Propagation Of Solitary Waves Research Articles

Evolution of ion-acoustic soliton waves in Venus’s ionosphere permeated by the solar wind

Abstract Wave observations are as yet an important technique to resolve fine structures in the plasma that cannot be identified by different instruments. In this way, we proposed the generation of electrostatic solitary waves during the interaction between the solar wind particles and Venus’s atmosphere at high altitude. The plasma system is treated as a multicomponent unmagnetized plasma consists of background electrons, positive ions (H+ and O+), and streaming solar wind electrons and protons. The dispersion relation is derived for linear waves and the stability/instability of electrostatic wavepackets is investigated. The dependence of the instability growth rate on the ion beam speed has been analyzed. Stability analysis reveals the occurrence of an imaginary frequency part in three regions. Using the reductive perturbation theory, the set of fluid equations is reduced to the Korteweg-de Vries (KdV) equation to describe the evolution of small but finite amplitude soliton waves. The model predicts the propagation of electrostatic soliton waves with an electric field of 1.2 mV/m and a time duration of 0.4 ms. The output of the fast Fourier transform of the electric field pulse is a broadband in the frequency range of ~ 3.2 to 199.5 kHz. It is proposed that the model can be a decent possibility for clarifying the observation of a wide variety of plasma oscillations by Galileo flyby of Venus.

A generalized integrable lattice hierarchy associated with the Toda and modified Toda lattice equations: Hamiltonian representation, soliton solutions

In this paper, we give an integrable four-field lattice hierarchy associated to a new discrete spectral problem. We obtain our hierarchy as the compatibility condition of this spectral problem and an associated equation, constructed herein, for the time-evolution of eigenfunctions. The Hamiltonian representation of the four-field lattice hierarchy are constructed by using the trace identity. We consider reductions of our hierarchy, and find that our hierarchy includes many well-known integrable hierarchies as special cases, including the Toda lattice hierarchy, the modified Toda lattice hierarchy, and some new integrable three-field lattice hierarchies. In addition, the modified Toda lattice equation is studied, the figures of one-, two-soliton and periodic solutions with properly parameters are shown graphically to illustrate the propagation of solitary waves, and we find that the waves pass through without change of shapes, amplitudes, wavelengths and directions, etc. The elastic and inelastic interactions among the two-soliton for the modified Toda lattice equation are also discussed. Furthermore, we generate the relationships between the structures of exact solutions and parameters, and present soliton solutions with free parameters. The results in this paper might be helpful for interpreting certain physical phenomena.

On the approximate solutions of a damped nonplanar modified Korteweg–de Vries equation for studying dissipative cylindrical and spherical solitons in plasmas

In this work, the effect of both nonplanar (cylindrical and spherical) geometry and the dust-neutral collision on the propagation of dissipative nonplanar electrostatic dust-acoustic solitary waves (DASWs) in a strongly coupled complex plasma (SCCP) is examined. The electrons and ions are assumed to follow a Maxwellian and non-Maxwellian trapped velocity distributions, respectively. The fluid governing equations of the plasma species are reduced to an evolution equation using the reductive perturbation technique (RPT). For describing the dynamical mechanism of the dissipative nonplanar DASWs, the evolution equation (the damped nonplanar Shamel Korteweg–de Vries (SKdV)) is solved numerically using both homotopy perturbation method (HPM) and the improved multistage homotopy perturbation method (MsHPM). The numerical solutions of the integrable planar Shamel-KdV (SKdV) equation using both HPM and MsHPM is compared with the exact solution of the SKdV. Also, the comparison between the numerical solutions of the damped nonplanar SKdV using both HPM and MsHPM is discussed. Moreover, the maximum global residual error for both HPM and MsHPM is estimated for measuring the accuracy of the obtained numerical solutions. Furthermore, the dependence of dissipative nonplanar solitons characteristics on various plasma parameters are investigated.

