Interfacial Waves Research Articles

Effect of substrate stiffness on interfacial Schallamach wave of flexible film/substrate bilayer structure: Cohesive contact insight

As the critical feature of the stick-slip for soft materials, the interfacial Schallamach waves of flexible composite structures are essential for smart tactile sensors to realize sliding perception. Herein, the Schallamach waves of polydimethylsiloxane film/substrate bilayer structures with three substrate stiffnesses regulated by porosities are investigated by setting up in-situ sliding tests and establishing finite element models with mixed-mode cohesive contact. Inhomogeneity in microcontact stiffness disrupts the continuity and synchronization of the Schallamach waves, resulting in non-periodic fluctuations in the contact force. The buckling phenomenon of the film structure marks the transition from stick to slip. This buckling induces a shift at the crack front from normal compressive stress to tensile stress, leading to mixed-mode damage.

What Happens When Two Ruptures Collide?

AbstractWe investigate the interaction between two rupture fronts as they propagate toward each other and ultimately collide. This phenomenon was observed during laboratory experiments conducted on poly methyl methacrylate. Subsequently, we used numerical simulations to elucidate key aspects of these observations and draw broader conclusions. Our findings indicate that the collision of the rupture fronts generates interface waves that propagate along the sliding interface at the Rayleigh wave speed. Additionally, the rupture fronts interact with the starting and stopping S‐wave phases radiated by the opposite rupture fronts, which can locally change their velocity and generate additional interface waves. We discuss the implications of these results for understanding earthquake source phenomena.

Evolution of linear internal waves over large bottom topography in three-layer stratified fluids

Evolutions of internal waves of different modes, particularly mode 1 and mode 2, passing over variable bathymetry are investigated based on a new numerical scheme. The problem is idealized as interfacial waves propagating on two interfaces of a three-layer density stratified fluid system with large-amplitude bottom topography. The Dirichlet-to-Neumann operators are introduced to reduce the spatial dimension by one and to adapt the three-layer system and significant topographic effects. However, for simplicity, nonlinear interactions between interfaces are neglected. Numerical techniques such as the Galerkin approximation, proven effective in previous works, are applied to save computational costs. Shoaling of linear waves on an uneven bottom is first studied to validate the proposed formulation and the corresponding numerical scheme. Then, for two-dimensional numerical experiments, mode transition phenomena excited by locally confined bottom obstacles and quickly varying topographies, including the Bragg resonance, mode-2 excitation, wave homogenization, etc., are investigated. In three-dimensional simulations, internal wave refraction by a Luneberg lens is considered, and good agreement is found in comparison with the ray theory. Finally, in the limiting case, when the top layer can be negligible (for example, a gas layer of extremely small density), the problem is reduced to a two-and-a-half-layer fluid system, where an interface and a surface are unknown free boundaries. In this situation, the surface signature of an internal wave is simulated and verified by introducing the realistic bathymetry of the Strait of Gibraltar and qualitatively compared with the satellite image.

Propagation of underwater wave groups in a compressible ocean coupled with an elastic seafloor

The overall system of interest is an infinite half-space in which a compressible ocean is the top layer and an elastic seafloor (together with the crust beneath) forms a semi-infinite bottom layer. Whereas water-column compression waves and seafloor waves individually have received considerable attention, not much is known about their propagation as groups. This work utilizes the group behaviour of these waves to derive energy balance relations for wavenumber spectra for wave groups propagating through a mildly non-uniform water-column–seafloor system. Dispersion relations for the coupled system are derived using known kinematic and kinetic conditions at the interface, and free and forced wave solutions for the wavenumber spectra are obtained, with particular attention to the case when certain frequency–wavenumber combinations in the forcing excite the two-media system into resonance. Wavenumber spectra predicted using the theory for mildly non-uniform media are found to be close to those predicted assuming uniform media, though the effect of non-uniformity becomes more noticeable as the groups propagate farther from the generation area. Here, nonlinear interactions among stationary, random multi-directional surface-wave fields provide the forcing for groups of compression waves in the water and surface waves on the seafloor. The formulation includes the cumulative effect of multiple generation areas along the group propagation direction. Comparisons with observational data from a sensor array in the Atlantic Ocean indicate that the theory can be applied to reconstruct plausible combinations of generation areas and interaction times that are consistent with the measured data, for deriving approximate predictions at down-wave distances along the group propagation directions. Implications of this and other findings are discussed for (i) the potential for energy conversion from water-column compression waves on the seafloor, (ii) tracking of tropical cyclones from the seafloor, and (iii) quantification and comparative assessment of low-frequency mid-ocean ambient noise and microseism activity.

