Propagation Of Interface Waves Research Articles

Turbulence and Interface Waves in Stratified Oil–Water Channel Flow at Large Viscosity Ratio

We investigate the dynamics of turbulence and interfacial waves in an oil–water channel flow. We consider a stratified configuration, in which a thin layer of oil flows on top of a thick layer of water. The oil–water interface that separates the two layers mutually interacts with the surrounding flow field, and is characterized by the formation and propagation of interfacial waves. We perform direct numerical simulation of the Navier-Stokes equations coupled with a phase field method to describe the interface dynamics. For a given shear Reynolds number, Reτ=300\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Re_\ au =300$$\\end{document}, and Weber number, We=0.5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$We=0.5$$\\end{document}, we consider three different types of oils, characterized by different viscosities, and thus different oil-to-water viscosity ratios μr=μo/μw\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu _r=\\mu _o/\\mu _w$$\\end{document} (being μo\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu _o$$\\end{document} and μw\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu _w$$\\end{document} oil and water viscosities). Starting from a matched viscosity case, μr=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu _r=1$$\\end{document}, we increase the oil-to-water viscosity ratio up to μr=100\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu _r=100$$\\end{document}. By increasing μr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu _r$$\\end{document}, we observe significant changes both in turbulence and in the dynamics of the oil–water interface. In particular, the large viscosity of oil controls the flow regime in the thin oil layer, as well as the turbulence activity in the thick water layer, with direct consequences on the overall channel flow rate, which decreases when the oil viscosity is increased. Correspondingly, we observe remarkable changes in the dynamics of waves that propagate at the oil–water interface. In particular, increasing the viscosity ratio from μr=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu _r=1$$\\end{document} to μr=100\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu _r=100$$\\end{document}, waves change from a two-dimensional, nearly-isotropic pattern, to an almost monochromatic one.

Evolution mechanism of fracture interface wave and microstructure during resistance butt spot welding

In this work, the interface wave was first shown in resistance butt spot welding of titanium (Ti) alloy and stainless steel (SS) as in explosive welding and magnetic pulse welding. Interface wave exhibited a fracture mode in the joint, so which were called fracture interface waves. The wavelength and the peak of the fracture interface wave weaken from the center of the joint to the outer edge. The formation of the wave is closely related to the interface microstructure. Fracture interface wave would have a direct impact on the joint properties. Analysis of the formation of fracture interface wave is helpful to improve the quality of the joint. Thermo-electric-mechanical-magnetic-flow coupling in resistance butt spot welding makes it difficult to explain the forming mechanism completely by existing theory and experiment methods. The key conditions of fracture interface wave propagation were analyzed by means of thermo-electric-mechanical numerical simulation. The formation process was explained in addition to the microstructure, mechanical properties.

Interfacial wave propagation in initially stressed compressible hyperelastic materials

In this paper, the propagation of interfacial waves at the joint boundary of two initially stressed compressible half-spaces is discussed. The materials are subject to pure homogeneous strain and the wave is assumed to travel along one of the principle axes. For mathematical formulation of the problem, non-linear theory of elasticity and theory of invariants are used. Boundary conditions at the interface are applied which lead to an implicit secular equation governing the wave speed. A prototype strain-energy function is used for specialized theoretical results to understand the physical behavior of waves at the interface. A special case of biaxial initial stress is considered and the results are presented theoretically and graphically for representative numerical values of parameters. It is observed that the wave speed is considerably affected by intrinsic properties, i.e., material parameters as well as the amount of initial stress.

