Nonlinear Acoustic Waves Research Articles

Shock Waves in Weakly Relativistic e-p-i Plasma: Application to Plasma Created by Ultraintense Short Pulse Laser

In this article, the role of the positrons shock waves generation in weakly relativistic laser-created plasma is investigated. The plasma considered is generated on the rear face of a target, irradiated by a high intensity short pulse laser, in the framework of target normal sheath acceleration (TNSA) mechanism. This plasma is composed of Boltzmann distributed positrons, hot and cold super-thermal electrons, and dynamic ions. Kinematic viscosity among the plasma constituents has been also considered. With the purpose of studying the behavior of nonlinear ion acoustic shock waves (IASHWs), the reductive perturbation method (RPM) has been employed and Korteweg-de Vries Burgers equation has been derived. It was observed that different plasma parameters (namely, electrons super-thermality, number of positrons, ion temperature, kinematic viscosity, etc.) have a real impact on the propagation of IASHWs. As electron–positron plasmas with ion possessing relativistic velocities are often detected in laboratory experiments, astrophysical, and space environments, the present work will help to explain the different types of collective processes and instabilities in regions where e-p-i plasmas can exist.

Dispersive nonlinear acoustic waves

The main phenomena and mathematical models of the theory of nonlinear dispersive acoustic waves are described. For the physical dispersion of the relaxation type, the form of the kernels of the integro-differential equation for several relaxation times and the continuous spectrum of such times is indicated. The possibility of obtaining simple equations for media with a finite “memory time” is indicated. As a medium with resonant dispersion, where the kernels have an oscillatory character, a liquid with gas bubbles is considered. The dispersion curves are analyzed. It is argued that the introduction of resonant elements into a homogeneous matrix is a special case of creating metamaterials with unusual nonlinear-dispersion properties. As an example of the geometric dispersion, important problems of nonlinear focusing are considered based on the Ostrovsky–Vakhnenko equation, which is interpreted here as the projection of the Khokhlov–Zabolotskaya equation onto the acoustic beam axis. When analyzing the nonlinear dispersion, it was indicated that in acoustics the dependence of the wave propagation velocity on the magnitude of the perturbation is a common phenomenon. It leads to a distortion of the wave profile in time, as well as to a deformation of the spatial shape of the beam — to effects like self-refraction. In acoustics, nonlinearities of odd degrees are encountered much less frequently than in optics; cubic nonlinearity is possessed, for example, by shear waves in solids. Nevertheless, it leads to original effects — the formation of trapezoidal sawtooth waves and unusual self-focusing. The article systematically presents both known and new results.

Linear and nonlinear modelling of far-field propagation of broadband shock-associated noise

A triple-scale computational model is implemented to simulate noise generated by a supersonic under-expanded screeching jet corresponding to the LTRAC (Laboratory for Turbulence Research in Aerospace and Combustion) experiment at different distances from the source. The investigation is focused on the broadband-associated noise, which is a prominent feature of the acoustic field of the LTRAC jet. In the jet near-field, the compressible Navier–Stokes equations are solved using the high-resolution CABARET Large Eddy Simulation (LES) method accelerated on Graphics Processing Units. The LES solution is substituted in the Ffowcs Williams–Hawkings (FW–H) model to obtain the noise solution in the acoustic mid field at 20 initial jet diameters from the jet nozzle exit. The mid-field acoustic solution is used as the input for the spherical generalised Burgers’ equation. The general form of Burgers’ equation is solved numerically in the frequency domain for a wide range of observer distances up to 18 million initial jet diameters, where viscous dissipation fully dominates for most frequencies. To answer the question if the nonlinear acoustic wave propagation effects for the LTRAC jet are important, the nonlinear and linear solutions of Burgers’ equation are compared.