Back‐Propagating Rupture: Nature, Excitation, and Implications

AbstractRecent observations show that certain rupture phase can propagate backward relative to the earlier one during a single earthquake event. Such back‐propagating rupture (BPR) was not well considered by the conventional earthquake source studies and remains a mystery to the seismological community. Here we present a comprehensive analysis of BPR, by combining theoretical considerations, numerical simulations, and observational evidences. First, we argue that BPR in terms of back‐propagating stress wave is an intrinsic feature during dynamic ruptures; however, its signature can be easily masked by the destructive interference behind the primary rupture front. Then, we propose an idea that perturbation to an otherwise smooth rupture process may make some phases of BPR observable. We test and verify this idea by numerically simulating rupture propagation under a variety of perturbations, including a sudden change of stress, bulk or interfacial property and fault geometry along rupture propagation path. We further cross‐validate the numerical results by available observations from laboratory and natural earthquakes, and confirm that rupture “reflection” at free surface, rupture coalescence and breakage of prominent asperity are very efficient for exciting observable BPR. Based on the simulated and observed results, we classify BPR into two general types: interface wave and high‐order re‐rupture, depending on the stress recovery and drop before and after the arrival of BPR, respectively. Our work clarifies the nature and excitation of BPR, and can help improve the understanding of earthquake physics, the inference of fault property distribution and evolution, and the assessment of earthquake hazard.

Trigger mechanism for a singing cavitating tip vortex

The discrete tone radiated from tip vortex cavitation (TVC), known as ‘vortex singing’, was recognized in 1989, but its triggering remains unclear for over thirty years. In this study, the desinent cavitation number and viscous correction are applied to describe the dynamics of cavitation bubbles and the dispersion relation of cavity interfacial waves. The wavenumber-frequency spectrum of the cavity radius from the experiment in CSSRC indicates that singing waves predominantly consist of the stationary double helical modes (kθ = 2- and -2+) and the breathing mode (kθ = 0-), rather than standing waves as assumed in previous literatures. Moreover, two trigger mechanisms, expressed by two triggering lines, are proposed: the twisted TVC, initially at rest, is driven into motion through the corrected natural frequency (fn) due to the step change of the far-field pressure. Subsequently, the frequency associated with the zero-group-velocity point (ῶzgv) at kθ = 0- is excited through ῶi, the frequency at the intersection of dispersion curves at kθ = 0- and -2+, or ῶj, the frequency at the intersection of dispersion curves at kθ = 0- and 2-, corresponding to two types of the vortex singing triggering. These solutions, without empirical parameters, are validated using singing conditions provided by CSSRC and G.T.H., respectively. Furthermore, the coherence and the cross-power spectral density spectrum indicates a large-scale breathing wave propagating along the singing cavity surface and travelling from downstream to hydrofoil tip, providing us a comprehensive understanding for the triggering of vortex singing.

Simulation of Interfacial Waves in Core-Annular Pipe Flow with a Turbulent Annulus

Abstract Numerical simulations are conducted for the wave initiation, growth, and saturation at the oil-water interface in core-annular flow. The focus is on conditions with a turbulent water annulus, but the laminar water annulus is also considered. The simulation results are compared with lab measurements. The growth rate for the linear instability of different wave lengths in the case of a turbulent water annulus is obtained from two-dimensional axisymmetric Reynolds-Averaged Navier-Stokes simulations with the Launder-Sharma low-Reynolds number k-e model. The latter simulation results provide the most unstable wave length for the turbulent water annulus. Our study also shows the following. The maximum wave growth rate for a turbulent water annulus is significantly higher than for a laminar water annulus. The most unstable wave length in the simulations is about 25% smaller than in the experiments. The wave amplitude for the different wave lengths in the simulations is typically 17% lower than in the experiments.