Analysis of vortex formation and energy dissipation during interaction of solitary-like waves with submerged breakwaters based on particle image velocimetry

This study evaluates the slight variation in flow fields and the process, location, variation, and diffusion of eddies during propagation of solitary waves over various types of submerged breakwaters using particle image velocimetry, additional measurements, and theoretical formulations. We conducted various hydraulic model tests to investigate the occurrence of eddies, relative positions of structures, and related phenomena of range expansion of vortices. In addition, we observed and analyzed the differences in flow fields of solitary waves passing through sets of undulating submerged breakwaters. We also analyzed wave reflection, transmission, attenuation, and the variation in vortex energy induced by the solitary wave–breakwater interactions.

Vortex generation due to internal solitary wave propagation past a sidewall constriction

Abstract

High-fidelity numerical simulation of solitary wave propagation

As a classic problem in oceanographic and coastal engineering hydrodynamics, solitary wave propagation is used to benchmark a novel high-fidelity numerical model based on the Navier–Stokes equations. The model combines the Finite Volume method based on Merged Stencil with 3rd-order reconstruction (FVMS3) and Tangent of Hyperbola for INterface Capturing method with Quadratic surface representation and Gaussian Quadrature (THINC/QQ) schemes. Accurate predictions are made of inviscid and viscous solitary waves propagating on plane and sloping beaches. Model performance is assessed by comparing the predictions with analytical solutions, alternative numerical results obtained using interFoam solver in OpenFOAM and commercial flow software ANSYS Fluent, as well as experimental data. It is demonstrated that the present model significantly reduces undesirable numerical effects, including energy loss, wave decay, phase shift, and overestimation of the velocity profile of propagating waves even after long duration computations, by suppressing numerical dissipation and dispersion.

Bäcklund transformation, infinite number of conservation laws and fission properties of an integro-differential model for ocean internal solitary waves

This paper presents an analytical investigation of the propagation of internal solitary waves in the ocean of finite depth. Using the multi-scale analysis and reduced perturbation methods, the integro-differential equation is derived, which is called the intermediate long wave (ILW) equation and can describe the amplitude of internal solitary waves. It can reduce to the Benjamin–Ono equation in the deep-water limit, and to the KdV equation in the shallow-water limit. Little attention has been paid to the features of integro-differential equations, especially for their conservation laws. Here, based on Hirota bilinear method, Bäcklund transformations in bilinear form of ILW equation are derived and infinite number of conservation laws are given. Finally, we analyze the fission phenomenon of internal solitary waves theoretically and verify it through numerical simulation. All of these have potential value for the further research on ocean internal solitary waves.

Generating Water Waves on Steady Currents Using Mass Source Wave Maker Coupled with Analytical Relaxation Wave Absorber

In order to numerically simulate the wave-current interaction problems frequently encountered by aquaculture structures, a two-dimensional numerical wave-current tank model was established here based on a mass source wave maker coupled with an analytical relaxation wave absorber. The wave-maker model and the wave-absorber model were embedded into a two-dimensional RANS solver, which was closed with RSM turbulence scheme. The volume of fluid (VOF) method was adapted to accurately capture the free surface between water and air. To generate a steady uniform current flow, the uniform current flow velocity was calculated at the left-hand-side (LHS) and right-had-side (RHS) outflow boundaries, respectively. Once the steady uniform current flow was generated over the whole computational domain, the target water wave was marked within a specified region by embedding the mass source function based on wave theory into the mass conservation equation and then propagated on the generated uniform current flow. To verify the accuracy of the numerical wave-current tank established here, some of the obtained numerical results were then compared with the experimental results and the analytical solutions, and they agreed well with each other, indicating that the model developed here has great ability in simulating water waves on uniform currents over constant water depth. The established numerical wave-current tank was then used to study the optimal layout of the mass source region and the effects of water current velocity on water surface wave parameters during regular wave coupling with uniform water currents. Meanwhile, the established model was extended to generate steep wave and apply in deep water conditions. Finally, the proposed methods were applied to investigate the wave-current-structure interaction problems and the propagation of solitary waves traveling with coplanar/counter currents. Model-data comparisons show that the developed model here is potentially useful and efficient for investigating the inevitable wave-current-structure interaction problems in aquaculture technologies.

