observed data, demonstrating its credibility. The spatial distribution of the occurrence probability of strong nonlinear waves during typhoons is shown, and the waves in the straits and the northeastern part of the South China Sea show strong nonlinear characteristics. The high-order spectral model HOS-ocean is employed to simulate the random wave surface series beneath five different platform areas. The waves during the typhoon exhibit strong nonlinear characteristics, and freak waves exist. The space-varying probability model is established to describe the short-term probability distribution of nonlinear wave series. The exceedance probability distributions of the wave surface beneath different platform areas are compared and analyzed. The results show that with an increase in the platform area, the probability of a strong nonlinear wave beneath the platform increases.展开更多
In a thin-walled, homogeneous, straight, long, circular, and incompressible fluid filled elastic tube, small but finite long wavelength nonlinear waves can be describe by a KdV (Korteweg de Vries) equation, while the ...In a thin-walled, homogeneous, straight, long, circular, and incompressible fluid filled elastic tube, small but finite long wavelength nonlinear waves can be describe by a KdV (Korteweg de Vries) equation, while the carrier wave modulations are described by a nonlinear Schr?dinger equation (NLSE). However if the elastic tube is slowly inhomogeneous, then it is found, in this paper, that the carrier wave modulations are described by an NLSE-like equation. There are soliton-like solutions for them, but the stability and instability regions for this soliton-like waves will change, depending on what kind of inhomogeneity the tube has.展开更多
Nonlinear internal waves(NLIWs)exhibit robust dynamic submesoscale motions,connecting large-scale tides to smallscale shear instabilities in the ocean.Previous studies have mainly focused on their generation mechanism...Nonlinear internal waves(NLIWs)exhibit robust dynamic submesoscale motions,connecting large-scale tides to smallscale shear instabilities in the ocean.Previous studies have mainly focused on their generation mechanisms and evolution along their paths.Considering their global distribution resulting from the primary origin in tide-topography interaction,there is an increasing cross-disciplinary interest in understanding how these energetic and ubiquitous NLIWs contribute to sediment redistribution in the ocean.This paper presents fundamental theories on NLIWs and comprehensively reviews triggering mechanisms,different types of instability,and sediment responses by summarizing recent theoretical parameterizations,numerical simulations,laboratory experiments,and in-situ observations.We specifically focus on elucidating various types of instability along with their impact on sediment dynamic processes.Finally,we outline several unresolved issues that require further exploration for a quantitative investigation into NLIWinduced sediment transfer in the ocean.展开更多
The flows of nonlinear waves overtopping an obstruction are studied numerically in the present paper. The finite difference method is used to solve the full two dimensional Navier Stokes equations, and the VOF metho...The flows of nonlinear waves overtopping an obstruction are studied numerically in the present paper. The finite difference method is used to solve the full two dimensional Navier Stokes equations, and the VOF method is adopted to deal with free surface deformations. Numerical results of a solitary wave and periodic waves overtopping an rectangular cylinder are obtained respectively. Many complex phenomena, such as water accumulation, wave run up, water jet flows, water jet impact both upon free surface and on a structure, and generation of new waves on the lee side during the process of the waves overtopping an obstacle, can be successfully simulated.展开更多
The wave crest is an important factor for the design of both fixed and floating marine structures.Wave crest height is a dominant parameter in assessing the likelihood of wave-in-deck impact and resultant severe damag...The wave crest is an important factor for the design of both fixed and floating marine structures.Wave crest height is a dominant parameter in assessing the likelihood of wave-in-deck impact and resultant severe damage.Many empirical and theoretical distribution functions for wave crest heights have been proposed,but there is a lack of agreement between them.It is of significance to develop a better new nonlinear wave crest height distribution model.The progress in the research of wave crest heights is reviewed in this paper.Based on Stokes' wave theory,an approximate nonlinear wave crest-height distribution formula with simple parameters is derived.Two sets of measured data are presented and compared with various theoretical distributions of wave crests obtained from nonlinear wave models and analysis of the comparison is given in detail.The new crest-height distribution model agrees well with observations.Also,the new theoretical distribution is more accurate than the other methods cited in this paper and has a greater range of applications.展开更多