Interfacial Wave Propagation Along Surface of Vertical Solid Partially Submerged in Horizontal Liquid Layer

Interfacial Wave Propagation Along Surface of Vertical Solid Partially Submerged in Horizontal Liquid Layer

Tunable control of subwavelength topological interface modes in locally resonance piezoelectric metamaterials

This paper reports the evidence of the tunable sub-wavelength topological interface state in local resonance piezoelectric metamaterials. An elastic beam serves as the host medium with periodically arranged local resonators and attached piezoelectric layers. Thus, the shunt circuits connected with the piezoelectric layers can easily change the electromechanical stiffness in any unit cell. By inspired the band-folding mechanism, doubling the primitive unit cell generates two Dirac points, whose one lower point falls below the locally resonant bandgap and is in the sub-wavelength region. Then, employing the shunt circuit’s tunability opens band-folding points to develop two bandgaps associated with the Bragg scattering effect. Band inversion and topological transition exist during the negative capacitance parameter variation. Numerical simulations demonstrate interface wave propagation for excitation at the interface frequency in the heterostructure, composted of two media with different topological invariants. With the assistance of the piezoelectric shunting circuit, our proposed design can induce wave localization over multiple frequency bands, which has potential for applications such as signal filters, energy harvesting and vibration isolation. Finally, we investigate the relationship between the interface frequency and capacitance and consider the local resonance effect on topological interface modes.

One-way interfacial waves in aflexuralplate with chiral double resonators.

In this paper, we demonstrate a new approach to control flexural elastic waves in a structured chiral plate. The main focus is on creating one-way interfacial wave propagation at a given frequency by employing double resonators in a doubly periodic flexural system. The resonators consist of two beams attached to gyroscopic spinners, which act to couple flexural and rotational deformations, hence inducing chirality in the system. We show that this elastic structure supports one-way flexural waves, localized at an interface separating two sub-domains with gyroscopes spinning in opposite directions, but with otherwise identical properties. We demonstrate that a special feature of double resonators is in the directional control of wave propagation by varying the value of the gyricity, while keeping the frequency of the external time-harmonic excitation fixed. Conversely, for the same value of gyricity, the direction of wave propagation can be reversed by tuning the frequency of the external excitation. This article is part of the theme issue 'Modelling of dynamic phenomena and localization in structured media (part 2)'.

Two-Layer Non-Hydrostatic Model for Generation and Propagation of Interfacial Waves

When pycnocline thickness of ocean density is relatively small, density stratification can be well represented as a two-layer system. In this article, a depth integrated model of the two-layer fluid with constant density is considered, and a variant of the edge-based non-hydrostatic numerical scheme is formulated. The resulting scheme is very efficient since it resolves the vertical fluid depth only in two layers. Despite using just two layers, the numerical dispersion is shown to agree with the analytical dispersion curves over a wide range of kd, where k is the wave number and d the water depth. The scheme was tested by simulating an interfacial solitary wave propagating over a flat bottom, as well as over a bottom step. On a laboratory scale, the formation of an interfacial wave is simulated, which also shows the interaction of wave with a triangular bathymetry. Then, a case study using the Lombok Strait topography is discussed, and the results show the development of an interfacial wave due to a strong current passing through a sill.

Inverse design of quantum spin hall-based phononic topological insulators

We propose a computational methodology to perform inverse design of quantum spin hall effect (QSHE)-based phononic topological insulators. We first obtain two-fold degeneracy, or a Dirac cone, in the band structure using a level set-based topology optimization approach. Subsequently, four-fold degeneracy, or a double Dirac cone, is obtained by using zone folding, after which breaking of translational symmetry, which mimics the effect of strong spin-orbit coupling and which breaks the four-fold degeneracy resulting in a bandgap, is applied. We use the approach to perform inverse design of hexagonal unit cells of C6 and C3 symmetry. The numerical examples show that a topological domain wall with two variations of the designed metamaterials exhibit topologically protected interfacial wave propagation, and also demonstrate that larger topologically-protected bandgaps may be obtained with unit cells based on C3 symmetry.

