Propagation Of Solitary Waves Research Articles

Study Based on FLUENT of Broken Internal Waves in Different Slope Angles

Internal waves will break in the process of communication, the broken will make water in upper and lower mixing, which has significant influence on the hydrodynamic and layered characteristics of density stratification of the water. In order to reveal the propagation of internal solitary waves, a 3d numerical wave flume was built. The research of the propagation of internal solitary waves in the regular topography and broken on slopes was based on FLUENT. Comparing the fragmentation degree of different slope angle and researching the energy dissipation of the wave propagation process , which are supposed to successfully match the results with the experiment results, can provide new methods and means for the further study of internal wave breaking characteristics and the improvement of ecological environment of water bodies.

The N-soliton solution of extended Korteweg-de Vries equation and SAR image simulation of internal solitary wave propagation

The extended Korteweg-de Vries (eKdV) equation is an important model for the description of internal solitary waves (ISWs) in shallow seas. The N-soliton solution of the eKdV equation is investigated by Hirota bilinear method. Direct simulation of the eKdV equation is performed for several ISWs phenomena including polarity conversion, packets and collisions by virtue of the N-soliton solution. Synthetic aperture radar (SAR) image simulations of those phenomena are also presented. Furthermore, the comparison between the simulated SAR image and the observed SAR image in the South China sea is provided, which shows that the N-soliton solution may describe various ISWs phenomena.

A new approach to model weakly nonhydrostatic shallow water flows in open channels with smoothed particle hydrodynamics

Summary A new approach to model weakly nonhydrostatic shallow water flows in open channels is proposed by using a Lagrangian meshless method, smoothed particle hydrodynamics (SPH). The Lagrangian form of the Boussinesq equations is solved through SPH to merge the local and convective derivatives as the material derivative. In the numerical SPH procedure, the present study uses a predictor–corrector method, in which the pure space derivative terms (the hydrostatic and source terms) are explicitly solved and the mixed space and time derivatives term (the material term of B1 and B2) is computed with an implicit scheme. It is thus a convenient tool in the processes of the space discretization compared to other Eulerian approaches. Four typical benchmark problems in weakly nonhydrostatic shallow water flows, including solitary wave propagation, nonlinear interaction of two solitary waves, dambreak flow propagation, and undular bore development, are selected to employ model validation under the closed and open boundary conditions. Numerical results are compared with the analytical solutions or published laboratory and numerical results. It is found that the proposed approach is capable of resolving weakly nonhydrostatic shallow water flows. Thus, the proposed SPH approach can supplement the lack of the SPH–Boussinesq researches in the literatures, and provide an alternative to model weakly nonhydrostatic shallow water flows in open channels.

Dynamics of periodic mechanical structures containing bistable elastic elements: from elastic to solitary wave propagation.

We investigate the nonlinear dynamics of a periodic chain of bistable elements consisting of masses connected by elastic springs whose constraint arrangement gives rise to a large-deformation snap-through instability. We show that the resulting negative-stiffness effect produces three different regimes of (linear and nonlinear) wave propagation in the periodic medium, depending on the wave amplitude. At small amplitudes, linear elastic waves experience dispersion that is controllable by the geometry and by the level of precompression. At moderate to large amplitudes, solitary waves arise in the weakly and strongly nonlinear regime. For each case, we present closed-form analytical solutions and we confirm our theoretical findings by specific numerical examples. The precompression reveals a class of wave propagation for a partially positive and negative potential. The presented results highlight opportunities in the design of mechanical metamaterials based on negative-stiffness elements, which go beyond current concepts primarily based on linear elastic wave propagation. Our findings shed light on the rich effective dynamics achievable by nonlinear small-scale instabilities in solids and structures.

High-amplitude elastic solitary wave propagation in 1-D granular chains with preconditioned beads: Experiments and theoretical analysis

Elastic solitary waves resulting from Hertzian contact in one-dimensional (1-D) granular chains have demonstrated promising properties for wave tailoring such as amplitude-dependent wave speed and acoustic band gap zones. However, as load increases, plasticity or other material nonlinearities significantly affect the contact behavior between particles and hence alter the elastic solitary wave formation. This restricts the possible exploitation of solitary wave properties to relatively low load levels (up to a few hundred Newtons). In this work, a method, which we term preconditioning, based on contact pre-yielding is implemented to increase the contact force elastic limit of metallic beads in contact and consequently enhance the ability of 1-D granular chains to sustain high-amplitude elastic solitary waves. Theoretical analyses of single particle deformation and of wave propagation in a 1-D chain under different preconditioning levels are presented, while a complementary experimental setup was developed to demonstrate such behavior in practice. The experimental results show that 1-D granular chains with preconditioned beads can sustain high amplitude (up to several kN peak force) solitary waves. The solitary wave speed is affected by both the wave amplitude and the preconditioning level, while the wave spatial wavelength is still close to 5 times the preconditioned bead size. Comparison between the theoretical and experimental results shows that the current theory can capture the effect of preconditioning level on the solitary wave speed.