In this paper, the wave velocity c is developed as an asymptotic series for weak nonlinear waves in non-uniform flow. Then Fredholm's alternative theorem is applied and it is verified that the first-order approxim...In this paper, the wave velocity c is developed as an asymptotic series for weak nonlinear waves in non-uniform flow. Then Fredholm's alternative theorem is applied and it is verified that the first-order approximation c1 equals zero, This generalizes the previous result.展开更多
We briefly review the recent progress in marine hydrodynamics.Developments in wave-structure interaction,wave-current interaction,Rogue waves,sloshing in liquid tanks and their applications in ocean engineering,such a...We briefly review the recent progress in marine hydrodynamics.Developments in wave-structure interaction,wave-current interaction,Rogue waves,sloshing in liquid tanks and their applications in ocean engineering,such as Floating Production Storage and Offloading facility(FPSO) and Very Large Floating Structure(VLFS),are presented.展开更多
For robust nonlinear wave simulation in a moving reference frame, we recast the free surface problem in Hamilton-Jacobi form and propose a Weighted Essentially Non-Oscillatory （WENO） scheme to automatically handle t...For robust nonlinear wave simulation in a moving reference frame, we recast the free surface problem in Hamilton-Jacobi form and propose a Weighted Essentially Non-Oscillatory （WENO） scheme to automatically handle the upwinding of the convective term. A new automatic procedure for deriving the linear WENO weights based on a Taylor series expansion is introduced. A simplified smoothness indicator is proposed and is shown to perform well. The scheme is combined with high-order explicit Runge-Kutta time integration and a dissipative Lax-Friedrichs-type flux to solve for nonlinear wave propagation in a moving frame of reference. The WENO scheme is robust and less dissipative than the equivalent order upwind-biased finite difference scheme for all ratios of frame of reference to wave propagation speed tested. This provides the basis for solving general nonlinear wave-structure interaction problems at forward speed.展开更多
Low-frequency phenomena in the atmosphere are intimately related to stationary waves and, in a sense, the former may even be viewed as the time-varying part of the quasi-stationary waves themselves, Much attention has...Low-frequency phenomena in the atmosphere are intimately related to stationary waves and, in a sense, the former may even be viewed as the time-varying part of the quasi-stationary waves themselves, Much attention has been focused on nonlinear interactions in the conceptual study on stationary waves. Linear and nonlinear primitive-equation baroclinic spectral models are adopted to investigate the response of stationary waves to large- scale mechanical forcing and steady-state thermal forcing, both idealized and realistic, followed by calculations of the EP fluxes and three-dimensional wave activity fluxes (Plumb, 1985) for both the linear and nonlinear solu- tions. Results show that when the forcing source grows intense enough to be comparable to the real one, non- linear interaction becomes very important, especially for the maintenance of tropical and polar stationary waves. Care should be taken, however, in using the EP flux and Plumb's 3-D flux for diagnostic analysis of observational data as they are highly sensitive to nonlinear interaction.展开更多
We uncover the virtual monopoles underlying the nontrivial phases of the one-dimensional nonlinear excitations of rogue waves by extending the Dirac magnetic monopole theory to a complex plane. We find that the densit...We uncover the virtual monopoles underlying the nontrivial phases of the one-dimensional nonlinear excitations of rogue waves by extending the Dirac magnetic monopole theory to a complex plane. We find that the density zeros of the nonlinear waves on the extended complex plane constitute the virtual monopole fields with a quantized flux of elementary π. We then explain the exotic properties of rogue waves by means of a virtual monopole collision mechanism and find that the maximum amplitude amplification ratio and multiple phase steps of the high-order rogue waves are closely related to the number of their contained monopoles. These results open a new avenue for studying topological properties of nonlinear waves and provide an alternative way to understand their dynamics.展开更多
