Propagation Of Solitary Waves Research Articles

Laboratory and numerical study of intense envelope solitons of water waves: Generation, reflection from a wall, and collisions

The investigation of dynamics of intense solitary wave groups of collinear surface waves is performed by means of numerical simulations of the Euler equations and laboratory experiments. The processes of solitary wave generation, reflection from a wall, and collisions are considered. Steep solitary wave groups with characteristic steepness up to kAcr ≈ 0.3 (where k is the dominant wavenumber and Acr is the crest amplitude) are concerned. They approximately restore the structure after the interactions. In the course of the interaction with the wall and collisions, the maximum amplitude of the wave crests is shown to enhance up to 2.5 times. A standing-wave-like structure occurs in the vicinity of the wall, with certain locations of nodes and antinodes regardless the particular phase of the reflecting wave group. A strong asymmetry of the maximal wave groups due to an anomalous setup is shown in situations of collisions of solitons with different frequencies of the carrier. In some situations of head-on collisions, the amplitude of the highest wave is larger than in overtaking collisions of the same solitons. The discovered effects in interactions of intense wave groups are important in the context of mechanisms and manifestations of oceanic rogue waves.

Propagation of localized waves in magnetized cold hadronic gas

Propagation of solitary waves and their stability conditions in a cold dense hadron gas as a non-relativistic fluid is investigated based on the ‘reductive perturbation method’, at the presence of sufficiently strong external magnetic field. We have shown that the magnetic field stabilizes breaking and shock waves into livelong solitonic profiles with small amplitudes which are governed by the Zakharov–Kuznetsov (ZK) equation. Our results show that the phase speed and amplitude of solitary waves corresponding to each kind of medium components are different. The effects of medium characters on the evolution of solitary profiles are investigated too.

Modeling Free-surface Solitary Waves with Smoothed Particle Hydrodynamics

A three-dimensional weakly compressible Smoothed ParticleHydrodynamics (SPH) solver is presented and applied tosimulate free-surface solitary waves generated in a quasi twodimensionaldam-break experiment. Test cases are constructedbased on the measurement layouts of a dam-break experiment.The simulated wave propagation speeds are compared to theexact solutions of the Korteweg-de Vries (KdV) equation as afirst order theory, and to a second order iterative approximationinvestigated in the literature. Free surface shapes of differentsimulation cases are investigated as well. The results show goodagreement with the free surface shapes of the KdV equation aswell as with the second order approximation of solitary wavepropagation speeds.

Depth-Averaged Non-Hydrostatic Hydrodynamic Model Using a New Multithreading Parallel Computing Method

Compared to the hydrostatic hydrodynamic model, the non-hydrostatic hydrodynamic model can accurately simulate flows that feature vertical accelerations. The model’s low computational efficiency severely restricts its wider application. This paper proposes a non-hydrostatic hydrodynamic model based on a multithreading parallel computing method. The horizontal momentum equation is obtained by integrating the Navier–Stokes equations from the bottom to the free surface. The vertical momentum equation is approximated by the Keller-box scheme. A two-step method is used to solve the model equations. A parallel strategy based on block decomposition computation is utilized. The original computational domain is subdivided into two subdomains that are physically connected via a virtual boundary technique. Two sub-threads are created and tasked with the computation of the two subdomains. The producer–consumer model and the thread lock technique are used to achieve synchronous communication between sub-threads. The validity of the model was verified by solitary wave propagation experiments over a flat bottom and slope, followed by two sinusoidal wave propagation experiments over submerged breakwater. The parallel computing method proposed here was found to effectively enhance computational efficiency and save 20%–40% computation time compared to serial computing. The parallel acceleration rate and acceleration efficiency are approximately 1.45% and 72%, respectively. The parallel computing method makes a contribution to the popularization of non-hydrostatic models.

Propagation of dust acoustic solitary waves in inhomogeneous plasma with dust charge fluctuations

Propagations of dust acoustic solitary waves are theoretically investigated in a collisionless, unmagnetized weakly inhomogeneous plasma. The plasma that is considered here consists of negatively charged dust grains and Boltzmann distributed electrons and ions in the presence of dust charge fluctuations. The fluid equations that we use for description of such plasmas are reduced to a modified Korteweg–de-Vries equation by employing a reductive perturbation method. In this investigation, we have used space–time stretched coordinates appropriate for the inhomogeneous plasmas. From the numerical results, we have observed a significant influence of inhomogeneity parameters on the propagation of dust acoustic solitary waves.

