Interfacial Waves Research Articles

Forces of fully nonlinear interfacial periodic waves on a cylindrical pile in a two-layer fluid with free-surface boundary conditions

In the frame of fully nonlinear potential flow theory, series solutions of interfacial periodic gravity waves in a two-layer fluid with free surface are obtained by the homotopy analysis method (HAM), and the related wave forces on a vertical cylinder are analyzed. The solution procedure of the HAM for the interfacial wave model with rigid upper surface is further developed to consider the free surface boundary. And forces of nonlinear interfacial periodic waves are estimated by both the classical and modified Morison equations. It is found that the estimated wave forces by the classical Morison equation are more conservative than those by the modified Morison’s formula, and the relative error between the total inertial forces calculated by these two kinds of Morison’s formulae remains over 25% for most cases unless the upper and lower layer depths are both large enough. It demonstrates that the convective acceleration neglected in the classical Morison equation is rather important for inertial force exerted by not only internal solitary waves but also interfacial periodic waves. All of these should further deepen our understanding of internal periodic wave forces on a vertical marine riser.

Attenuation in hydroelastic response of floating-elastic-plate by porous membrane in two-layer fluid with bottom undulation

The prime intention of this article is to study the effects of bottom undulation and a porous membrane barrier on the hydroelastic response of an elastic plate floating in a two-layer fluid with changing bottom topography assuming the small amplitude waves and potential flow theory. Finite and semi-infinite plates coupled with porous membrane barriers are considered in this study. As a mathematical technique, the eigenfunction expansion method along with an approximation method mild-slope are adopted for the uniform bottom and variable bottom topographies, respectively. In the variable bottom topography, a system of differential equations is solved. By using matching and jump conditions, the solution is expressed as a linear algebraic system, from which the unknown constants of interest are computed. The effects of fluid density ratio, water depth ratio, bottom topography, and porous membrane on the bending moment, shear force, and deflection of the elastic plate are studied. It is found that when the density ratio becomes closer to one, the bending moments and shear forces acting on the elastic plates tend to diminish. The variations in the bending moments, shear forces, and plate deflection with respect to changing density ratios are found to be in opposite trends caused by surface and interfacial waves, respectively. With higher tension and a less porous membrane, the bending moment, shear forces, and pate deflection are reduced. Concave-up bottoms reflect more surface wave energy, whereas concave-down bottoms reflect more interfacial wave energy. The observations made in this article may help in analyzing the response of very-large floating structures in the presence of an undulating seabed.

Stability and Bifurcation Analysis of Two-Immiscible Liquids Film Down an Inclined Slippery Solid Substrate

In this work, the dynamic behavior of linear and nonlinear waves propagating at the separating surface between two thin layers of viscous Newtonian fluids is studied in the presence of the effect of insoluble surface surfactant. The two liquids are confined between two infinite rigid parallel plates and assumed to have different densities and viscosities. The equations of evolution for surface-wave elevation and concentration of surfactant are derived using the lubrication approximation. In the linear stage, by utilizing the normal mode approach, we have derived the dispersion relation that relates the wave angular frequency to the wave number and other parameters that is solved numerically to inspect the influences of some selected parameters on the stability criteria of the fluid flow. Also, analytical expressions for the growth rate as well as its maximum value with corresponding wave number are obtained in the special case of long-wave limiting. It is concluded that the Marangoni number text {Ma} has acquired a significant stabilizing influence on the fluid flow, whereas the inverse of the slippery length of substrate plate beta, resorts to the destabilize the motion of the interfacial waves. Consequently, both of the Marangoni number and the substrate slippy coefficient can be utilized to control the film flow regime, where they preserve the film laminar flow and tend to prevent the film breakdown. These can be useful in many industrial applications such as coating processes, heat exchangers, cooling microelectronic devices, chemical reactors, food processing, thermal protection design of combustion chambers in rocket engines and operation of Laser cutting and heavy casting production processes.

Surface wave height distributions and rogue wave probabilities on two-layer fluids

Rogue waves are individual ocean surface waves much larger than the prevailing wave field. In high sea states they can be a danger to marine operations. Rogue waves are well studied for unstratified water. However, on a two-layer fluid the surface wave spectra are modified due to triad interactions with interfacial waves. Such triad interactions are not possible in homogeneous water. We find the modified surface spectrum reduces rogue waves. These findings are relevant for the changing polar oceans where prolonged ice melt is expected to facilitate open water with higher sea states while also creating a surface layer of freshwater overlaying salt water, as in our idealized model calculations.