The initial-boundary value problem of the propagation of nonlinear longitudinal elastic waves in an initially strained rod is considered. The rod is assumed to interact with the surrouding elastic and viscous external...The initial-boundary value problem of the propagation of nonlinear longitudinal elastic waves in an initially strained rod is considered. The rod is assumed to interact with the surrouding elastic and viscous external medium. The long time behavior of solutions are derived and global attractors in E-1 space is obtained.展开更多
文摘The characteristics of nonlinear and supernonlinear Alfvén waves propagating in a multicomponent plasma composed of a double spectral electron distribution and positive and negative ions were investigated.The Sagdeev technique was employed,and an energy equation was derived.Our findings show that the proposed system reveals the existence of a double-layer solution,periodic,supersoliton,and superperiodic waves.The phase portrait and potential analysis related to these waves were investigated to study the main features of existing waves.It was also found that decreasing the electron temperature helps the superperiodic structure to be excited in our plasma model.Our results help interpret the nonlinear and supernonlinear features of the recorded Alfvén waves propagating in the ionosphere D-region.
基金Trans-Century Training program Fund for the Talent,Ministry of Education of China
文摘A composite model, which is the combination of Boussinesq equations and Volume of Fluid (VOF) method, has been developed for 2-D time-domain computations of nonlinear waves in a large region. The whole computational region Omega is divided into two subregions. In the near-field around a structure, Omega(2), the flow is governed by 2-D Reynolds Averaged Navier-Stokes equations with a turbulence closure model of k-epsilon equations and numerically solved by the improved VOF method; whereas in the subregion Omega(1) (Omega(1) = Omega - Omega(2)) the flow is governed by one-D Boussinesq equations and numerically solved with the predictor-corrector algorithm. The velocity and the wave surface elevation are matched on the common boundary of the two subregions. Numerical tests have been conducted for the case of wave propagation and interaction with a wave barrier. It is shown that the composite model can help perform efficient computation of nonlinear waves in a large region with the complicated flow fields near structures taken into account.
基金supported by the National Natural Science Foundation of China (Grant Nos. 41072235 and 50809008)the Hong Kong Research Council (HKU 7171/06E)+1 种基金the Natural Science Foundation of Liaoning Province of China (Grant No. 20102006)the Open Foundation of Hunan Province Key Laboratory of Water & Sediment Science and Water Hazard Prevention (Grant No.2008SS04)
文摘A 3-D time-domain numerical coupled model is developed to obtain an efficient method for nonlinear waves acting on a box-shaped ship fixed in a harbor. The domain is divided into the inner domain and the outer domain. The inner domain is the area beneath the ship and the flow is described by the simplified Euler equations. The remaining area is the outer domain and the flow is defined by the higher-order Boussinesq equations in order to consider the nonlinearity of the wave motions. Along the interface boundaries between the inner domain and the outer domain, the volume flux is assumed to be continuous and the wave pressures are equal. Relevant physical experiment is conducted to validate the present mode/and it is shown that the numerical results agree with the experimental data. Compared the coupled model with the flow in the inner domain governed by the Laplace equation, the present coupled model is more efficient and its solution procedure is simpler, which is particularly useful for the study on the effect of the nonlinear waves acting on a fixed box-shaped ship in a large harbor.
基金Supported by the National Natural Science Foundation of China under Grant No.10675020the National 973 Nonlinear Science Project
文摘Recently, inwardly propagating waves （called antiwaves, AWs） in nonlinear oscillatory systems have attracted much attention. An interesting negative refraction phenomenon has been observed in a bidomain system where one medium supports forwardly propagating waves （normal waves, NWs） and the other AWs. In this paper we find that negative refraction （NR） in nonlinear media has an asymmetric property, i.e., NR can be observed only by applying wave source with proper frequency to one medium, but not the other. Moreover, NR appears always when the incident waves are dense and the refractional waves are sparse. This asymmetry is a particular feature for nonlinear NR, which can neither be observed in linear refraction processes （both positive and negative refractions） nor in nonlinear positive refraction. The mechanism underlying the asymmetry of nonlinear NR are fully understood based on the competition of nonlinear waves.
