Nonplanar Waves Research Articles

Influence of thermal boundary condition on gas drainage from a semi-sealed narrow channel

Draining a viscous gas from a semi-sealed narrow conduit is a pore-scale problem of fundamental interest to primary fluid recovery from a petroleum reservoir as well as other applications. Such a drainage flow is entirely driven by the volumetric expansion of the gas and its mass flow rate is determined by the time-rate of decrease of the gas density within the conduit. It was found previously that when thermal effect is completely neglected, the drainage rate differs significantly from that based on the lubrication theory. The present work parametrically explores the influence of thermal boundary condition on the non-isothermal drainage flow from a narrow channel. It is found that as the wall transitions from adiabatic to isothermal condition, the excess density changes from a plane wave solution to a non-plane wave solution; and the drainage rate increases due to thermal damping on the wall, as a strong damping of the acoustic wave accelerates the process towards the final equilibrium. It is shown that when the exit is also cooled and the wall is non-adiabatic, the total recovered fluid mass exceeds the amount based on the isothermal theory determined by the initial and final density difference alone. The isothermal wall condition with the wall maintained at the initial gas temperature produces the most amount of fluid in the shortest time.

Nonplanar ion acoustic waves in dusty plasma with two temperature electrons: Application to Saturn's E ring

In the present paper, we have studied the cylindrical/spherical ion acoustic waves in dusty plasma consisting of positive ions, immobile dust particles, and q nonextensive distributed cold and hot electrons. A multiple scale expansion method is employed to derive a modified Korteweg–de Vries (mKdV) equation. Exact analytical solution for the mKdV equation in nonplanar geometry is obtained using the weighted residual method. This solution is, then, plotted for different physical parameters relevant to Saturn's E ring through 2D figures. We show that the amplitude of the wave decreases faster as one departs away from the axis of the cylinder or the center of the sphere. Such a decaying behavior continues as time progresses. This is expected from the obtained solution where the cylindrical (spherical) amplitude component (τ∞/τ)m decreases as the time progresses. We have also studied the role of the nonadiabatic dust charging fluctuating dissipation process and analyzed the resulting damped mKdV equation. Furthermore, the parametric dependence of wave properties (amplitude and width) on the q nonextensive parameter, density, and temperature of cold and hot electrons, concentration of dust particles, and thermal effects of ions has been studied in detail, and findings obtained here will be beneficial to further astrophysical investigations.

Planar and Nonplanar Electron-Acoustic Solitary Waves in the Presence of Positrons

The propagation of planar and nonplanar electron-acoustic waves composed of stationary ions, cold electrons, superthermal hot electrons, and positrons is studied by using Korteweg–de Vries (KdV) equation in the planar and nonplanar coordinates. The analytical and numerical solutions of KdV equation reveal that the nonplanar electron-acoustic solitons are modified significantly with positron concentration and behave differently in different geometries. It is found that the positron concentration β and positron temperature σ have a negative effect on the wave potential and width of the wave, there is a decrease in the amplitude as well as width of the wave. Thus, it is noticed that the strength of the wave decreases with the growing values of β and σ. From the examination, it is discovered that this increase in height and steepness is more articulated in the spherical geometry than in the cylindrical one. The strength of the wave grows with increment of superthermal particles (low value of κ). There is also an increase in the width of the solitary wave with decreasing the value of κ, which is in agreement with the results of [1]. Further, it is noticed that the spherical wave moves faster than cylindrical waves. This difference arises due to the presence of the geometry term $$m{\text{/}}2\tau $$ , whose value becomes zero in the planar case ( $$m = 0$$ ), $$1{\text{/}}(2\tau )$$ in the cylindrical and $$2{\text{/}}2\tau $$ in the spherical case. Results of our work may be helpful in analyses of the physical behaviour of solitary waves features in different astrophysical and space environments like the supernovas, polar regions and in the vicinity of black holes.