Small amplitude electron acoustic solitary waves in a magnetized superthermal plasma

The propagation of electron acoustic solitary waves in a magnetized plasma consisting of fluid cold electrons, electron beam and superthermal hot electrons (obeying kappa velocity distribution function) and ion is investigated in a small amplitude limit using reductive perturbation theory. The Korteweg–de-Vries–Zakharov–Kuznetsov (KdV–ZK) equation governing the dynamics of electron acoustic solitary waves is derived. The solution of the KdV–ZK equation predicts the existence of negative potential solitary structures. The new results are: (1) increase of either the beam speed or temperature of beam electrons tends to reduce both the amplitude and width of the electron acoustic solitons, (2) the inclusion of beam speed and temperature pushes the allowed Mach number regime upwards and (3) the soliton width maximizes at certain angle of propagation (αm) and then decreases for α>αm. In addition, increasing the superthermality of the hot electrons also results in reduction of soliton amplitude and width. For auroral plasma parameters observed by Viking, the obliquely propagating electron-acoustic solitary waves have electric field amplitudes in the range (7.8–45)mV/m and pulse widths (0.29–0.44)ms. The Fourier transform of these electron acoustic solitons would result in a broadband frequency spectra with peaks near 2.3–3.5kHz, thus providing a possible explanation of the broadband electrostatic noise observed during the Burst a.

Radiating subdispersive fractional optical solitons.

It was recently found [Fujioka et al., Phys. Lett. A 374, 1126 (2010)] that the propagation of solitary waves can be described by a fractional extension of the nonlinear Schrödinger (NLS) equation which involves a temporal fractional derivative (TFD) of order α > 2. In the present paper, we show that there is also another fractional extension of the NLS equation which contains a TFD with α < 2, and in this case, the new equation describes the propagation of radiating solitons. We show that the emission of the radiation (when α < 2) is explained by resonances at various frequencies between the pulses and the linear modes of the system. It is found that the new fractional NLS equation can be derived from a suitable Lagrangian density, and a fractional Noether's theorem can be applied to it, thus predicting the conservation of the Hamiltonian, momentum and energy.

Numerical study of interfacial solitary waves propagating under an elastic sheet.

Steady solitary and generalized solitary waves of a two-fluid problem where the upper layer is under a flexible elastic sheet are considered as a model for internal waves under an ice-covered ocean. The fluid consists of two layers of constant densities, separated by an interface. The elastic sheet resists bending forces and is mathematically described by a fully nonlinear thin shell model. Fully localized solitary waves are computed via a boundary integral method. Progression along the various branches of solutions shows that barotropic (i.e. surface modes) wave-packet solitary wave branches end with the free surface approaching the interface. On the other hand, the limiting configurations of long baroclinic (i.e. internal) solitary waves are characterized by an infinite broadening in the horizontal direction. Baroclinic wave-packet modes also exist for a large range of amplitudes and generalized solitary waves are computed in a case of a long internal mode in resonance with surface modes. In contrast to the pure gravity case (i.e without an elastic cover), these generalized solitary waves exhibit new Wilton-ripple-like periodic trains in the far field.

Modified Korteweg–de Vries equation in a negative ion rich hot adiabatic dusty plasma with non-thermal ion and trapped electron

In this report, the investigation of the properties of dust acoustic (DA) solitary wave propagation in an adiabatic dusty plasma including the effect of the non-thermal ions and trapped electrons is presented. The reductive perturbation method has been employed to derive the modified Korteweg–de Vries (mK-dV) equation for dust acoustic solitary waves in a homogeneous, unmagnetized, and collisionless plasma whose constituents are electrons, singly charged positive ions, singly charged negative ions, and massive charged dust particles. The stationary analytical solution of the mK-dV equation is numerically analyzed and where the effect of various dusty plasma constituents DA solitary wave propagation is taken into account. It is observed that both the ions in dusty plasma play as a key role for the formation of both rarefactive as well as the compressive DA solitary waves and also the ion concentration controls the transformation of negative to positive potentials of the waves.

Laboratory study of flow field for ISW evolution on a flat bottom

Spatial variation of the velocity field induced by propagation of an interfacial solitary wave (ISW) is one of the most important research themes in marine science. This velocity field together with the vortex within the system can affect marine operations as the ISW propagates in the ocean. The governing equations presently available are modified to model the velocity and vortex, and are used in numerical experiments. This paper presents the results of laboratory experiments and numerical modeling of the velocity field induced by the propagation of an ISW in depression and elevation on a flat bottom. Laboratory observations reveal that the water particle orbits in different water layers have different motion trails due to the effect of the ISW. In addition, the numerical and laboratory experiments show a self-generated vortex above the interface of a depression ISW as it propagates in a stratified two-layer fluid system on a flat bottom. Interestingly, the interface itself may limit the vertical transfer of mass between the upper and bottom layers in a stratified fluid system.