基金Project supported by the National Natural Science Foundation of China under (Grant Nos 10575082 and 10247008)the Scientific Research Foundation (SRF) for the Returned Overseas Chinese Scholars (ROCF), State Education Ministry (SEM)
文摘This paper investigates the collision between two nonlinear waves with arbitrary angle in two-dimensional nonlinear lattice. By using the extended Poincarge-Lighthill-Kuo perturbation method, it obtains two Korteweg-de Vries equations for nonlinear waves in both the ζ and η directions, respectively, and derives the analytical phase shifts after the collision of two nonlinear waves. Finally, the solution of u（υ） up to O（ε^3） order is given.
基金Project supported by the National Natural Science Foundation of China(Grant No.10875098)the Scientific and Technical Innovation Foundation of Northwest Normal University(Grant No.NWNU-KJCXGC-0348)
文摘This paper investigates the collision between two nonlinear waves with different propagation directions in two- dimensional dust crystals. Using the extended Poincare-Lighthill-Kuo perturbation method, two Korteweg-de Vries equations for nonlinear waves in both the ξ and η directions are obtained, respectively, and the analytical phase shifts and trajectories after the collision of two nonlinear waves are derived. Finally, the effects of parameters of the lattice constant a, the arbitrary constant u0η, the forces f（r）, and the colliding angle θ on the phase shifts of both colliding nonlinear waves are examined.
基金Project supported by the National Natural Science Foundation of China (No. 10472076).
文摘A nonlinear wave equation of elastic rod taking account of finite deformation, transverse inertia and shearing strain is derived by means of the Hamilton principle in this paper. Nonlinear wave equation and truncated nonlinear wave equation are solved by the Jacobi elliptic sine function expansion and the third kind of Jacobi elliptic function expansion method. The exact periodic solutions of these nonlinear equations are obtained, including the shock wave solution and the solitary wave solution. The necessary condition of exact periodic solutions, shock solution and solitary solution existence is discussed.
文摘By using Hamilton-type variation principle in non-conservation system, the nonlinear equation of wave motion of a elastic thin rod was derived according to Lagrange description of finite deformation theory. The dissipation caused due to viscous effect and the dispersion introduced by transverse inertia were taken into consideration so that steady traveling wave solution can be obtained. Using multi-scale method the nonlinear equation is reduced to a KdV-Burgers equation which corresponds with saddle-spiral heteroclinic orbit on phase plane. Its solution is called the oscillating-solitary wave or saddle-spiral shock wave. If viscous effect or transverse inertia is neglected, the equation is degraded to classical KdV or Burgers equation. The former implies a propagating solitary wave with homoclinic on phase plane, the latter means shock wave and heteroclinic orbit.
基金This research was financially supported by China National Key Basic Research Project "Circulation Principal and Mathematic Model" (Grant No. 1999043810) Guangdong Science and Technology Innovation Project: "Disaster Diagnoses of Sea Walls" (99B07102G)
文摘Based on the high order nonlinear and dispersive wave equation with a dissipative term, a numerical model for nonlinear waves is developed, It is suitable to calculate wave propagation in water areas with an arbitrarily varying bottom slope and a relative depth h/L(0)less than or equal to1. By the application of the completely implicit stagger grid and central difference algorithm, discrete governing equations are obtained. Although the central difference algorithm of second-order accuracy both in time and space domains is used to yield the difference equations, the order of truncation error in the difference equation is the same as that of the third-order derivatives of the Boussinesq equation. In this paper, the correction to the first-order derivative is made, and the accuracy of the difference equation is improved. The verifications of accuracy show that the results of the numerical model are in good agreement with those of analytical Solutions and physical models.