Nonlinear Acoustic Waves in Liquids with Gas Bubbles: A Review

Nonlinear Acoustic Waves in Liquids with Gas Bubbles: A Review

An iterative method to evaluate one-dimensional pulsed nonlinear elastic wavefields and mixing of elastic waves in solids

Over the last 15 years, literature on nondestructive testing has shown that the generation of higher harmonics and nonlinear mixing of waves could be used to obtain the nonlinearity parameters of an elastic medium and thereby gather information about its state, e.g., aging and fatigue. To design ultrasound measurement setups based on these phenomena, efficient numerical modeling tools are needed. In this paper, the iterative nonlinear contrast source method for numerical modeling of nonlinear acoustic waves is extended to the one-dimensional elastic case. In particular, nonlinear mixing of two collinear bulk waves (one compressional, one shear) in a homogeneous, isotropic medium is considered, taking into account its third-order elastic constants ( A, B, and C). The obtained results for nonlinear propagation are in good agreement with a benchmark solution based on the modified Burgers equation. The results for the resonant waves that are caused by the one-way and two-way mixing of primary waves are in quantitative agreement with the results in the literature [Chen, Tang, Zhao, Jacobs, and Qu, J. Acoust. Soc. Am. 136(5), 2389-2404 (2014)]. The contrast source approach allows the identification of the propagating and evanescent components of the scattered wavefield in the wavenumber-frequency domain, which provides physical insight into the mixing process and explains the propagation direction of the resonant wave.

Dust-ion acoustic rogue waves in six-component dusty plasma

In this work, we investigate the modulational instability of finite amplitude dust-ion acoustic nonlinear waves in a six-component cometary dusty plasma. Such plasma system is composed of Oxygen ion-pair, negative dust particles, kappa distributed light ions of Hydrogen, solar electrons and cometary electrons of the comet tail. By employing the standard reductive perturbation technique, a nonlinear Schrödinger-type equation is obtained. This equation governs the investigation of the modulational instability of finite amplitude dust-ion acoustic nonlinear waves. Our analysis shows two parametric domains, where the dust-ion acoustic waves are modulationally stable and unstable depending on the plasma configurational parameters. Within the unstable domain, rogue waves could be generated due to the nonlinear and dispersion properties of plasma system. The effects of some relevant plasma parameters on the profile of rogue waves are studied. The obtained results might be useful for better understanding the modulational instability of nonlinear plasma waves and formation of dust-ion acoustic rogue waves in space plasmas.

Transcendental surface wave to the symmetric regularized long-wave equation

The symmetric regularized long-wave (SRLW) equation describes the attribute of the nonlinear ion acoustic waves, space charge waves, undular bore in meteorology etc. In this article, we investigate the SRLW equation to rummage transcendental shape of surface wave solution using the auxiliary equation approach and the improved Bernoulli sub-equation function technique. The solutions are ascertained in the form of trigonometric, hyperbolic, rational and exponential functions containing several ascendant parameters to the SRLW equation through the stated approaches which are compatible, dependable and simple to use. We extract a variety of rich structured surface solitons from the generic solution obtained including parabolic, kink, bell-shaped, lump soliton, etc. The implications of the various parameter values associated with the resulting solution are explicitly discussed to demonstrate their importance in explaining wave profiles behavior which may be convenient for analyzing nonlinear ion acoustic wave and space charge waves.

Simulating acoustic waves in acoustic black hole analogues

We present a physical model and a numerical method to simulate nonlinear acoustic waves emitted from moving boundaries in a moving background flow field with transition from subsonic to supersonic flow speeds. The physical model is based on a convective form of the Westervelt equation and accounts for the motion of the background medium and the progressive distortion of a finite amplitude acoustic wave. A suitable coordinate transformation in physical space allows us to accommodate the motion of the wave emitting boundary, while solving the governing equation in a fixed computational domain using standard finite difference techniques. We present the case of an oscillating spherical wave emitting boundary with an induced spherical flow as a prototypical example of an acoustic black hole analogue, where the acoustic waves cannot escape from the horizon of sonic flow speed during the contraction phase. It is demonstrated that the accelerating motion of the wave emitting boundary gives rise to frequency sidebands and amplitude modulations of the acoustic wave. The influence of the background flow speed on this nonlinear Doppler effect is investigated with the present methodology, thus contributing to an improved understanding of the acoustic wave behavior in the proximity of a sonic horizon.