Large amplitude slow ion-acoustic solitons, supersolitons, and double layers in a warm negative ion plasma with superthermal electrons

The pseudopotential approach is used to investigate the ion thermal and electron superthermal effects on the slow mode solitary wave propagation characteristics in a negative ion plasma, comprising warm positive and negative ions and kappa-distributed electrons. The Sagdeev pseudopotential for the plasma model is derived and analyzed in a systematic way. While it is well known that a negative ion plasma supports the propagation of the fast mode normal solitons, it is found that it supports, in addition to the slow mode normal solitons, the propagation of the slow mode supersolitons and double layers for high values of the negative ion density. The double layers occur as the lower limit to the supersoliton existence range and as the limiting factor for the propagation of normal solitons. When the relative temperature of the two ion species decreases, it is found that the Mach number range supporting the propagation of the nonlinear structures reduces, while the amplitudes of solitons and supersolitons decrease, and these effects are enhanced by the superthermal behavior of the electrons. The amplitudes of the double layers increase with a decrease in the relative temperature of the two ion species but decrease with an increase in the electron superthermality.

Solitary Wave Diffraction with a Single and Two Vertical Circular Cylinders

This study investigates the three-dimensional (3-D) solitary wave interaction with two cylinders in tandem and side-by-side arrangements for two wave heights. The solitary wave generation and propagation are predicted using the volume of fluid method (VOF) coupled with the NavierStokes transport equations. The PHOENICS code is used to solve these transport equations. The solitary wave generation based on the source line developed by Hafsia et al. (2009) is extended in three-dimensional wave flow and is firstly validated for solitary waves propagating on a flat bottom. The comparison between numerical results and analytical solution for small wave height H / h = 0.1 and 0.2 shows good agreements. The wave crest and the pseudo-wavelength are well reproduced. Excellent agreements were found in terms of maximum run-up and wave forces by comparison with the present model and analytical studies. The present model can be tested for the extreme solitary wave to extend its application to a more realistic case study as the solitary wave diffraction with an offshore oil platform.

Research on the modal intensity fluctuation during the dynamic propagation of internal solitary waves in the shallow water

内孤立波是一种常见于浅海海域的非线性内波, 具有振幅大、周期短和流速强等特点, 它通过扰动水体中的温盐分布使声速剖面产生明显的距离依赖性, 进而影响水下声传播特性. 内波自生成后通常以 O(1) m/s 量级的速度传播, 运动的内波使声传播路径上声波模态能量在空间和时间上剧烈起伏. 本文定义模态强度为模态系数模值(模态幅度)的平方, 并用其衡量各阶模态所含声能量的大小. 文中基于耦合简正波理论, 推导了内波运动时声波模态强度起伏的表达式, 将模态强度表征为振荡项和趋势项的线性叠加. 以往的工作大多局限于单独从时域或频域研究内波运动时声波模态强度的时变规律, 本文则结合短时傅里叶变换在时频平面上揭示了模态强度的起伏机理. 理论推导和数值仿真均表明内孤立波使各阶声波模态之间发生能量交换, 即模态耦合. 内波的动态传播进一步引起模态干涉, 这种干涉效应表现为模态强度中的振荡项并使模态强度随时间快速起伏. 受模态剥离效应(不同阶模态之间衰减系数的差异)的影响, 趋势项的幅度随时间不断变化, 进而对模态干涉引起的振荡叠加了时变的偏置. 模态强度的整体走势和振荡项中各频率分量振幅的时变特征均与模态衰减密切相关. 同时, 本文使用深度积分声强作为总接收声场强度的度量, 研究了内波运动时模态强度起伏对接收阵位置处声能量的影响. 结果表明, 能量较大且起伏剧烈的模态强度将主导总接收声强的变化.