基金financially supported by the National Key R&D Program of China(No.2022YFC3104205)the National Natural Science Foundation of China(No.42377457).
文摘The generation and propagation mechanism of strong nonlinear waves in the South China Sea is an essential research area. In this study, the third-generation wave model WAVEWATCH Ⅲ is employed to simulate wave fields under extreme sea states. The model, integrating the ST6 source term, is validated against observed data, demonstrating its credibility. The spatial distribution of the occurrence probability of strong nonlinear waves during typhoons is shown, and the waves in the straits and the northeastern part of the South China Sea show strong nonlinear characteristics. The high-order spectral model HOS-ocean is employed to simulate the random wave surface series beneath five different platform areas. The waves during the typhoon exhibit strong nonlinear characteristics, and freak waves exist. The space-varying probability model is established to describe the short-term probability distribution of nonlinear wave series. The exceedance probability distributions of the wave surface beneath different platform areas are compared and analyzed. The results show that with an increase in the platform area, the probability of a strong nonlinear wave beneath the platform increases.
基金The project supported by National Natural Science Foundation of China under Grant No.10247008the Natural Science Foundation of Northwest Normal University under Grant No.NWNU-KJCXGC-215
文摘In a thin-walled, homogeneous, straight, long, circular, and incompressible fluid filled elastic tube, small but finite long wavelength nonlinear waves can be describe by a KdV (Korteweg de Vries) equation, while the carrier wave modulations are described by a nonlinear Schr?dinger equation (NLSE). However if the elastic tube is slowly inhomogeneous, then it is found, in this paper, that the carrier wave modulations are described by an NLSE-like equation. There are soliton-like solutions for them, but the stability and instability regions for this soliton-like waves will change, depending on what kind of inhomogeneity the tube has.
基金The Interdisciplinary Joint Research Projects of Tongji University,Southern Marine Science and Engineering Guangdong Laboratory(Zhuhai).
文摘Nonlinear internal waves(NLIWs)exhibit robust dynamic submesoscale motions,connecting large-scale tides to smallscale shear instabilities in the ocean.Previous studies have mainly focused on their generation mechanisms and evolution along their paths.Considering their global distribution resulting from the primary origin in tide-topography interaction,there is an increasing cross-disciplinary interest in understanding how these energetic and ubiquitous NLIWs contribute to sediment redistribution in the ocean.This paper presents fundamental theories on NLIWs and comprehensively reviews triggering mechanisms,different types of instability,and sediment responses by summarizing recent theoretical parameterizations,numerical simulations,laboratory experiments,and in-situ observations.We specifically focus on elucidating various types of instability along with their impact on sediment dynamic processes.Finally,we outline several unresolved issues that require further exploration for a quantitative investigation into NLIWinduced sediment transfer in the ocean.
文摘The flows of nonlinear waves overtopping an obstruction are studied numerically in the present paper. The finite difference method is used to solve the full two dimensional Navier Stokes equations, and the VOF method is adopted to deal with free surface deformations. Numerical results of a solitary wave and periodic waves overtopping an rectangular cylinder are obtained respectively. Many complex phenomena, such as water accumulation, wave run up, water jet flows, water jet impact both upon free surface and on a structure, and generation of new waves on the lee side during the process of the waves overtopping an obstacle, can be successfully simulated.