Steady-state interfacial gravity waves with one-dimensional class-III triad resonance

Steady-state interfacial gravity waves with one-dimensional class-III triad resonance

Evolution of static and dynamic magnetic properties of Re/Co/Pt and Pt/Co/Re trilayers with enhanced Dzyaloshinskii-Moriya interaction

The influence of Re layer insertion either at the bottom or top interface of epitaxially grown Pt/Co/Pt heterostructures on their static and dynamic magnetic properties is discussed in terms of their crystalline structure. Magnetic properties were studied as a function of both Re and Co layer thicknesses (dRe and dCo, respectively) in the matrix-like samples with a double-wedge structure, in which the layer thickness gradients were oriented orthogonally. The comprehensive investigations of the changes in coercivity, perpendicular magnetic anisotropy, spin reorientation transition, interfacial Dzyaloshinskii-Moriya interaction (iDMI) and spin wave damping are reported. Two different magnetic phases depending on the Co layer thickness with volume anisotropies (determined without demagnetization term) of KV∼0.25 (low) and KV∼0.75 MJ/m3 (high) were observed. The relation between these phases depends on the stack sequence and thickness of Re inserted layer. For dRe = 0.2 ÷ 0.7 nm deposited as the bottom interface, dCo induced transition at dtr ∼ 2 nm from low to high volume anisotropy phases was observed. Low and high volume anisotropy phases are associated to Co fcc and hcp structural phases. The insertion of half atomic layer of Re had no influence on surface anisotropy but significantly enhanced iDMI above 1 pJ/m and reduced spin wave damping.

Insights into the fluid dynamics of bioaerosol formation in a model respiratory tract

Bioaerosols produced within the respiratory system play an important role in respiratory disease transmission. These include infectious diseases such as common cold, influenza, tuberculosis, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) among several others. It is, therefore, of immense interest to understand how bioaerosols are produced within the respiratory system. This has not been extensively investigated. The present study computationally investigates how bioaerosols are produced in a model respiratory tract due to hydrodynamic interactions between breathed air and a thin mucus layer, which lines the inner surface of the tract. It is observed that Kelvin–Helmholtz instability is established in the thin mucus layer due to associated fluid dynamics. This induces interfacial surface waves which fragment forming bioaerosols under certain conditions. A regime map is created—based on pertinent dimensionless parameters—to enable identification of such conditions. Analysis indicates that bioaerosols may be produced even under normal breathing conditions, contrary to expectations, depending on mucus rheology and thickness of the mucus layer. This is possible during medical conditions as well as during some treatment protocols. However, such bioaerosols are observed to be larger (∼O(100)μm) and are produced in less numbers (∼100), as compared to those produced under coughing conditions. Treatment protocols and therapeutic strategies may be suitably devised based on these findings.

The best whistler: A cavitating tip vortex

The discrete tone radiated from a cavitating tip vortex, known as “vortex singing,” was first recognized in 1989, but its sound generation mechanism has remained a mystery for over 30 years. In this Letter, by means of the correction for the cavitation bubble dynamics and the dispersion relation of cavity interfacial waves, we found that after the far-end disturbances propagate upstream, the whistling vortex should be triggered by near-end sound sources, the breathing mode waves. Further utilizing the theoretical solutions for singing lines and the potential singing cavitation number with frequency, we accurately identified all available tests for seeking the vortex singing over the past three decades, which not only demonstrates that the vortex singing frequency is only determined by the measurable mean cavity radius (rc), cavitation number (σ), and desinent cavitation number (σd) in experiments, but also responses to a long-standing perplexity: why such a best whistler is able to appear only within a narrow range of the cavitation number.

Multi-field coupling in the scrape-off layer of tokamak plasma

Abstract We study a reduced electrostatic fluid model for the tokamak scrape-off layer (SOL), which incorporates temperature gradient and vorticity gradient as two free energy fields. Two scenarios of field coupling are addressed: (1) sheath condition; (2) vortex wave coupling. For the sheath condition induced field coupling, the poloidal E×B flow shear is coupled with the temperature gradient. Combining an eigenmode analysis and the nonlinear phase dynamics approach, our findings indicate that in the absence of a vorticity gradient, the overall effect of the sheath condition induced flow shear can either stabilize or destabilize the interchange mode, depending on the competition between the flow shear suppression and the temperature gradient driving. This is different from the case where the gradient drive and shear damping are decoupled. When the field coupling is mediated by wave interactions, by setting an idealized step-like temperature and vorticity profiles, a joint mode forms through resonant interaction between the interfacial waves driven by the temperature and vorticity gradients, respectively. Near the phase locking condition, the joint mode can be more unstable than pure temperature gradient driven mode.