The use of microperforated materials as duct liners: Comparison with fibrous linings

The acoustical performance of a microperforated duct liner and a fibrous lining was compared to confirm that a microperforated panel lining can be used to re- place a fibrous liner as a sound attenuator in a duct. Fibrous materials are often used to line ducts in order to attenuate HVAC noise, for example. These treatments are often primarily useful in a limited frequency range owing to the characteristics of non-planar wave propagation in ducts. At the same time, microperforated mate- rials backed by a finite-depth air space are effective in a limited frequency range owing to the nature of the reactive impedance of this combination. Here, it will be shown that microperforated materials may be used to create duct linings that produce attenuation comparable with that of fibrous materials in the latter's high- performance region. The characteristics of the microperforated panel were studied based on the Maa model. To compare the performance of these two linings, theoret- ical, numerical and experimental tools were used. In the various case studies, both extended reaction and locally reacting treatments were considered. For the analyti- cal approach, Morse's theory was applied in the local reaction case. On the other hand, Scott's analysis was used to study the extended reaction case. In the experi- mental work, the transmission losses of various liner configurations were measured in a square impedance tube. To tune the performance of a microperforated sheet to reproduce that of a fibrous material, the hole size, porosity, thickness, density, and air-backing depth were modified. To validate the experimental and analytical data and to handle situations that are not easily modeled using an analytical approach, a finite element model was also used for the calculations. For the finite element model analysis, COMET/VISION and SAFE were used. Since that software does not include explicit microperforated material models, an alternative approach was used. The alternative model was based on the Attala and Sgard model for perforated panels. This alternative approach in which the perforated panel is modeled as a thin porous layer was successfully implemented in finite element form. Finally, it was demonstrated that the microperforated panel can successfully reproduce the acous- tical performance of glass fiber as a duct lining material.

Homoclinic bifurcations and chaotic dynamics of non-planar waves in axially moving beam subjected to thermal load

The homoclinic bifurcations and nonplanar chaotic waves in axially moving beam (AMB) under thermal excitation are investigated. By the multiple scale technique, the equivalent nonlinear system is derived to explore qualitatively the dynamical characteristics of AMB system for the case of primary resonance. Using Melnikov approach as well as geometric analysis, the criterion for homoclinic chaos and complex nonplanar motions for AMB system is discussed. The theoretical predictions are tested by the numerical approach. For the design and application of the AMB, some inspiration and guidance are provided by the results from theory and simulation.

A Subwavelength-Laser-Driven Transmitting Optical Nanoantenna for Wireless Communications

Nanoantennas are efficient devices exhibiting large confined electric field enhancements. So far, they have been extensively researched mainly in the receiving mode, which means that the illuminating field is essentially a plane wave. In this article, we consider the problem of designing an efficient and highly directive transmitting nanoantenna where the system is energized by a nonplane wave field, a subwavelength laser excitation. The main objective of this article is to establish through an accurate computational model a basic understanding of how a dipole-type radiator can be made to resonate with such complex nonplane-wave type of near-field illumination. Including short-wavelength components allowed us to achieve a 200-nm spot radius, which is a quarter of its incident wavelength (800 nm). Near- and far-field antenna quantities are introduced and calculated using an efficient full-wave finite-element method-based multiphysics solver. A nanoscale optical antenna is then presented with optimized dimensions and material settings. Various design data and insights are also discussed in connection with issues such as how to define efficiency and determine whether the system is radiating properly.

Receiver function imaging of the 410 and 660 km discontinuities beneath the Australian continent

SUMMARYTo provide constraints on a number of significant controversial issues related to the structure and dynamics of the Australian continent, we utilize P-to-S receiver functions (RFs) recorded by 182 stations to map the 410 and 660 km discontinuities (d410 and d660, respectively) bordering the mantle transition zone (MTZ). The RFs are stacked in successive circular bins with a radius of 1° under a non-plane wave front assumption. The d410 and d660 depths obtained using the 1-D IASP91 earth model show a systematic apparent uplifting of about 15 km for both discontinuities in central and western Australia relative to eastern Australia, as the result of higher seismic wave speeds in the upper mantle beneath the former area. After correcting the apparent depths using the Australian Seismological Reference Model, the d410 depths beneath the West Australia Craton are depressed by ∼10 km on average relative to the normal depth of 410 km, indicating a positive thermal anomaly of 100 K at the top of the MTZ which could represent a transition from a thinner than normal MTZ beneath the Indian ocean and the normal MTZ beneath central Australia. The abnormally thick MTZ beneath eastern Australia can be adequately explained by subducted cold slabs in the MTZ. A localized normal thickness of the MTZ beneath the Newer Volcanics Province provides supporting evidence of non-mantle-plume mechanism for intraplate volcanic activities in the Australian continent.