基金supported by the Research Fund for the Doctoral Program of Higher Education of China (Grant No.20060423009)the Key Technological Research and Development Program of Shandong Province (Grant No.2008GGB01099)
文摘The wave crest is an important factor for the design of both fixed and floating marine structures.Wave crest height is a dominant parameter in assessing the likelihood of wave-in-deck impact and resultant severe damage.Many empirical and theoretical distribution functions for wave crest heights have been proposed,but there is a lack of agreement between them.It is of significance to develop a better new nonlinear wave crest height distribution model.The progress in the research of wave crest heights is reviewed in this paper.Based on Stokes' wave theory,an approximate nonlinear wave crest-height distribution formula with simple parameters is derived.Two sets of measured data are presented and compared with various theoretical distributions of wave crests obtained from nonlinear wave models and analysis of the comparison is given in detail.The new crest-height distribution model agrees well with observations.Also,the new theoretical distribution is more accurate than the other methods cited in this paper and has a greater range of applications.
文摘In this paper, the wave velocity c is developed as an asymptotic series for weak nonlinear waves in non-uniform flow. Then Fredholm's alternative theorem is applied and it is verified that the first-order approximation c1 equals zero, This generalizes the previous result.
文摘We briefly review the recent progress in marine hydrodynamics.Developments in wave-structure interaction,wave-current interaction,Rogue waves,sloshing in liquid tanks and their applications in ocean engineering,such as Floating Production Storage and Offloading facility(FPSO) and Very Large Floating Structure(VLFS),are presented.
文摘For robust nonlinear wave simulation in a moving reference frame, we recast the free surface problem in Hamilton-Jacobi form and propose a Weighted Essentially Non-Oscillatory （WENO） scheme to automatically handle the upwinding of the convective term. A new automatic procedure for deriving the linear WENO weights based on a Taylor series expansion is introduced. A simplified smoothness indicator is proposed and is shown to perform well. The scheme is combined with high-order explicit Runge-Kutta time integration and a dissipative Lax-Friedrichs-type flux to solve for nonlinear wave propagation in a moving frame of reference. The WENO scheme is robust and less dissipative than the equivalent order upwind-biased finite difference scheme for all ratios of frame of reference to wave propagation speed tested. This provides the basis for solving general nonlinear wave-structure interaction problems at forward speed.
文摘Low-frequency phenomena in the atmosphere are intimately related to stationary waves and, in a sense, the former may even be viewed as the time-varying part of the quasi-stationary waves themselves, Much attention has been focused on nonlinear interactions in the conceptual study on stationary waves. Linear and nonlinear primitive-equation baroclinic spectral models are adopted to investigate the response of stationary waves to large- scale mechanical forcing and steady-state thermal forcing, both idealized and realistic, followed by calculations of the EP fluxes and three-dimensional wave activity fluxes (Plumb, 1985) for both the linear and nonlinear solu- tions. Results show that when the forcing source grows intense enough to be comparable to the real one, non- linear interaction becomes very important, especially for the maintenance of tropical and polar stationary waves. Care should be taken, however, in using the EP flux and Plumb's 3-D flux for diagnostic analysis of observational data as they are highly sensitive to nonlinear interaction.
基金supported by the National Natural Science Foundation of China (Grant Nos.12375005,12022513,and12235007)the National Safety Academic Fund(Grant No.U2330401)。
文摘We uncover the virtual monopoles underlying the nontrivial phases of the one-dimensional nonlinear excitations of rogue waves by extending the Dirac magnetic monopole theory to a complex plane. We find that the density zeros of the nonlinear waves on the extended complex plane constitute the virtual monopole fields with a quantized flux of elementary π. We then explain the exotic properties of rogue waves by means of a virtual monopole collision mechanism and find that the maximum amplitude amplification ratio and multiple phase steps of the high-order rogue waves are closely related to the number of their contained monopoles. These results open a new avenue for studying topological properties of nonlinear waves and provide an alternative way to understand their dynamics.
基金National Natural Science Foundation of China!(No:19861004)
文摘The initial-boundary value problem of the propagation of nonlinear longitudinal elastic waves in an initially strained rod is considered. The rod is assumed to interact with the surrouding elastic and viscous external medium. The long time behavior of solutions are derived and global attractors in E-1 space is obtained.