Abundant general solitary wave solutions to the family of KdV type equations

This work explores the construction of more general exact traveling wave solutions of some nonlinear evolution equations (NLEEs) through the application of the (G′/G, 1/G)-expansion method. This method is allied to the widely used (G′/G)-method initiated by Wang et al. and can be considered as an extension of the (G′/G)-expansion method. For effectiveness, the method is applied to the family of KdV type equations. Abundant general form solitary wave solutions as well as periodic solutions are successfully obtained through this method. Moreover, in the obtained wider set of solutions, if we set special values of the parameters, some previously known solutions are revived. The approach of this method is simple and elegantly standard. Having been computerized it is also powerful, reliable and effective.

Local bifurcation of electrohydrodynamic waves on a conducting fluid

We are concerned with progressive waves propagating on a two-dimensional conducting fluid when a uniform electric field is applied in the direction perpendicular to the undisturbed free surface. The competing effects of gravity, surface tension, and electrically induced forces are investigated using both analytical and numerical techniques for an inviscid and incompressible fluid flowing irrotationally. We simplify the full Euler equations by expanding and truncating the Dirichlet-Neumann operators in the Hamiltonian formulation of the problem. The numerical results show that when the electric parameter is in a certain range, the bifurcation structure near the minimum of the phase speed is rich with Stokes, solitary, generalized solitary, and dark solitary waves. In addition to symmetric solutions, asymmetric solitary waves featuring a multi-packet structure are found to occur along a branch of asymmetric generalized solitary waves that itself bifurcates from Stokes waves of finite amplitude. The detailed bifurcation diagrams, together with typical wave profiles, are presented.

Dark spatial solitary waves in a cubic-quintic-septimal nonlinear medium

We consider the evolution of light beams in nonlinear media exhibiting nonlinearities up to the seventh order wherein the beam propagation is governed by the cubic-quintic-septimal nonlinear Schr\odinger equation. An exact analytic solution that describes dark solitary wave propagation is obtained, based on a special ansatz. Unlike the well-known $\text{tanh}$-profile dark soliton in Kerr media, the present one has a functional form given in terms of ``${\text{sech}}^{2/3}$''. The requirements concerning the optical material parameters for the existence of this localized structure are discussed. This propagating solitary wave exists due to a balance among diffraction, cubic, quintic, and septimal nonlinearities. We also investigate its stability under initial pertubations by employing numerical simulations. The modulational stability of the continuous-wave background, which supports the dark soliton, is also studied analytically. Collisions between stable dark solitons are finally investigated.

Solitary wave solutions of three special types of Boussinesq equations

In this paper, the \((G'/G)\)-expansion method is employed to construct more general solitary wave solutions of three special types of Boussinesq equation, namely Boussinesq equation, improved Boussinesq equation and variant Boussinesq equation, where the French scientist Joseph Valentin Boussinesq (1842–1929) described in the 1870s model equations for the propagation of long waves on the surface of water with a small amplitude. Our work is motivated by the fact that the \((G'/G)\)-expansion method provides not only more general forms of solutions but also periodic, solitary waves and rational solutions. The method appears to be easier and faster by means of a symbolic computation.

A numerical study of rotation effect on the propagation of nonlinear internal solitary waves in the northern South China Sea

In the paper, the rotation effect on the propagation of internal solitary waves (ISWs) in the northern South China Sea (SCS) is studied by applying non-dimensional analysis and a modified two-dimensional regularized long wave equation model. First, the contribution of each term in the model equation with rotation effect is estimated. It is shown that, the rotation effect is important once the scale of the propagating ISWs is larger than 100 km. Then, the model equation is differentiated and set up for the numerical simulation of ISWs in the northern SCS. Several numerical experiments are designed, and it is found that, the rotation effect mainly affects the symmetry of the ISW crestline, the amplitudes of the leading ISW and the north/south-ward extension crestline. With the rotation effect, the ISW crestline is not symmetrical, and the ISW amplitude decreases faster. For an incident depression internal soliton with an amplitude larger than 60 m, after the leading ISW propagates a distance of 330 km, the length of ISW crestline gets larger than 150 km, the contribution of rotation effect on the variation of leading ISW amplitude can reach more than 8%; the rotation effect and the bottom topographic effect on the variation of ISW amplitudes are opposite. The contribution of rotation effect on the variation of leading ISW amplitude decreases with an increase in amplitude of incident soliton, but it increases with the extension distance from the center of ISW crestline for the northern/southern crestlines of propagating ISWs.