Nonlinear piezoelectric surface acoustic waves.

The theory for nonlinear surface acoustic waves in crystals developed using Hamiltonian mechanics [Hamilton, Il'inskii, and Zabolotskaya, J. Acoust. Soc. Am. 105, 639 (1999)] is modified to account for piezoelectric material properties. The derived spectral evolution equations permit analysis of nonlinear surface wave propagation along a cut surface of any orientation with respect to the crystallographic axes and for piezoelectric crystals with any symmetry. Numerical simulations of waveform distortion in the particle velocity and electric field components are presented for surface wave propagation in Y-cut lithium niobate along the X- and Z-crystallographic axes. The influence of piezoelectricity is illustrated by comparing the nonlinear evolution of waveforms along a surface bounded by a vacuum (free space) and an ideal conductor (short circuit). Contributions to the nonlinearity from elasticity, piezoelectricity, electrostriction, and dielectricity are quantified separately for the two boundary conditions.

Nonlinear acoustic wave structures to the Zabolotskaya-Khokholov dynamical model

In this study, the abundant families of nonlinear acoustic wave structures are constructed for Zabolotskaya-Khokholov (Z-K) model which provides information about the propagation of sound beam or confined wave beam in nonlinear media and studies of beam deformation. These wave structures are observed in single (shock and singular) and mixed shock, (complex solitary-shock, shock-singular and periodic-singular) forms. The rational solutions are also emerged during the derivation. The new modified extended direct algebraic (NMEDA) technique and mathematics software are used to obtain the solutions. Moreover, for different values of parameters, the graphs in 3D and 2D-dimensions are also drawn.

Explicit predictor–corrector method for nonlinear acoustic waves excited by a moving wave emitting boundary

We present an explicit finite difference time domain method to solve the lossless Westervelt equation for a moving wave emitting boundary in one dimension and in spherical symmetry. The approach is based on a coordinate transformation between a moving physical domain and a fixed computational domain. This allows to simulate the combined effects of wave profile distortion due to the constitutive nonlinearity of the medium and the nonlinear Doppler modulation of a pressure wave due to the acceleration of the wave emitting boundary. A predictor–corrector method is employed to enhance the numerical stability of the method in the presence of shocks and grid motion. It is demonstrated that the method can accurately predict the Doppler shift of nonlinear wave distortion and the amplitude modulation caused by an oscillating motion of the wave emitting boundary. The novelty of the presented methodology lies in its capability to reflect the Doppler shift of the rate of nonlinear wave profile distortion and shock attenuation for finite amplitude acoustic waves emitted from an accelerating boundary.

Effect of Space Fractional Parameter on Nonlinear Ion Acoustic Shock Wave Excitation in an Unmagnetized Relativistic Plasma

In this work, the model equation with space fractional-order (FO) is used to investigate the nonlinear ion acoustic shock wave excitations (NIASWEs) in an unmagnetized collisionless weakly relativistic plasma having inertial relativistic ions fluid with viscous effects, inertial-less non-thermal electrons and inertial-less Boltzmann positrons. To do it, the Korteweg-de Vries Burgers equation (KdVBE) is derived from the considered fluid model equations by implementing the standard reductive perturbation method. Accordingly, such equation is converted to space fractional KdVBE via Agrawal’s variational principle with the help of the beta fractional derivative and its properties. The exact analytical solutions of KdVBE with space FO are determined via the modified Kudryashov method. The influence of space fractional and other related plasma parameters on NIASWEs are investigated. The outcomes would be useful to understand the nature of shocks with the presence of non-local or local space in many astrophysical and space environments (especially in the relativistic wind of pulsar magnetosphere, polar regions of neutron stars, etc.) and further laboratory verification.