Electron-Acoustic Shock Waves in Cylindrical and Spherical Geometry with Non-Extensive Electrons

We consider nonplanar electron acoustic shock waves composed of stationary ions, cold and non-extensive hot electrons under multiple temperature electrons model in unmagnetized plasma. In this model Modified Korteweg-de Vries–Burger (KdVB) equation is obtained in the cylindrical/spherical coordinates. On the basis of the solutions of KdVB equation, the variation of shock waves features (amplitude, velocity, and width) with different plasma parameters are analyzed. Dissipation effect is introduced in the model by means of kinematic viscosity term. KdVB equation always leads to monotonic solitons and no oscillatory part or peak may appear. It is observed that the combined effect of particle density $$(\alpha )$$, nonextensivity parameter q, electron temperature ratio $$(\theta )$$, and kinetic viscosity $$({{\eta }_{0}})$$ significantly changes the properties of shock waves in nonplanar geometry especially in spherical coordinates. Results could be helpful to analyze the soliton features in laboratory and in the space environments.

Twisted gravitational waves in the presence of a cosmological constant

We find exact nonlinear solutions of general relativity that represent twisted gravitational waves (TGWs) in the presence of a cosmological constant. A TGW is a nonplanar wave propagating along a fixed spatial direction with a null Killing wave vector that has a nonzero twist tensor. The solutions all turn out to have wave fronts with negative Gaussian curvature. Among the classes of solutions presented in this paper, we find a unique class of simple conformally flat TGWs that is due to the presence of a negative cosmological constant and therefore represents part of anti-de Sitter spacetime. The properties of this special solution are studied in detail.

Analytical solution for nonplanar waves in a plasma with q-nonextensive nonthermal velocity distribution: Weighted residual method

Abstract The basic nonlinear equations describing the dynamics of a two component plasma consisting of cold positive ions and electrons obeying hybrid q- nonextensive nonthermal velocity distribution are examined in the cylindrical(spherical) coordinates through the use of reductive perturbation method and the cylindrical(spherical) KdV and the modified KdV equations are obtained. An approximate analytical method for the progressive wave solution is presented for these evolution equation in the sense of weighted residual method. It is observed that both amplitudes and the wave speeds decrease with the time parameter τ. Since the wave profiles change with τ, the waves cannot be treated as solitons. It is further observed that the amplitudes of spherical waves are larger than those of the cylindrical waves; and the wave amplitudes of modified KdV equation are much larger than those of the KdV equation. The effects of physical parameters (α, q) on the wave characteristics are also discussed.

Numerical study of the Richtmyer–Meshkov instability induced by non-planar shock wave in non-uniform flows

ABSTRACTThe effects of non-uniformity of flows and initial disturbance intensity of the incident shock wave on Richtmyer–Meshkov instability (RMI) when a sinusoidal shock wave with Ma = 1.25 impinging an unperturbed interface are numerically investigated. The interface morphology, turbulent mixing zone width (TMZW), Y-integrated vorticity, circulation, and turbulent kinetic energy (TKE) are qualitatively and quantitatively compared before and after reshock. The numerical results indicate that the non-uniformity of flows and initial disturbance intensity of sinusoidal shock wave are significant factors of RMI evolution. On the one hand, the TMZW and its growth rate increase with the decrease of the parameter of non-uniformity before reshock; while, those discrepancies are reduced after reshock. On the other hand, the increase of the initial disturbance intensity of sinusoidal shock wave leads to the increase of the vorticity, circulation and TKE, the TMZW and it growth rate increase accordingly, all the time. Further analysis points out that the TMZW evolves with time as a power law before reshock, and the value of θ is sensitive to the initial conditions. After reshock and the first reflected rarefaction wave, the TMZW grows in time as a negative exponential law , but t* is different for the two stages.

Analysis of acoustic characteristics of the expansion chamber water muffler considering acoustic-structure interaction

Influences of acoustic-structure interaction on the acoustic characteristics of the expansion chamber water muffler have been studied. The acoustic-structure physics module and the acoustic-shell physics module are adopted. The applicability of the methods in the analysis of mufflers involving strong acoustic-structure interactions has been proved. The acoustic characteristics of water mufflers with elastic walls have been discussed using a 1/4 axisymmetric model. The reliability is validated by comparing the results based on 1/4 model and full model. The calculated transmission loss (TL) of thick-wall muffler is close to that of rigid-wall muffler, which verifies the accuracy of numerical simulation. Effects of elastic walls at different locations have been analyzed. It is found that material properties of the solid have important influences on the acoustic characteristics of water mufflers. The acoustic-structure interaction is enhanced with the decrease of wall thickness. The circumferential elastic wall may cause reduction of the passing fr uency and its frequency bandwidth, while increasing to some extent the maximum noise attenuation. The elastic end chamber wall may change the dome behavior of the TL curve in the considered frequency band with anti-resonance peaks and sharp peaks. The anti-resonance peak is related to the (0, n) radial modes of the end chamber wall. The sharp peak is related to non-planar waves caused by the interaction. The short main pipe elastic wall has little effect on the acoustic characteristics of water mufflers. © 2019 Institute of Noise Control Engineering.