Propagation characteristics of pseudo-Scholte waves at the interface between finite-thickness fluid layer and quasi-saturated porous half-space

The propagation of interface waves at the interface between a fluid-saturated porous medium and a fluid has been extensively investigated in the last three decades due to its various and wide applications in several fields including earthquake engineering and materials testing. Although the sea floor is usually covered with porous marine sediment, the previous interface wave theories are rarely used for submarine acoustic problems for the following reasons. 1) In addition to hard porous media, unconsolidated soft porous media exist widely in the seabed, which are seldom considered in previous studies. 2) The depth of seawater is limited, and in many cases it cannot be regarded as a half-space. 3) The fluid-saturated porous medium model cannot describe the effect of a small number of bubbles caused by decomposition of organic matter in the sediment. Hence, the present paper focuses on the low-frequency pseudo-Scholte waves at the interface between an overlying fluid layer of finite thickness and a quasi-saturated porous half-space. The overlying fluid is assumed to be ideal compressible water and the quasi-saturated porous media are assumed to be sandstone and unconsolidated sediment and modeled by Biot theory. A fluid equivalent model is used to analyze the effects of the bubbles in the pores. Based on the boundary conditions, the closed-form dispersion equations of far-field interface waves are derived by using classical potential function method. The velocity and attenuation of pseudo-Scholte wave are determined by Newton iteration in a reasonable rooting interval. The analytical expressions of the displacement field and fluid pressure distribution caused by pseudo-Scholte waves are also derived. Then, based on the derived theoretical formulation, the numerical examples of calculations are presented. Our calculation results show that the stiffness of porous medium significantly affects the mode, phase velocity, displacement and fluid pressure distribution of interface waves; the phase velocity of the pseudo-Scholte wave in the finite-thickness fluid/fluid-saturated porous half-space is related to the ratio of the wavelength to the thickness of the fluid layer; the phase velocity of the shear wave is insensitive to a small number of bubbles dissolved in the pores, but the existence of bubbles has a significant influence on the phase velocity of the compressional wave and the pseudo-Scholte wave. Furthermore, the existence of bubbles can significantly affect the distribution of the pore pressure.

Supersonic Liquid Jets Into Quiescent Gaseous Media: An Adaptive Numerical Study

A computational tool is introduced and applied to the emergence of supersonic liquid jets in quiescent compressible gas. A diffuse interface wave propagation method along with an interface sharpening technique is employed to solve the governing equations of compressible multiphase flows. Adaptive mesh refinement (AMR) strategy is utilized to improve the ability of the solver in better resolving the flow features. The accuracy of our method is benchmarked with four experimental and numerical test problems. Then, the evolution of supersonic liquid jets in compressible gaseous media is simulated; demonstrating a good agreement with experimental observations. Moreover, the impact of physical parameters, such as increment in ambient pressure and inlet velocity on the flow characteristics, is examined. The results indicate that the penetration length of the liquid jet decreases with an increase in the ambient pressure. The values of this parameter compare reasonably well with the experiment-based correlations. Further, with lower ambient pressure the Mach cone generated ahead of the liquid jet has a narrower half angle, situated closer to the jet tip. A similar behavior is demonstrated by the induced shock-front when the inlet Mach number of the liquid jet is increased. The simulations indicate the applicability of our numerical methodology to supersonic liquid jet flows for the analysis of shock waves dynamics and shock–interface interaction.

Interface wave propagation and edge conversion at a low stiffness interphase layer between two solids: A numerical study

The Rayleigh-to-interface wave conversion and the propagation of the resulting symmetric and antisymmetric modes on a bonded interface between solids is analyzed by the two dimensional finite difference time domain method. The propagated patterns were visualized to improve understanding of the phenomena. It is found that the partition of the energy of the interface waves above and below the interface changes repeatedly with propagation distance due to interference between the two modes which have slightly different phase velocities. The destructive interference of those two modes results in dips in the amplitude spectrum of the interface waves, which shift in frequency with propagation distance. The Rayleigh wave received that is created by the interface wave at the exit corner of the joint also shows interference dips in its spectrum. Those dips depend on the interface properties and can potentially be used for interface characterization. Conversion factors related to the interface wave at the upward and downward corners are determined and discussed. As a result, the total transition factor through the upward and downward corners for the interface wave was estimated as 0.37 and would be sufficiently large to probe the interface by coupling from the Rayleigh to the interface wave.