A weakly nonlinear wave equation for damped acoustic waves with thermodynamic non-equilibrium effects

The problem of propagating nonlinear acoustic waves is considered; the solution to which, both with and without damping, having been obtained to-date starting from the Navier–Stokes–Duhem equations together with the continuity and thermal conduction equation. The novel approach reported here adopts instead, a discontinuous Lagrangian approach, i.e. from Hamilton’s principle together with a discontinuous Lagrangian for the case of a general viscous flow. It is shown that ensemble averaging of the equation of motion resulting from the Euler–Lagrange equations, under the assumption of irrotational flow, leads to a weakly nonlinear wave equation for the velocity potential: in effect a generalisation of Kuznetsov’s well known equation with an additional term due to thermodynamic non-equilibrium effects.

(3 + 1) dimensional nonlinear ion acoustic waves in multicomponent plasma containing Kappa distributed electrons

The (3 + 1) dimensional nonlinear ion acoustic waves in multicomponent complex plasma with Kappa electron distribution are studied in this work. The Zakharov-Kuznetsov (ZK) equation for ion acoustic wave is investigated by the reductive perturbation method. The variation of nonlinear ion acoustic wave with system parameter is obtained. Meanwhile, the Sagdeev potential function is obtained by using the Sagdeev potential method. And the phase diagram in a two-dimensional autonomous system of the multicomponent complex plasma with Kappa electron distribution is studied. Finally, the important influence of system parameter on the phase diagram, the Sagdeev potential function and the propagating characteristics of (3 + 1) dimensional nonlinear acoustic solitary waves are discussed in detail.

Propagation characteristics of (2 + 1) dimensional dust acoustic solitary waves in hot dusty plasma

The propagation characteristics of (2 + 1) dimensional nonlinear dust acoustic solitary wave in an unmagnetized hot dusty plasma composed of dust particles, electrons and nonthermal ions are studied in the paper. Firstly, the Kadomtsev-Petviashvili (KP) equation, which is used to describe the (2 + 1) dimensional nonlinear dust acoustic solitary wave, is derived by the reduced perturbation method, and the phase diagram and the Sagdeev potential equation of the system are obtained by using the traveling wave solution method. Then, the effects of different parameters in the hot dusty plasma system on the nonlinear coefficient, dispersion coefficient of the KP equation, system phase diagrams, Sagdeev potential function and the solitary wave solution in isothermal and adiabatic states are discussed by using numerical simulation and analysis method of mathematical software. Finally, the results show that the mass of dust particles, temperature, number density and distribution state of electrons and nonthermal ions have important effects on the amplitude, width and waveform of the nonlinear dust acoustic solitary wave under isothermal and adiabatic conditions.

New computations for the two-mode version of the fractional Zakharov-Kuznetsov model in plasma fluid by means of the Shehu decomposition method

<abstract><p>In this research, the Shehu transform is coupled with the Adomian decomposition method for obtaining the exact-approximate solution of the plasma fluid physical model, known as the Zakharov-Kuznetsov equation (briefly, ZKE) having a fractional order in the Caputo sense. The Laplace and Sumudu transforms have been refined into the Shehu transform. The action of weakly nonlinear ion acoustic waves in a plasma carrying cold ions and hot isothermal electrons is investigated in this study. Important fractional derivative notions are discussed in the context of Caputo. The Shehu decomposition method (SDM), a robust research methodology, is effectively implemented to generate the solution for the ZKEs. A series of Adomian components converge to the exact solution of the assigned task, demonstrating the solution of the suggested technique. Furthermore, the outcomes of this technique have generated important associations with the precise solutions to the problems being researched. Illustrative examples highlight the validity of the current process. The usefulness of the technique is reinforced via graphical and tabular illustrations as well as statistics theory.</p></abstract>

A Semianalytical Approach for the Solution of Nonlinear Modified Camassa–Holm Equation with Fractional Order

This paper presents the approximate solution of the nonlinear acoustic wave propagation model is known as the modified Camassa–Holm (mCH) equation with the Caputo fractional derivative. We examine this study utilizing the Laplace transform (ℒ T) coupled with the homotopy perturbation method (HPM) to construct the strategy of the Laplace transform homotopy perturbation method (ℒ T‐HPM). Since the Laplace transform is suitable only for a linear differential equation, therefore ℒ T‐HPM is the suitable approach to decompose the nonlinear problems. This scheme produces an iterative formula for finding the approximate solution of illustrated problems that leads to a convergent series without any small perturbation and restriction. Graphical results demonstrate that ℒ T‐HPM is simple, straightforward, and suitable for other nonlinear problems of fractional order in science and engineering.