Modulation of the wake of a horizontal cylinder by pycnocline thickness in stratified flow

This study investigates the modulating effect of the pycnocline thickness in two-dimensional stratified flow on a cylinder. It encompasses three typical flow regimes identified by Boyer in experiments conducted within the Reynolds number range of Re = 260–2000. Quantitative control of the modulation effect of internal interface waves on the cylinder wake is achieved by varying the thickness of the pycnocline. Under appropriate thickness of the pycnocline, a multiple-centerline-structure can transition to isolated-mixed-structure flow regimes and Double-Eddy-Wavy-Wake flow regimes. Similar modulation patterns are also observed in isolated-mixed flow regimes. Normalized pressure distribution and velocity fields indicate that in low Reynolds number flow regimes (Re < 600), downstream isolated mixed regions generate dynamic pressure that periodically cascades upstream. This periodic reverse energy transfer provides favorable adverse pressure gradients, cyclically reducing the drag force on the cylinder. The cyclic period is, for the first time, classified into four stages: dynamic pressure storage stage, dynamic pressure transfer stage, dynamic pressure consumption stage, and dynamic pressure exhaustion stage. Despite the highly nonlinear modulation effect of internal interface waves in low Reynolds number conditions, the linear predictive theory of lee waves based on streamline equations remains instructive in predicting the trend of lee waves wavelength variation with pycnocline thickness. Drawing upon the modulation study results concerning the pycnocline thickness on lee waves, a regime map is constructed, illustrating the directional evolution of lee waves flow patterns based on variations in pycnocline thickness.

NUMERICAL COMPUTATION OF ONE- AND TWO-LAYER SHALLOW FLOW MODEL

In this research, we study a proficient computational model designed to simulate shallow flows involving one- and two-layer shallow flow. This numerical model is built upon the Saint Venant equations, which are widely used in hydraulics to depict the behavior of shallow water flow. The numerical scheme used here is constructed based on the conventional leapfrog technique implemented on a staggered grid framework, referred to as MCS. The primary objective of this research is to re-examine and implement the MCS in accurately modelling the free surface and interface waves produced by different flows passing through irregular geometries. Unlike the conventional MCS, we modify the momentum conservation principle to be more general, accommodating a non-negative wet cross-sectional area due to irregular geometry. We successfully conduct numerous numerical simulations by examining various scenarios involving one-layer and two-layer flow through irregularly shaped channels or structures. Our results show that the correct surface wave profile generated by a one-dimensional dam break through the triangular obstacle in the open channel can be simulated very well. Comparison with the existing experimental data seems promising although some disparities are being found due to dispersive phenomena with RMSE less than 5%. Furthermore, our scheme is successfully extended to simulate the steady sub-maximal exchange in two-layer flows using specific boundary conditions. The alignment between the submaximal numerical results with exchange flow theory is noticeable in the interface profile, characteristics of flow conditions and the flux values achieved when the steady situation occurs. These satisfying results indicate that our proposed numerical model can be used for practical needs involving various flow situations both one and two-layer cases

Scaling of turbulence-forced capillary waves

We simulate the propagation of capillary waves at the interface between two liquid layers of equal density, viscosity and thickness, which flow in stratified conditions inside a turbulent Poiseuille channel. This setup gives us the possibility to single out the effect of inertia and surface tension – in isolation from gravity – on the propagation of interfacial capillary waves. Numerical simulations, which are based on a combined pseudo spectral/phase field method, are run keeping the shear Reynolds number constant, Reτ=300, and considering four different values of the Weber number: We=0.5, We=1.0, We=1.5 and We=2.0. In the present case, waves are naturally forced by turbulence over a broad range of scales, from the larger ones, whose size is of order of the channel height h, down to the smaller dissipative scales. We show that, by increasing the Weber number, the interface is deformed more vigorously, and is prone to sustain the propagation of waves over a broader range of scales. Upon computation of the power spectra of wave elevation, we show that the behavior of waves agrees with the theoretical predictions given by the weak wave turbulence theory, which predicts a decay Sη(k)∼k−4 in the inertial regime, followed by a steeper decay at large k, in the surface-tension-dominated regime. We clearly show that the transition between the inertial and the surface-tension-dominated regime is pushed towards larger k by increasing the Weber number. In addition, we show that the two-dimensional frequency–wavenumber spectra of the wave elevation – the dispersion relation – is in good agreement with well established theoretical prediction, ω(k)∼k3/2, and that the range of validity of such prediction broadens for increasing Weber number.