Investigations of interfacial waves at the inlet section in stratified oil–water flows

The formation and evolution of oil–water interfacial waves at the inlet section of a horizontal test pipe was investigated experimentally via high-speed imaging. Images were collected with a Phantom Miro 4 high-speed camera at a rate of 1000fps. Wave velocity, amplitude, frequency and wave length at different oil–water flow rates (input ratios, r=0.6–2.5; mixture velocities, Umix=0.8–2ms−1) were calculated from the images. The fluids used were tap water (ρ=1000kgm−3, μ=0.001kgm−1s−1) and Exxsol D140 oil (ρ=830kgm−3, μ=0.0055kgm−1s−1). The waves formed via a KH mechanism immediately after the junction where the two fluids joined and at a velocity roughly equal to half the mixture velocity with a frequency in the range 11–20Hz for all flowrate combinations. Once formed, and at a short distance from the junction the wave amplitudes decreased while the wave velocities and the wavelengths increased. The frequency, however, remained constant. Experimental data was compared against predictions of the wave theory and the instability analysis. The propagation of interfacial waves at half the mixture velocity was predicted by the theory of dynamic waves. Results from the inviscid stability analysis at the inlet agreed qualitatively with the flow pattern map observed well further downstream the inlet, but quantitative differences were seen, which could be due to the viscosity of the oil phase.

Waves Generated at the Interface Between an Elastic and a Thermo Elastic Solid

In the present note, we study the conditions for propagation of interface waves when one of the solids is a thermo-elastic halfspace and the other an elastic halfspace. The propagation of plane waves along the interface is studied and the frequency equation is derived. In view of the complicated form of this equation, two limiting cases corresponding to very high or very low frequencies are studied. It is also shown that when the coupling constant in the thermo-elastic solid is put equal to zero, the frequency equation reduces to the equation derived by Stoneley. As another particular case, the frequency equations corresponding to very high or very low wave lengths are obtained.

Wavenumber analysis of interface wave characteristics using elastic parabolic equation solutions

Interface waves that travel along the ocean bottom are known as Scholte waves and can contribute to the deep ocean acoustic field, even at depths below the ray-theoretical turning point. Scholte waves spread by the inverse of the square root of range and propagate greater distances along the ocean floor than ocean acoustic energy. Elastic parabolic equation solutions are effective for analysis of Scholte wave behavior with respect to environmental parameters since these waves represent interactions between dilatational and rotational elastic waves resulting from elastic boundary conditions. Generation of interface waves by water column and buried seismic sources will be demonstrated. Hankel transforms of calculated acoustic pressure will be used to evaluate impact of elastic parameters on interface wave amplitudes and ducting effects in elastic sediment layers. The effect of large-scale bathymetry on interface wave propagation will also be investigated. [Work supported by ONR.]

Offshore impact pile driving as a source of opportunity for geoacoustic investigations

Noise generated by offshore impact pile driving can radiate into and propagate through the air, water, and sediment. Most of the recent studies have focused on predicting acoustic pressure field in water to assess environmental impacts. In this study, we focus on the propagation of acoustic energy along the interface between water and ocean bottom. We modeled the interface wave propagation using the commercial Finite Element (FE) code, Abaqus 6.11. A field test is planned for this summer using a scaled model impact pile driving off the dock in the Bay Campus University of Rhode Island (URI). Interface data (particle velocities at the water-sediment interface) will be collected using the Shear Measurement System. Our efforts will focus on identifying the arrivals corresponding to various wave types using data-model comparison. In addition to the interface waves, we will also model the Mach wave front arrival angle. We will explore the possibility of utilizing the arrival times and angles corresponding to these wave types for setting up an inverse problem. This test will also verify the possibility calculating compressional wave speed using a single three-axis geophone by measuring arrival angle of Mach wave front at the interface generated by impact pile driving. [Work sponsored by the Link Foundation Ocean Engineering and Instrumentation PhD Fellowship program.]