Spectral stability of nonlinear gravity waves in the atmosphere

AbstractWe apply spectral stability theory to investigate nonlinear gravity waves in the atmosphere. These waves are determined by modulation equations that result from Wentzel-Kramers-Brillouin theory. First, we establish that plane waves, which represent exact solutions to the inviscid Boussinesq equations, are spectrally stable with respect to their nonlinear modulation equations under the same conditions as what is known as modulational stability from weakly nonlinear theory. In contrast to Boussinesq, the pseudo-incompressible regime does fully account for the altitudinal varying background density. Second,we show for the first time that upward-traveling non-plane wave fronts solving the inviscid nonlinear modulation equations, that compare to pseudo-incompressible theory, are unconditionally unstable. Both inviscid regimes turn out to be ill-posed as the spectra allow for arbitrarily large instability growth rates. Third, a regularization is found by including dissipative effects. The corresponding nonlinear traveling wave solutions have localized amplitude. As a consequence of the nonlinearity, envelope and linear group velocity, as given by the derivative of the frequency with respect to wavenumber, do not coincide anymore. These waves blow up unconditionally by embedded eigenvalue instabilities but the instability growth rate is bounded from above and can be computed analytically. Additionally, all three types of nonlinear modulation equations are solved numerically to further investigate and illustrate the nature of the analytic stability results.

On the numerical solution of nonplanar dust-acoustic super rogue waves in a strongly coupled dusty plasma

The occurrence of cylindrical and spherical low-frequency dust-acoustic freak waves (DAFWs) in a strongly coupled dusty plasma is numerically investigated in the framework of the phenomenological generalized hydrodynamic model. The basic equations are reduced to a modified/nonplanar nonlinear Schrödinger equation (mNLSE) using a reductive perturbation method. The existing regions of instability structures have been carefully identified. For studying the propagation of rogue waves in case of nonplanar (cylindrical and spherical coordinates), the mNLSE has been solved numerically. The effects of nonplanar geometries on the basic features of the DAFWs for the first- and second-orders rogue waves are discussed. Finally, our results are of relevance in ultradense situations where nonplaner geometrical effects are significant. In particular, we expect for our findings to be important to understand the DA breathers experimentally in a strongly coupled dusty plasma.

Non-planar electron-acoustic waves with hybrid Cairns–Tsallis distribution

Non-planar electron-acoustic waves having Cairns–Tsallis distributed hot electrons are investigated under multiple temperature electrons model in unmagnetised plasma. In this model, Korteweg–de Vries (KdV) equation is obtained in the cylindrical / spherical coordinates. On the basis of the solutions of KdV equation, variation of solitary wave features (amplitude, velocity and width) with different plasma parameters are analysed. Dispersion and nonlinear coefficients obtained depend on the particle density $$\alpha $$ , non-extensive parameter q, electron temperature ratio $$\theta $$ and non-thermal parameter $$\gamma $$ . Combined effect of all these plasma parameters significantly changes the properties of the solitary waves in non-planar geometry. It is observed that increasing the number of non-thermal electrons in the medium increases the amplitude, velocity as well as width of the non-planar waves whereas with the increase in temperature, the velocity of waves decreases and this impact is dominant in spherical waves. This two-parameter $$(\gamma , q)$$ distribution model (C–T) is applicable to a wide range of observed plasmas, i.e. auroral region and magnetosphere of the Earth.

A Numerical Mode Matching Method for Wave Scattering in a Layered Medium with a Stratified Inhomogeneity

Numerical mode matching (NMM) methods are widely used for analyzing wave propagation and scattering in structures that are piecewise uniform along one spatial direction. For open structures that are unbounded in transverse directions (perpendicular to the uniform direction), the NMM methods use the perfectly matched layer (PML) technique to truncate the transverse variables. When incident waves are specified in homogeneous media surrounding the main structure, the total field is not always outgoing, and the NMM methods rely on reference solutions for each uniform segment. Existing NMM methods have difficulty handing grazing incident waves and special incident waves related to the onset of total internal reflection, and are not very efficient at computing reference solutions for nonplane incident waves. In this paper, a new NMM method is developed to overcome these limitations. A hybrid Dirichlet-Robin boundary condition is proposed to ensure that nonpropagating and nondecaying wave field components are not reflected by truncated PMLs. Exponential convergence of the PML solutions based on the hybrid Dirichlet--Robin boundary condition is established theoretically. A fast method is developed for computing reference solutions for cylindrical incident waves. The new NMM is implemented for two-dimensional structures and polarized electromagnetic waves. Numerical experiments are carried out to validate the new NMM method and to demonstrate its performance.