Interfacial wave of the gas-liquid two-phase flow in unsaturated reservoir pores

Unsaturated reservoir pores exist widely in porous self-lubricating materials for the continuous consumption of lubricant. The complex gas-liquid two-phase flow behavior in the pores significantly affects the self-lubricating performance. In this paper, the two-phase flow model in unsaturated pores was established based on the Couple Level Set and Volume of Fluid method. Two kinds of porous materials with significantly different wettability, stainless steel and polytetrafluoroethylene (PTFE), were concerned. The two-phase flow behaviors were investigated to reveal the flow mechanism in the unsaturated pores. The different flow behaviors caused by the wettability of materials were quantitative characterization. Results show that, the gas rises with a convex interface in the stainless steel pore, and the bubble is generated after the contact line is pinned on the edge of the pore at 35 ms. While in the PTFE pore, the gas rises with a concave interface. And the gas profile changes from concave to convex after the contact line is pinned at 32 ms. In the two pores, the gas-liquid interface fluctuates periodically. In the hydrophilic stainless steel pore, the fluctuation amplitude decreases and finally tends to be stable with the increase of time. In the hydrophobic PTFE pore, the interface has constant fluctuation amplitude for the attraction between gas and the hole wall. The fluctuation of the gas-liquid interface has an important influence on the flow state of the lubricant film. The results help to clarify the two-phase flow mechanism within unsaturated pores, and provide guidance for the self-lubrication design of the porous materials.

Mechanism of transition between separated and non-separated oil-water flows in inclined pipe

The analysis of drop formation and the transition between separated and non-separated oil–water flows enables us to better regulate flow parameters and pipe inclination angle, which is of great significance for improving the efficiency of oil transportation. Previous studies mainly carried out qualitative analysis through experiments and studied the transition between separated flows, very few studies are conducted on the transition between separated flow and dual continuous flow or intermittent flow. In addition, the influence of pipe inclination angle was not considered in the study of drop formation, which results in inadequate force analysis of drop. This article presents the use of dimensionless numbers to predict the transition between separated flow and dual continuous flow or intermittent flow. The relation expression between dimensionless numbers is obtained by regression of experimental data. The critical values of flow parameters and pipe inclination angle can be calculated by the relation expression between dimensionless numbers and flow parameters. In addition, this article proposes a three-dimensional interfacial wave shear deformation mechanism by adding volume forces to the force analysis for the possible inclined pipe. The prediction equation is obtained and the critical value of flow parameters and pipe inclination angle for drop formation can be calculated, which are in good agreement with the experimental data.

Dynamics of Taylor bubble interface in vertical turbulent counter-current flow

Dynamics of the Taylor bubble interface in the vertical counter-current flow was analyzed with video recordings at 100 – 800 frames per second. Taylor bubbles in air-water mixture were studied on time intervals of up to several minutes in stagnant conditions, where buoyancy is dynamically balanced by the inertial bubble drag in the downward turbulent flow. Taylor bubbles of length from 4 to 10 cm were observed in a pipe of 26 mm diameter at Reynolds numbers based on liquid superficial velocity around 6000. Algorithms, developed for analysis of the interface from the video frames were dedicated to the analysis of the cap and the body of the Taylor bubble. The long time averaging of up to 10 min samples do not end up with axisymmetric time-averaged shape of the bubble, but with an asymmetric bullet-train shape, with the thinnest liquid film observed on the belly of the bullet-train shape bubble. The main result of this study is based on high relative sensitivity of our measurements, which was sufficient to track the dynamics of the tiny disturbance waves with a tenth of mm amplitudes traveling along the interface of the Taylor bubble. Cross-correlations of time-dependent interface fluctuations measured at different spatial positions allowed us to measure propagation speeds of the interface waves. When averaged over sufficiently long time intervals of around a minute, the time averaged propagation velocities are shown to be equal to the convective velocity of the interface. Moreover, waves propagating on both sides of the two-dimensional photographs show clear correlation; crest of the wave on one side of the bubble photograph corresponds to the trough of the wave on the other side.