Analysis and experimental verification of the relation between Scholte wave velocity and sediment containing two-phase fluid properties

Based on several ultrasonic suspension models, i.e. Urick, Urick-Ament, HT and Mcclements, the Scholte wave propagation characteristics are analyzed at the interface between sediment concentration two-phase fluid and porous medium solid. The interface wave propagation characteristic equation are found using the complex wave number equation given by the aforementioned four models. Relationships between Scholte velocity and the two-phase fluid properties, (e.g., dispersion, volume content, particle size) are discussed. Scholte wave propagation and signal are obtained by Comsol simulation. By using the time delay estimation method, it is found that the obtained Scholte wave velocity are in accord with that given in Urick-Ament and HT models.

Refraction of interfacial waves over a circular hump

Based on the mild-slope equation derived by Smith and Sprinks and the extended refraction–diffraction equation developed by Massel, a two-layer mild-slope equation is constructed for interfacial waves propagating on the interface of a two-layer ocean model. First, Smith and Sprinks's approach is followed to derive the mild-slope equation for the propagation of interfacial waves, with the higher-order terms proportional to the bottom slope and bottom curvature all being neglected. The extended version of the mild-slope equation is then derived with the higher-order terms included. While it is possible to solve the first equation analytically, a numerical solution is presented for the second equation. As part of a verification process, both solutions are compared with each other and also with the single-layer mild-slope equation when the density of the upper layer tends to zero. The new solution is then used to study the effect of the hump dimensions on the refraction of the interfacial waves over a circular hump.

Interfacial wave propagation due to an interfacial line source

Abstract Interfacial wave propagation parallel to a dielectric interface has been studied by considering an electric current line source present at the interface. The first order asymptotic evaluation of field components shows a null of the electric field at the interface. An amplitude null represents an unstable structure in the phase map and a phase front discontinuity across the interface. Higher order asymptotic evaluation has been employed to gain further insight into this propagation problem. The results show that the wavefronts need not be discontinuous. The continuity of the phase fronts is preserved with the help of interesting and stable structures such as saddle points and center points in the phase map of the electric field in both half spaces.

S0803-3-1 超音速蒸気流中の水噴流界面挙動と伝熱流動特性(原子力発電システムおよび要素技術(3))

Supersonic steam injector is a passive jet pump without rotating machine and high efficient heat exchanger because of the direct contact condensation between the supersonic steam and the subcooled water jet. It is considered that flow behavior in the steam injector is governed by the direct contact condensation and complicated turbulent flow with large shear stress induced by velocity difference between the steam and water. However, the studies about the turbulent flow under the large shear stress with direct contact condensation are not enough. Especially mechanisms of the momentum and the heat transfer are not clarified in detail. Objective of the present study is to investigate the turbulent behaviors of the water jet and the interface between the supersonic steam and the water jet. Interfacial wave in the mixing nozzle is observed by using a high speed camera. It is suggested that there are some correlations between the interfacial wave propagation velocity and heat transfer of water jet in the mixing nozzle.

Effect of magnetic field and initial stress on the propagation of interface waves in transversely isotropic perfectly conducting media

Elasto-dynamical equations for transversely isotropic solids have been employed to investigate the general theory of transversely isotropic magneto-elastic interface waves in conducting media under initial hydrostatic tension or compression. Particular cases of interface waves such as Rayleigh, Love and Stoneley waves have been investigated in details. In all cases, the wave velocity equations have been deduced which are in complete agreement with the corresponding results of classical surface waves of the same types where magnetic fields and initial stresses are absent. Results obtained in this paper may be considered as more general and important in the sense that the corresponding results of classical surface waves due to Rayleigh, Love and Stoneley can readily be deduced from our results as special cases. Numerical calculations and graphs have been presented in the case of Love waves and conclusions are drawn.