Insight on Interfacial Microstructure and Corrosion Characteristics of Mg/Al Explosive Welded Composite Plates

Interfacial corrosion performance is crucial to the reliability of Mg/Al explosively welded composite plates. Nevertheless, more understanding is required concerning such interfacial corrosion. In this work, a combination of numerical simulation and experimental investigation was used to clarify the microstructure evolutions of AZ80‐Mg alloy/1060‐Al explosively welded composite plate. The formation of interfacial wave structure and the thermodynamic state were insighted through numerical simulation, which further enhanced the correlation between the interfacial microstructural heterogeneities and the interfacial corrosion characteristics. Galvanic corrosion was produced by the significant potential difference between the AZ80‐Mg and 1060‐Al, with multiple micro‐galvanic couples in the vortex zone. The corrosion occurred near the interface and gradually advanced away from the interface. After 1 h, the composite plates exhibited severe corrosion with deep pits on the Mg side, while the Al side was less affected. Within the vortex, however, the Mg‐rich region underwent little corrosion, whereas the Al‐rich region underwent significant corrosion, attributed to the increase in pH value caused by the Mg corrosion.

Interfacial waves in a piezoelectric/piezomagnetic/piezoelectric structure with magneto-electro-mechanical imperfect interfaces

In this paper, we study the propagation of Shear Horizontal (SH) waves in the interfaces of a piezoelectric/piezomagnetic/piezoelectric (PiezoE/ PiezoM/ PiezoE) structure with a magnetical, imperfect magnetic, electric, and mechanical condition at interfaces. The inclusion of magnetical imperfections produced several new results, such as a general dispersion relation and expressions for some limit cases, which were not reported previously in the literature, predicting the existence of interfacial waves. Employing numerical calculations, dispersion curves for this kind of structure are presented for the first time. It can be shown that the magnetical imperfection interface influences the dispersion curves. Our results show that especially magnetic imperfections have a significant influence on the dispersion curves.

High-level Green–Naghdi model for large-amplitude internal waves in deep water

In this paper, a high-level Green–Naghdi (HLGN) model for large-amplitude internal waves in a two-layer fluid system, where the upper-fluid layer is of finite depth and the lower-fluid layer is of infinite depth, is developed under the rigid-lid free-surface approximation. The equations of the present HLGN model follow Euler's equations under the sole assumption that the horizontal and vertical velocity distributions along the vertical column are presented by known shape functions for each layer. The linear dispersion relations of the HLGN model for different levels are presented and compared with those obtained by other strongly nonlinear models for deep water, including the fully nonlinear models that include the dispersion effects $O(\mu )$ (where $\mu$ is the ratio of the upper-fluid layer depth to a typical wavelength) derived by Choi & Camassa (Phys. Rev. Lett., vol. 77, 1996, pp. 1759–1762) and $O(\mu ^2)$ derived by Debsarma et al. (J. Fluid Mech., vol. 654, 2010, pp. 281–303). It is shown that the HLGN model has a wider application range than other models. Solutions of travelling large-amplitude internal solitary waves in the absence and presence of background shear-current are then investigated by using the HLGN model. For the no-current cases, results obtained by the HLGN model show better agreement with Euler's solution on wave profile, velocity profile at the maximum interface displacement and wave speed compared with those obtained by other models. For the background shear-current cases, results obtained by the HLGN model also show good agreement with those obtained by solving the Dubreil-Jacotin–Long equation.

Unveiling multi-wave patterns: dynamic characterization and sensitivity analysis of the Yu-Toda-Sasa-Fukuyama model in lattice and liquid

In this study, an examination of the Yu-Toda-Sasa-Fukuyama equation is undertaken, a model that characterizes elastic waves in a lattice or interfacial waves in a two layer liquid. Our emphasis lies in conducting a comprehensive analysis of this equation through various viewpoints, including the examination of soliton dynamics, exploration of bifurcation patterns, investigation of chaotic phenomena, and a thorough evaluation of the model’s sensitivity. Utilizing a simplified version of Hirota’s approach, multi-soliton pattens, including 1-wave, 2-wave, and 3-wave solitons, are successfully derived. The identified solutions are depicted visually via 3D, 2D, and contour plots using Mathematica software. The dynamic behavior of the discussed equation is explored through the theory of bifurcation and chaos, with phase diagrams of bifurcation observed at the fixed points of a planar system. Introducing a perturbed force to the dynamical system, periodic, quasi-periodic and chaotic patterns are identified using the RK4 method. The chaotic nature of perturbed system is discussed through Lyapunov exponent analysis. Sensitivity and multistability analysis are conducted, considering various initial conditions. The results acquired emphasize the efficacy of the methodologies used in evaluating solitons and phase plots across a broader spectrum of nonlinear models.

Relating interfacial Rossby wave interaction in shear flows with Feynman's two-state coupled quantum system model for the Josephson junction

Relating interfacial Rossby wave interaction in shear flows with Feynman's two-state coupled quantum system model for the Josephson junction