Phase-locked measurements of linear and weakly nonlinear interfacial waves in a stratified turbulent gas–liquid pipe flow

The present work reports an experimental characterization of linear and weakly nonlinear interfacial waves in a stratified air–water horizontal pipe flow. An oscillating paddle was employed to generate controlled waves at the liquid interface. The driving signal of the oscillating paddle was controlled and synchronized with image acquisitions, enabling phase-locked measurements and the application of ensemble averaging techniques. Velocity field measurements in the liquid and gas phases were performed simultaneously using an off-axis particle image velocimetry setup and shadowgraphy. The combined techniques allowed us to extract the coherent part of flow fluctuations related to the excited waves. This was done for a range of flow rates and wave frequencies. The selected conditions are close to the transition from stratified to slug/plug flow regimes. In the presence of linear waves, the coherent disturbances in both phases were weakly dependent on near-wall disturbances. Flow changes in the presence of weakly nonlinear waves were also investigated. In these cases, noticeable modifications in the mean flow and in turbulence distribution were observed near the interface, whereas close to the wall, the flow was weakly affected. This investigation follows the work of Farias et al. [“Characterization of interfacial waves in stratified turbulent gas-liquid pipe flow using Particle Image Velocimetry and controlled disturbances,” Int. J. Multiphhase Flow 161, 104381 (2023)], where the threshold for linear and weakly nonlinear waves was studied. Here, a clear comparison between wave-induced disturbances in linear and weakly nonlinear regimes is reported in the literature for the first time for stratified turbulent gas–liquid pipe flows. The methodology proposed is relatively simple and can contribute to describe wave-related phenomena in stratified pipe flows.

Theoretical model on the slug/churn transition based on the generation and evolution of the huge waves

Previous experimental studies have proved that the flooding of the falling film surrounding the Taylor bubble is attributed to the transition from the slug flow to the churn flow, which is related to the generation and evolution of huge waves. In the present study, theoretical models on the basis of the Kelvin–Helmholtz instability of the falling film around the Taylor bubble and kinematic analysis of the interfacial wave traveling on the falling film are, respectively, established to reveal the mechanism of the slug/churn transition. The formation of the liquid bridge or pseudo-liquid bridge is taken as the judgment basis to determine the transition. A term named “most dangerous wave” is introduced in the present study, and its criteria is related to the ratio of wave amplitude to pipe diameter. Verified by the data and models in the literature, the proposed model is demonstrated to have satisfactory predicting accuracy. In addition, parameters, including pipe diameter and system pressure, are analyzed in detail to discuss their effect on the slug/churn transition. The results indicate that the slug/churn boundaries move downward as the system pressure increases but upward with the increasing pipe diameter. We believe that the findings in this paper benefit a better understanding of the relation between the huge waves and slug/churn transition.

A mathematical study of water wave interaction with a thin perforated barrier in a two-layer fluid over a permeable bottom

This article studies the impact of a submerged interface-piercing perforated barrier in a two-layer fluid flowing over a permeable bottom. We investigate oblique wave scattering, trapping and radiation due to the structure focusing on the bottom permeability. The dead water phenomenon is analysed with the consideration of the bottom permeability, which results in a higher variation of the interfacial wave due to the bottom permeability. The matched eigenfunction expansion method and the least square technique are used to calculate various hydrodynamic coefficients. Wave energy identity relation is derived for the scattering scenario, and the associated energy loss due to the barrier is calculated. In order to attain the maximum wave dissipation, an ideal porous-effect parameter of the barrier is proposed for consideration, and it is observed that larger values of porous-effect parameter result in the lowest feasible pressure distribution. A good comparison with a prior result justifies the current semi-analytical procedure. Furthermore, the verification of the energy-identity terms aid in the validation of the computed results. Additionally, wave trapping in a confined region is examined by investigating reflection coefficients by considering a rigid wall. The thin perforated barrier model is further considered for examining the radiation aspect while considering its slow motion. For various porous-effect parameters of the barrier, the amplitude ratio of the radiated potential is investigated, and it is clearly observed that higher frequency significantly lowers the amplitude for both free surface and interfacial propagating modes. The impact of the perforated barrier is analysed by investigating the essential hydrodynamic coefficients, namely, added mass and damping coefficient.