Generation of internal solitary waves over a large sill: From Knight Inlet to Luzon Strait

A fully nonlinear, nonhydrostatic numerical model is utilized to investigate the generation of Internal Solitary Waves (ISWs) upstream of the Knight Inlet sill. While an upstream hydraulic jump initiates the ISW generation and both hydraulic jump and upstream influence contribute to the generation, it is found that upstream influence is dominant and the hydraulic jump is not necessary for the ultimate generation of ISWs. Decreasing the tidal forcing or upstream sill width may render the flow subcritical (i.e., the hydraulic jump disappears) and ISWs can be generated by nonlinear steepening of long wave disturbances induced by upstream influence. Increasing the tidal forcing or upstream sill width may generate a hydraulic jump blocking strong upstream propagating disturbances. The jump subsequently becomes a turbulent bore and later disperses into a train of ISWs as the tide relaxes. Further increase in the tidal forcing may sweep the turbulent bore downstream and a train of ISWs is emitted upstream toward the end of waning tide. By reducing the stratification strength by 1 order of magnitude, the near-sill flow is in the transcritical regime and ISWs are resonantly generated over the lee side slope. Connections to the internal tide release mechanism at Luzon Strait and to the unsteady lee wave model are also discussed. The present work provides some more insights into the ISW generation process at Knight Inlet and the connection between the generation mechanism at Knight Inlet and that at Luzon Strait is identified.

Oblique propagation of solitary electrostatic waves in magnetized plasmas with cold ions and nonthermal electrons

Oblique propagation of large amplitude electrostatic waves and solitary structures is investigated in magnetized plasmas, comprising cold fluid ions and Cairns nonthermally distributed electrons, by using a Sagdeev pseudopotential formalism. To perform the analysis, quasineutrality is assumed, so that in normalized variables the electrostatic potential and the occurrence of solitary structures are governed by three parameters: the Mach number M, the typical Cairns parameter β, and the angle ϑ between the directions of propagation and the static magnetic field. Below a critical β, only positive compressive solitons are possible, and their amplitudes increase with increasing β, M, and ϑ. Above the critical β, there is coexistence between negative rarefactive and positive compressive solitons, and the range of negative solitons, at increasing M, ends upon encountering a double layer or a singularity. The double layer amplitudes (in absolute value) increase with β but are independent of ϑ. Roots of the Sagdeev pseudopotential beyond the double layer are not accessible from the undisturbed conditions, because of an intervening singularity where the pseudopotential becomes infinite. Recent claims of finding supersolitons beyond a double layer appear to be based on a misinterpretation of the nature of the singularity.

Solitary waves in dimer binary collision model

Solitary wave propagation in nonlinear diatomic (dimer) chains is a very interesting topic of research in the study of nonlinear lattices. Such waves were recently found to be supported by the essentially nonlinear granular lattice and Toda lattice. An interesting aspect of this discovery is attributed to the realization of a spectrum of the mass ratio (the only system parameter governing the dynamics) that supports the propagation of such waves corresponding to the considered interaction potential. The objective of this exposition is to explore solitary wave propagation in the dimer binary collision (BC) model. Interestingly, the dimer BC model supports solitary wave propagation at a discrete spectrum of mass ratios similar to those observed in granular and Toda dimers. Further, we report a qualitative and one-to-one correspondence between the spectrum of the mass ratio corresponding to the dimer BC model and those corresponding to granular and Toda dimer chains.

Polarization domain walls in optical fibres as topological bits for data transmission.

Domain walls are topological defects which occur at symmetry-breaking phase transitions. While domain walls have been intensively studied in ferromagnetic materials, where they nucleate at the boundary of neighbouring regions of oppositely aligned magnetic dipoles, their equivalent in optics have not been fully explored so far. Here, we experimentally demonstrate the existence of a universal class of polarization domain walls in the form of localized polarization knots in conventional optical fibres. We exploit their binding properties for optical data transmission beyond the Kerr limits of normally dispersive fibres. In particular, we demonstrate how trapping energy in well-defined train of polarization domain walls allows undistorted propagation of polarization knots at a rate of 28 GHz along a 10 km length of normally dispersive optical fibre. These results constitute the first experimental observation of kink-antikink solitary wave propagation in nonlinear fibre optics.

Stability Analysis of the Jacobian Elliptic Solutions for the Twisted Peyrard-Bishop-Dauxois Model with Solvent Interaction

We consider a twisted Peyrard-Bishop-Dauxois (PBD) model and construct the exact analytical solutions, which can describe the propagation of solitary waves by invoking a discrete Jacobian elliptic function method. These solutions include the Jacobian periodic solution as well as bubble solitons. Through the Fourier series approach, we have found that the DNA dynamics is governed by a modified discrete nonlinear Schrodinger (MDNLS) equation. A detailed analysis of the role of the twisted angle in the process of bio energy localization is presented in the form of coherent localized breather modes in a PBD model. A linear stability analysis is performed and we obtain that the stability of the solutions also depends on the twisted angle.