Finite-amplitude acoustic responses of large-amplitude vibration objects with complex geometries in an infinite fluid

High-intensity acoustic waves existing commonly in aeronautical and aerospace vehicles manifest nonlinear propagation behaviors. Large-amplitude vibration and irregular shape of the aerospace vehicles further complicate the acoustic responses. This paper is concerned with numerical analysis of finite-amplitude acoustic responses of complex-shaped vibration objects. The time-dependent effect of the solid boundary position due to the large-amplitude vibration of the objects is considered. A set of first-order differential equations is derived to govern the finite-amplitude acoustic wave. A fourth-order dispersion-relation-preserving finite difference formulation is employed to solve the nonlinear acoustic equations on a fixed Cartesian grid. Acoustic responses of the fluid and the vibration of the complex-shaped object are coupled by considering the compatibility conditions on the fluid-solid interface. A ghost-cell sharp-interface immersed boundary method is utilized to relax the conformity requirement between the computational grid and solid boundary. Numerical filters are employed in the computational procedure to suppress numerical oscillations. The present method is validated through several numerical tests. Numerical analysis of finite-amplitude acoustic responses of a complex-shaped object is performed. The nonlinear effect of a finite-amplitude acoustic wave, the time-dependent effect of solid boundary position, and the coupling effect between them on the propagation behaviors of nonlinear acoustic waves are discussed.

A robust computational approach for Zakharov-Kuznetsov equations of ion-acoustic waves in a magnetized plasma via the Shehu transform

The application of the q-homotopy analysis Shehu transform method (q-HAShTM) to discover the estimated solution of fractional Zakharov-Kuznetsov equations is investigated in this study. In the presence of a uniform magnetic field, the Zakharov-Kuznetsov equations regulate the behaviour of nonlinear acoustic waves in a plasma containing cold ions and hot isothermal electrons. The q-HAShTM is a stable analytical method that combines homotopy analysis and the Shehu transform. This q-homotopy investigation Shehu transform is a constructive method that leads to the Zakharov-Kuznetsov equations, which regulate the propagation of nonlinear ion-acoustic waves in a plasma. It is a more semi-analytical method for adjusting and controlling the convergence region of the series solution and overcoming some of the homotopy analysis method’s limitations.

Contribution of the generalized (r, q) distributed electrons in the formation of nonlinear ion acoustic waves in upper ionospheric plasmas

The properties of ion acoustic solitary and periodic structures are studied in magnetized two-ion component (O+ − H+ − e) plasmas with (r, q) distributed electrons. It is found that two modes of ion acoustic waves, namely, fast and slow modes, can propagate in such a plasma. The nonlinear Zakharov–Kuznetsov equation is derived using the well-known reductive perturbation method. Employing the theory of planar dynamical systems, the system under consideration is found to admit compressive (hump) and rarefactive (dip) solitary structures and periodic wave solutions. It is found that behavior of propagation of nonlinear ion acoustic solitary structures is different for fast and slow modes owing to the difference in physics of the two modes. The effect of the double spectral indices r and q is thoroughly explored. It is shown that altering the shape of the distribution function through these indices radically alter the propagation characteristics of nonlinear ion acoustic waves. The ratio of concentration of heavy (O+) to light ions (H+) is found to change the fast mode, whereas the temperature ratio is observed to alter the slow mode. We have applied our study to the upper ionosphere where bi-ion plasmas and the presence of non-Maxwellian electrons have been observed by various satellite missions.