Solitary waves in a two-dimensional graphene-based superlattice

The article is about the features of the propagation of solitary electromagnetic waves in the two-dimensional graphene superlattice both in the collisionless mode and in the collision mode. The quasiclassical approach has been used, in which the law of the dispersion of charge carriers is determined by the approximation of the quantum mechanical calculations. The magnitude of the electric current has been calculated by using the classic kinetic Boltzman equation with the model collision integral in the constant relaxation frequency approximation. The effect of the high-frequency electric field and the nonadditivity of the energy spectrum on the propagation of a solitary electromagnetic pulse in the arbitrary directions inside a sample has been determined. The numerical simulation of the evolution of solitary electromagnetic pulses is performed by using the method of difference schemes.

Theoretical analysis of equatorial near-inertial solitary waves under complete Coriolis parameters

An investigation of equatorial near-inertial wave dynamics under complete Coriolis parameters is performed in this paper. Starting from the basic model equations of oceanic motions, a Korteweg de Vries equation is derived to simulate the evolution of equatorial nonlinear near-inertial waves by using methods of scaling analysis and perturbation expansions under the equatorial beta plane approximation. Theoretical dynamic analysis is finished based on the obtained Korteweg de Vries equation, and the results show that the horizontal component of Coriolis parameters is of great importance to the propagation of equatorial nonlinear near-inertial solitary waves by modifying its dispersion relation and by interacting with the basic background flow.

Heart-cusp and bell-shaped-cusp optical solitons for an extended two-mode version of the complex Hirota model: application in optics

In this work, we present a new two-mode version to the complex Hirota equation. This new model arises in many applications in the field of optics, communications and other engineering sciences. It describes the propagation of two-symmetric solitary waves moving simultaneously with dependent phase-velocity parameter. The extended tanh-coth expansion method and the polynomial-function method are used to extract novel new cusp-type solutions to the Hirota model. A comprehensive graphical analysis is conducted to show physical aspects of this new type of nonlinear equations. The findings of this work are from mathematical point of view and we propose some benefits regarding the concept of two-mode where it could be visualized and practically applied.

Toward understanding solitary wave propagation in composite-cylinders-based 1D granular crystals

One-dimensional (1D) granular crystals are demonstrated to be outstanding nonlinear systems for supporting various types of novel stress waves. This letter reports on the investigation of solitary wave propagation within 1D granular crystals based on composite cylinders. We design two types of composite particles by creating a material mismatch within the granular, i.e., core–shell and sandwich types. We discover that such 1D composite granular chains support the formation of strongly nonlinear solitary waves. A finite element model is constructed to describe wave propagation behaviors fully validated by experiments. We conduct a theoretical analysis that agrees with numerical results and uncovers the physical mechanisms of solitary wave propagation in 1D composite granular chains through the parametric study. Finally, the fundamental understanding of dynamic responses is extended to more generalized composite granular chains with sandwich configurations. Results provide in-depth physical understanding and engineering design guidance to quantitatively tailor wave properties through simple 1D granular structures.

Characteristics of nonlinear ion-acoustic waves in collisional plasmas with ionization effects

In this work, we have investigated the linear and nonlinear propagation of ion-acoustic solitary waves in a collisional plasma composed of isothermal warm ions and a population of nonthermal electrons generated from the Kappa, Tsallis, and Cairns distribution. The effects of ionization, ion loss, and ion-neutral collision on ion-acoustic waves are also considered here. The standard reductive perturbation theory has been used to study the small but finite amplitude solitons. It is found that the nonlinear dynamics of the considered system are governed by the damped Korteweg-de Vries (dK-dV) equation. The solution of the damped K-dV equation is analyzed numerically. The effects of the nonthermal parameters, namely , , and on the ion-acoustic wave structures are discussed. Moreover, the effects ionization, ion loss, and ion-neutral collisions on solitary wave structures are also investigated here. It is shown that ionization effects lead to the growth of the IA solitons whereas collisions reduce this growth rate.