Incompressible SPH simulation of solitary wave interaction with movable seawalls

In this paper, we applied an incompressible Smoothed Particle Hydrodynamics (SPH) method to investigate the impact of solitary waves on seawalls, especially movable seawalls. The SPH method is a mesh-free numerical approach particularly suitable for dealing with large free surface deformations and complex fluid-structure interactions. The incompressible SPH (ISPH) method solves the pressure field using the pressure Poisson equation (PPE), rather than relying on the equation of state. It has the advantage of producing more stable and accurate pressure fields and impact forces on structures. We first applied the model to simulate the solitary wave propagation and runup against a fixed vertical wall. The computations compared well with previous experimental and numerical results. Then, the solitary wave impact on a movable structure was investigated by replacing the fixed wall with a spring-controlled seawall subject to different spring stiffness and mass settings. Particular attention was paid to the prediction of the seawall movement, wave runup height and hydrodynamic loading. The incident wave height was found to be the dominant factor for the movable seawall movement during and immediately after the wave crest arrival at the seawall. Other factors, such as the seawall mass and spring stiffness, become important to the seawall's responses only after the maximum impact.

Numerical simulation for the solitary wave of Zakharov–Kuznetsov equation based on lattice Boltzmann method

The Zakharov–Kuznetsov equation is considered, which is an equation describing two dimensional weakly nonlinear ion-acoustic waves in plasma. We focus on using the lattice Boltzmann method to study the Zakharov–Kuznetsov equation. A lattice Boltzmann model is constructed. In numerical experiments, the propagation of the single solitary wave and the collision of double solitary waves are simulated. The results with different parameters are investigated and compared.

Generation of internal solitary waves by frontally forced intrusions in geophysical flows.

Internal solitary waves are hump-shaped, large-amplitude waves that are physically analogous to surface waves except that they propagate within the fluid, along density steps that typically characterize the layered vertical structure of lakes, oceans and the atmosphere. As do surface waves, internal solitary waves may overturn and break, and the process is thought to provide a globally significant source of turbulent mixing and energy dissipation. Although commonly observed in geophysical fluids, the origins of internal solitary waves remain unclear. Here we report a rarely observed natural case of the birth of internal solitary waves from a frontally forced interfacial gravity current intruding into a two-layer and vertically sheared background environment. The results of the analysis carried out suggest that fronts may represent additional and unexpected sources of internal solitary waves in regions of lakes, oceans and atmospheres that are dynamically similar to the situation examined here in the Saguenay Fjord, Canada.

Transcritical Flow and Generation of Internal Solitary Waves off the Amazon River: Synthetic Aperture Radar Observations and Interpretation

Transcritical Flow and Generation of Internal Solitary Waves off the Amazon River: Synthetic Aperture Radar Observations and Interpretation

On the generation and evolution of internal solitary waves in the southern Red Sea

Satellite observations recently revealed trains of internal solitary waves (ISWs) in the off-shelf region between 16.0°N and 16.5°N in the southern Red Sea. The generation mechanism of these waves is not entirely clear, though, as the observed generation sites are far away (50 km) from the shelf break and tidal currents are considered relatively weak in the Red Sea. Upon closer examination of the tide properties in the Red Sea and the unique geometry of the basin, it is argued that the steep bathymetry and a relatively strong tidal current in the southern Red Sea provide favorable conditions for the generation of ISWs. To test this hypothesis and further explore the evolution of ISWs in the basin, 2D numerical simulations with the non-hydrostatic MIT general circulation model (MITgcm) were conducted. The results are consistent with the satellite observations in regard to the generation sites, peak amplitudes and the speeds of first-mode ISWs. Moreover, our simulations suggest that the generation process of ISWs in the southern Red Sea is similar to the tide-topography interaction mechanism seen in the South China Sea. Specifically, instead of ISWs arising in the immediate vicinity of the shelf break via a hydraulic lee wave mechanism, a broad, energetic internal tide is first generated, which subsequently travels away from the shelf break and eventually breaks down into ISWs. Sensitivity runs suggest that ISW generation may also be possible under summer stratification conditions, characterized by an intermediate water intrusion from the strait of Bab el Mandeb. This article is protected by copyright. All rights reserved.