Sound propagation in a lined nozzle with shear and bias flows

In this study, the propagation of waves in a two-dimensional parallel-sided nozzle is considered allowing for the combination of: (a) distinct impedances of the upper and lower walls; (b) upper and lower boundary layers with different thicknesses with linear shear velocity profiles matched to a uniform core flow; and (c) a uniform cross-flow as a bias flow out of one and into the other porous acoustic liner. The model involves an “acoustic triple deck” consisting of third-order non-sinusoidal non-plane acoustic-shear waves in the upper and lower boundary layers coupled to convected plane sinusoidal acoustic waves in the uniform core flow. The acoustic modes are determined from a dispersion relation corresponding to the vanishing of an 8 × 8 matrix determinant, and the waveforms are combinations of two acoustic and two sets of three acoustic-shear waves. The eigenvalues are calculated and the waveforms are plotted for a wide range of values of the four parameters of the problem, namely: (i/ii) the core and bias flow Mach numbers; (iii) the impedances at the two walls; and (iv) the thicknesses of the two boundary layers relative to each other and the core flow. It is shown that all three main physical phenomena considered in this model can have a significant effect on the wave field: (c) a bias or cross-flow even with small Mach number [Formula: see text] relative to the mean flow Mach number [Formula: see text] can modify the waveforms; (b) the possibly dissimilar impedances of the lined walls can absorb (or amplify) waves more or less depending on the reactance and inductance; (a) the exchange of the wave energy with the shear flow is also important, since for the same stream velocity, a thin boundary layer has higher vorticity, and lower vorticity corresponds to a thicker boundary layer. The combination of all these three effects (a–c) leads to a large set of different waveforms in the duct that are plotted for a wide range of the parameters (i–iv) of the problem.

Nonplanar Electron - Acoustic Shock Waves with Superthermal Hot Electrons

Nonplanar electron-acoustic shock waves having superthermal hot electrons are investigated with two temperature electrons model in unmagnetized plasma. Using reductive perturbation method, Korteweg-de Vries-Burgers (KdVB) equation is obtained in the cylindrical/spherical coordinates. Dissipation effect is introduced in the model by means of kinematic viscosity term. On the basis of the solutions of KdVB equation, variation of shock waves features (amplitude, velocity and width) with different plasma parameters are analysed. KdV-Burgers equation always leads to monotonic solitons and no oscillatory peak may appear. The combined effect of particle density (α), superthermal parameter (κ), electron temperature ratio (𝜃) and kinetic viscosity (η0) is numerically studied, and it is observed that these parameters significantly change the properties of the shock waves in nonplanar geometry especially in spherical coordinates. Results could be helpful to analyse the soliton features in laboratory as well as in the space environments.

Spinning particles in twisted gravitational wave spacetimes

Twisted gravitational waves (TGWs) are nonplanar waves with twisted rays that move along a fixed direction in space. We study further the physical characteristics of a recent class of Ricci-flat solutions of general relativity representing TGWs with wave fronts that have negative Gaussian curvature. In particular, we investigate the influence of TGWs on the polarization of test electromagnetic waves and on the motion of classical spinning test particles in such radiation fields. To distinguish the polarization effects of twisted waves from plane waves, we examine the theoretical possibility of existence of spin-twist coupling and show that this interaction is generally consistent with our results.

Intrinsic thermoacoustic modes and their interplay with acoustic modes in a Rijke burner

The interplays between acoustic and intrinsic modes in a model of a Rijke burner are revealed and their influence on the prediction of thermoacoustic instabilities is demonstrated. To this end, the system is examined for a range of time delays, temperature ratios and reflection coefficients as adjustable parameters. A linear acoustic network model is used and all modes with frequency below the cut-on frequency for non-planar acoustic waves are considered. The results show that when reflection coefficients are reduced, the presence of a pure ITA mode limits the reduction in the growth rate that usually results from a reduction of the reflection coefficients. In certain conditions, the growth rates can even increase by decreasing reflections. As the time delay of the flame and thus the ITA frequency decreases, the acoustic modes couple to and subsequently decouple from the pure ITA modes. These effects cause the maximum growth rate to alternate between the modes. This investigation draws a broad picture of acoustic and intrinsic modes, which is crucial to accurate prediction and interpretation of thermoacoustic instabilities.