Theoretical method for generating solitary waves using plunger-type wavemakers and its Smoothed Particle Hydrodynamics validation

ABSTRACT Although solitary wave generation using a piston-type wavemaker has been common, the method cannot be applied to all wave tanks because many of them have been or will be equipped with plunger-type wavemakers. How to use a plunger to generate solitary waves as good as those generated by a piston is an unsolved but practically significant problem. Herein, a theoretical method is proposed. New formulae for the precise descent of an arbitrary-geometry plunger are derived and constraints on the produced wave height are given. Taking wedge-shaped, box-shaped, and cylinder-shaped plungers as examples, the generic wave-making theory and constraints are then specified. On their bases a Smoothed Particle Hydrodynamics (SPH) model is applied to simulate the solitary wave generation, and its reliability is validated in advance by reproducing available experiments. The SPH-simulated wave profiles, velocity fields, and pressure fields are examined by comparing SPH results with analytical solutions. In addition, plunger-type and piston-type as well as Rayleigh-based and Boussinesq-based solitary wave generation are compared. The results show that the solitary wave generated by a plunger-type wavemaker can be as accurate as the one generated by a piston-type wavemaker, provided that the plunger does not have a sharp corner or an incompatible surface with the wave profile. It is therefore anticipated that the proposed theory will extend the functionalities of existing plunger-type wavemakers and benefit plunger design in the future.

Delta-shaped basis functions-pseudospectral method for numerical investigation of nonlinear generalized equal width equation in shallow water waves

In this work, we examine generalized equal width (GEW) equation which is a highly nonlinear partial differential equation and describes plasma waves and shallow water waves. Nonlinearity of the equation is tackled by a linearization technique and finite difference approach is utilized for time derivatives. For spatial derivatives we first introduce delta-shaped basis functions which are relatively less studied in literature. Then, by using delta-shaped basis functions, pseudospectral differentiation matrices are constructed for spatial derivatives. Therefore combining finite difference approach for time derivatives and pseudospectral differentiation matrices for spatial derivatives, we obtain a system of linear equations. Solution of this system of equations gives nodal values of numerical solution of the GEW equation for each time step. Stability of the proposed method is given by using linear matrix stability analysis. To measure performance of the proposed method, four classic test problems are chosen namely the propagation of a single solitary wave, interaction of two solitary waves, Maxwellian initial condition and collision of solitons. Also, conservations of mass, momentum and energy are monitored during simulations. The results of numerical computations are compared with exact results if available and with previous studies in the literature such as Petrov–Galerkin, B-spline Galerkin and some collocation methods. From the comparison we can deduce that the proposed method gives reliable and accurate results in less computational cost.

Interaction of a soliton wave with nanopores in stoichiometry crystals A3B

Solitons are essentially nonlinear and stable objects in various environments. In this work, the molecular dynamics method is used to study the propagation of solitary waves in a discrete medium in the form of an A3B stoichiometry crystal and their interaction with nanopores. The model under consideration was a Pt 3Al crystal, the atoms of which interacted through the potential obtained by the immersed atom method. Such waves can propagate to hundreds of nanometers across the crystal. We have studied the passage of waves through a cell containing nanopores of various diameters. The mechanisms of energy dissipation in the process under consideration are shown. The distance after the obstacle at which the wave front is restored is estimated. The energy characteristics of a solitary wave after interaction with a topological defect in the form of a cylindrical nanopore are calculated. The results obtained can be useful both from a fundamental point of view in studying the properties of solitons, and from practical for non-destructive testing methods.

Waves and structure interaction using multi-domain couplings for Navier-Stokes solvers in OpenFOAM®. Part II: Validation and application to complex cases

In this work, we present several applications of the 2D-3D multi-domain couplings for Navier-Stokes models developed and validated in its companion (Di Paolo et al., submitted). The methodology is used to carry out some relevant simulations which include long regular and irregular waves, solitary wave propagation on a shallow foreshore, focused wave group transformation on a planar beach, wave impact on a cylinder and finally, the numerical twin of a complex laboratory experiment to analyse the performance of a perforated breakwater under wave action.Results agree well with the full 3D simulations and laboratory experiments and demonstrate the feasibility of using the 2D-3D coupled methodologies presented in Part I to successfully replace full 3D modelling. For all the cases considered, the application of coupled methodologies have resulted in a drastic reducing of the computational time without decreasing the accuracy of the full solution.