Schoch Effect in Topological Phononic Crystals

This article investigates the Schoch negative displacement phenomenon at the interface between two-dimensional topological acoustic materials and traditional materials. The results show that a negative Schoch displacement occurs at the frequency of the Dirac point in the phononic crystal. At this point, the reciprocal of the effective bulk modulus of the phononic crystal tends to zero, making it an acoustic metamaterial with a refractive index close to zero. At the same time, the maximum value of the effective impedance of the phononic crystal and the real part of the reflection coefficient undergo a 2π phase transition at the corresponding frequency. When the phononic crystal is spliced into a topological supercell structure, a larger negative Schoch displacement is observed. This study demonstrates that topological phononic crystals can achieve negative Schoch displacement. The negative Schoch displacement realized in this article provides a new theoretical reference for designing acoustic devices based on interface waves.

Effect of Strain Rate on Compressive Properties of Aluminium-Graphene Composites

Graphene-reinforced aluminium composites have been widely studied due to their excellent mechanical properties. However, only a few studies have reported their dynamic compression properties. The purpose of this study is to investigate the quasi-static and dynamic compression properties of graphene-reinforced aluminium composites. The addition of graphene improved the compressive stress resistance and energy absorption capacity of the aluminium matrix. An aluminium-0.5 wt.% graphene composite exhibited good compressive properties due to the different interfacial wave impedance generated by the additional grain boundaries or Aluminium-Graphene interfaces.

Interface transmittance and interface waves in acoustic Willis media

Acoustics Willis media, known as bianisotropic acoustic media, incorporate additional coupling between pressure and velocity and between momentum and volumetric strain in their constitutive equation. The extra coupling terms have a significant influence on acoustic wave behavior. In this paper, the unusual wave phenomena relevant to interfaces between homogeneous acoustic Willis media are theoretically studied. We show that Willis media offer more flexible control in wave front and energy flow when waves are transmitted through an interface. Different from traditional acoustic fluid, Willis acoustic media support edge and interface waves, for which the existence conditions and corresponding wave features are systematically investigated. The study unveils more possibilities for manipulating acoustic waves and may inspire new functional designs with acoustic Willis metamaterials.

A mathematical analysis of the Kakinuma model for interfacial gravity waves. Part I: Structures and well-posedness

We consider a model, which we named the Kakinuma model, for interfacial gravity waves. As is well known, the full model for interfacial gravity waves has a variational structure whose Lagrangian is an extension of Luke’s Lagrangian for surface gravity waves, that is, water waves. The Kakinuma model is a system of Euler–Lagrange equations for approximate Lagrangians, which are obtained by approximating the velocity potentials in the Lagrangian for the full model. In this paper we first analyze the linear dispersion relation for the Kakinuma model and show that the dispersion curves highly fit that of the full model in the shallow water regime. We then analyze the linearized equations around constant states and derive a stability condition, which is satisfied for small initial data when the denser water is below the lighter water. We show that the initial value problem is in fact well posed locally in time in Sobolev spaces under the stability condition, the noncavitation assumption, and intrinsic compatibility conditions, in spite of the fact that the initial value problem for the full model does not have any stability domain so that its initial value problem is ill posed in Sobolev spaces. Moreover, it is shown that the Kakinuma model enjoys a Hamiltonian structure and has conservative quantities: mass, total energy, and in the case of a flat bottom, momentum.

Airborne coherent wind lidar measurements of the momentum flux profile from orographically induced gravity waves

Abstract. In the course of the GW-LCYCLE II campaign, conducted in Jan/Feb 2016 from Kiruna, Sweden, coherent Doppler wind lidar (2 µm DWL) measurements were performed from the DLR Falcon aircraft to investigate gravity waves induced by flow across the Scandinavian Alps. During a mountain wave event on 28 January 2016, a novel momentum flux (MF) scan pattern with fore and aft propagating laser beams was applied to the 2 µm DWL. This allows us to measure the vertical wind and the horizontal wind along the flight track simultaneously with a high horizontal resolution of ≈800 m and hence enables us to derive the horizontal MF profile for a broad wavelength spectrum from a few hundred meters to several hundred kilometers. The functionality of this method and the corresponding retrieval algorithm is validated using a comparison against in situ wind data measured by the High Altitude and Long Range (HALO) aircraft which was also deployed in Kiruna for the POLSTRACC (Polar Stratosphere in a Changing Climate) campaign. Based on that, the systematic and random error of the wind speeds retrieved from the 2 µm DWL observations are determined. Further, the measurements performed on that day are used to reveal significant changes in the horizontal wavelengths of the vertical wind speed and of the leg-averaged momentum fluxes in the tropopause inversion layer (TIL) region, which are likely to be induced by interfacial waves as recently presented by Gisinger et al. (2020).