Tracking the internal waves in the South China Sea with environmental satellite sun glint images

The propagation of internal solitary waves (ISWs) in the South China Sea (SCS) was tracked using National Aeronautics and Space Administration (NASA) Moderate Resolution Imaging Spectroradiometer (MODIS) and the Visible Infrared Imaging Radiometer Suite (VIIRS) sun glint image pairs. The acquisition times of the two images comprising the same pair is usually separated by about 2 hours. Four pairs of images in May and August 2013 were analysed. The ISW phase speeds were derived using the horizontal displacement of the ISW patterns and the time difference between the 2 satellite images. The phase speeds were in good agreement with the theoretical calculations using the Sturm–Louisville (S − L) equation with a non-linear term. Monthly ocean stratification data and bathymetry were used in the theoretical calculations. The ISW phase speeds are mainly affected by bottom depth, with seasonal variations. The ISWs propagated faster in August than in May. Our results also show that the ISW propagation in northern SCS can be mapped using environmental satellite sun glint images in short period of time with the advantage of large scale.

Optimal dispersion with minimized Poisson equations for non-hydrostatic free surface flows

A non-hydrostatic shallow-water model is proposed to simulate the wave propagation in situations where the ratio of the wave length to the water depth is small. It exploits the reduced-size stencil in the Poisson pressure solver to make the model less expensive in terms of memory and CPU time. We refer to this new technique as the minimized Poisson equations formulation. In the simplest case when the method applied to a two-layer model, the new model requires the same computational effort as depth-integrated non-hydrostatic models, but can provide a much better description of dispersive waves. To allow an easy implementation of the new method in depth-integrated models, the governing equations are transformed into a depth-integrated system, in which the velocity difference serves as an extra variable. The non-hydrostatic shallow-water model with minimized Poisson equations formulation produces good results in a series of numerical experiments, including a standing wave in a basin, a non-linear wave test, solitary wave propagation in a channel and a wave propagation over a submerged bar.

Numerical studies on the degeneration of internal waves induced by an initial tilted pycnocline

The pycnocline in a closed domain is tilted by external wind forcing and tends to restore to a level position when the wind falls. An internal seiche oscillation exhibits if the forcing is weak, otherwise internal surge and internal solitary waves emerge, which serve as a link to cascade energy to small-scale processes. A two-dimensional non-hydrostatic code with a turbulence closure model is constructed to extend previous laboratory studies. The model could reproduce all the key phenomena observed in the corresponding laboratory experiments. The model results further serve as a comprehensive and reliable data set for an in-depth understanding of the related dynamical process. The comparative analyses indicate that nonlinear term favors the generation of internal surge and subsequent internal solitary waves, and the linear model predicts the general trend reasonably well. The vertical boundary can approximately reflect all the incoming waves, while the slope boundary serves as an area for small-scale internal wave breaking and energy dissipation. The temporal evolutions of domain integrated kinetic and potential energy are also analyzed, and the results indicate that about 20% of the initial available potential energy is lost during the first internal wave breaking process. Some numerical tactics such as grid topology and model initialization are also briefly discussed.

Few-cycle optical solitary waves in cascaded-quadratic–cubic–quintic nonlinear media

We study the propagation of few-cycle optical solitary waves in a nonlinear media under the combined action of quadratic, cubic and quintic nonlinearities in a large phase-mismatched second harmonic (SHG) process. Exact bright and dark soliton solutions to the nonlinear evolution equation for cascaded quadratic media beyond the slowly varying envelope approximations is reported. The analytical solutions obtained are verified through numerical simulations.

Solitary waves on a ferrofluid jet

AbstractThe propagation of axisymmetric solitary waves on the surface of an otherwise cylindrical ferrofluid jet subjected to a magnetic field is investigated. An azimuthal magnetic field is generated by an electric current flowing along a stationary metal rod which is mounted along the axis of the moving jet. A numerical method is used to compute fully nonlinear travelling solitary waves, and the predictions of elevation waves and depression waves made by Rannacher and Engel (New J. Phys., vol. 8, 2006, pp. 108–123) using a weakly nonlinear theory are confirmed in the appropriate ranges of the magnetic Bond number. New nonlinear branches of solitary wave solutions are identified. As the Bond number is varied, the solitary wave profiles may approach a limiting configuration with a trapped toroidal-shaped bubble, or they may approach a static wave (i.e. one with zero phase speed). For a sufficiently large axial rod, the limiting profile may exhibit a cusp.

On mathematical modelling of solitary pulses in cylindrical biomembranes.

The propagation of action potentials in nerve fibres is usually described by models based on the ionic hypotheses. However, this hypothesis does not provide explanation of other experimentally verified phenomena like the swelling of fibres and heat production during the nerve pulse propagation. Heimburg and Jackson (Proc Natl Acad Sci USA 102(28):9790-9795,2005, Biophys Rev Lett 2:57-78,2007) have proposed a model describing the swelling of fibres like a mechanical wave related to changes of longitudinal compressibility of the cylindrical membrane. In this paper, the possible dispersive effects in such microstructured cylinders are analysed from the viewpoint of solid mechanics, particularly using the information from the analysis of the well-known rod models. A more general governing equation is proposed which satisfies the conditions imposed by the physics of wave processes. The numerical simulations demonstrate the influence of nonlinearities, the role of various dispersion terms and the formation and propagation of solitary waves along the wall together with the corresponding transverse displacement. It is conjectured that due to the coupling effects between longitudinal and transverse displacements of a cylinder, the transverse displacement (i.e. swelling) is related to the derivative of the longitudinal displacement. In this way, the correspondence between theoretical and experimental (Tasaki in Physiol Chem Phys Med NMR 20:251-268,1988) results can be described.

Kinetic ion-acoustic solitary waves in collisional plasmas

The excitation and the propagation of solitary waves of ion-acoustic nature are analyzed by means of kinetic Eulerian simulations, in both collision-free and collisional plasmas, composed of kinetic warm protons and linear Boltzmannian electrons. The process of soliton formation is discussed in detail through the description of the time evolution of the electrostatic potential and of the associated phase space portraits of the proton distribution function. We study the effects of collisions on the propagation of solitary waves, by modeling proton-proton interactions through the one-dimensional nonlinear Dougherty operator, which is a collisional operator of the Fokker-Planck type. We show how, in a case of non-negligible collisionality, short spatial scales in the electrostatic potential are dissipated in time and the phase space structures, observed in the distribution function in absence of collisions, are significantly smoothed out. Finally, by exploiting the analogy between ion-acoustic waves in neutral infinite plasma and Trivelpiece-Gould waves in nonneutral plasmas columns, a recipe to observe solitary structures in nonneutral plasma devices is proposed.

Simulation of solitary waves in a monodisperse granular chain using COMSOL multiphysics: localized plastic deformation as a dissipation mechanism

Solitary wave propagation in a monodisperse granular chain was simulated using the finite element method. The model was built to address a discrepancy between numerical and experimental results from Lazaridi and Nesterenko (J Appl Mech Tech Phys 26(3):405–408 1985). In their work, solitary waves were generated in a chain of particles through impact of a piston, and results were quantified by comparing the chains’ reactions to a rigid wall. Their numerical calculations resulted in a solitary wave with a force amplitude of 83 N, while it was measured experimentally to be 71 N. In the present work, the configuration of the granular chain and piston was duplicated from Lazaridi and Nesterenko (J Appl Mech Tech Phys 26(3):405–408, 1985). Qualitatively similar solitary waves were produced, and von Mises stress values indicated that localized plastic deformation is possible, even at low piston impact velocities. These results show that localized plastic deformation was a likely source of dissipation in experiments performed by Lazaridi and Nesterenko.

Exact cascading nonlinearity in quasi-phase-matched quadratic media.

The evolution of light pulses and beams in a quasi-phase-matched (QPM) quadratic medium is usually described by considering only the spatial harmonic of the QPM grating that minimizes the residual phase-mismatch. I show that, for strongly phase-mismatched interactions (the cascading regime), several harmonics need to be accounted for in order to obtain the correct value of the effective cubic nonlinearity, for which I find a simple analytical expression. I discuss the effects of the higher order harmonics of the grating on solitary wave propagation.

Comment on ‘Propagation of solitary waves and shock wavelength in the pair plasma (J. Plasma Phys. 78, 525–529, 2012)’

In a recent paper ‘Propagation of solitary waves and shock wavelength in the pair plasma (J. Plasma Phys. 78, 525–529, 2012)’, Malekolkalami and Mohammadi investigate nonlinear electrostatic solitary waves in a plasma comprising adiabatic electrons and positrons, and a stationary ion background. The paper contains two parts: First, the solitary wave properties are discussed through a pseudopotential approach, and then the influence of a small dissipation is intuitively sketched without theoretical underpinning. Small dissipation is claimed to lead to a shock wave whose wavelength is determined by linear oscillator analysis. Unfortunately, there are errors and inconsistencies in both the parts, and their combination is incoherent.