Dynamic response of an elliptic cylinder inclusion with imperfect interfaces subjected to plane SH wave

Underground chambers or tunnels often contain inclusions, the interface between the inclusion and the surrounding rock is not always perfect, which influences stress wave propagation. In this study, the imperfect interface and transient seismic wave were represented using the spring model and Ricker wavelet. Based on the wave function expansion method and Fourier transform, an analytical formula for the dynamic stress concentration factor (DSCF) for an elliptical inclusion with imperfect interfaces subjected to a plane SH-wave was determined. The theoretical solution was verified via numerical simulations using the LS-DYNA software, and the results were analyzed. The effects of the wave number (k), radial coordinate (ξ), stiffness parameter (β), and differences in material properties on the dynamic response were evaluated. The numerical results revealed that the maximum DSCF always occurred at both ends of the elliptical minor axis, and the transient DSCF was generally a factor of 2–3 greater than the steady-state DSCF. Changes in k and ξ led to variations in the DSCF value and spatial distribution, changes in β resulted only in variations in the DSCF value, and lower values of ωp and β led to a greater DSCF under the same parameter conditions. In addition, the differences in material properties between the medium and inclusion significantly affected the variation characteristics of the DSCF with k and ξ.

Temperature Dependence of Interface Characterization and Mechanical Properties of TA1/Q235 Composite Fabricated by Explosive Welding

Herein, the interface characterization and tensile properties of TA1/Q235 composite fabricated by explosive welding are investigated in the temperature range 650–950 °C. The explosive‐welded TA1/Q235 composite presents the periodic wavy bonding interface with both the vortex and solid–solid bonding regions. Some defects, including cavities, cracks, and brittle intermetallic compounds, are located in the melted zone of the interface wave. The compound layer comprises FeTi and Fe2Ti, with a thickness of 25 μm. In terms of high‐temperature tensile tests, the elongation of the TA1/Q235 composite exhibits a tendency of first increasing and then decreasing with increasing tensile temperature. And the elongation reaches the peak value of 95% at 800 °C. The tensile strength basically decreases with increasing temperature, except for a slight increase at 900 °C. The failure of the TA1/Q235 composite is affected by both the discontinuous compound and the continuous compound layers. With the increase in tensile temperature, a continuous compound layer with a certain thickness dominates the failure of the TA1/Q235 composite.

Experimental and numerical investigations on interface microstructure characteristics and wave formation mechanism of Sn/Cu explosive welded plates

ABSTRACT The interface characteristics and formation mechanism of explosive welded waveform structures still lack a detailed and in-depth research. Thus, a combination of advanced characterization and numerical simulation methods were performed in this study to investigate the phase constitution, texture distribution, 3D interface morphology and wave formation mechanism of Sn/Cu explosive welded interface. The microstructure analyses indicated that the typical waveform structures composed of fine crystal band and elongated grains zone were formed at the Sn/Cu joining interface. The dynamic recrystallized structures and local high strain at the waveform were attributed to severe rheological deformation and rapid solidification of liquid metals. In addition, the S, copper, brass and fiber deformation textures and the cube and gross recrystallization textures were found. The CT results indicated the 3D Sn/Cu joining interface morphology presents a regular convex waveform feature, which is related to periodic pulse load caused by explosive detonation. Furthermore, based on the simulation results, the 2D joining interface presents similar experimental waveform structure, and the 3D interface evolution characteristic was consistent with the shock wave propagation characteristics on the flying plate to some extent, which was in good agreement with the experimental results.

Stability analysis from higher order nonlinear Schrödinger equation for interfacial capillary-gravity waves

Stability analysis from higher order nonlinear Schrödinger equation for interfacial capillary-gravity waves

Nonlocal antiplane shear interfacial waves

In this paper, non-local shear interfacial waves between two non-local elastic half-spaces in perfect contact along a common boundary are investigated. For the sake of simplicity, an anti-plane problem formulated through the framework of Eringen’s theory is considered. The non-locality is taken only in the transverse coordinate making the analysis of the problem easier than that of non-local problems of 2D. Effective boundary conditions are obtained, with the help of a small internal characteristic length scale, along the interface utilizing an asymptotic approach enabling one to write the non-local stresses through their local counterparts. Antiplane non-local shear interfacial waves are analysed by the derived formulation. Numerical results are presented for certain characteristic values of the problem parameters.