Vertical Wave Research Articles

Vertical bending and aerodynamic performance in flying snake-inspired aerial undulation

This paper presents a numerical investigation into the aerodynamic characteristics and fluid dynamics of a flying snake-like model employing vertical bending locomotion during aerial undulation in steady gliding. In addition to its typical horizontal undulation, the modeled kinematics incorporates vertical undulations and dorsal-to-ventral bending movements while in motion. Using a computational approach with an incompressible flow solver based on the immersed-boundary method, this study employs topological local mesh refinement mesh blocks to ensure the high resolution of the grid around the moving body. Initially, we applied a vertical wave undulation to a snake model undulating horizontally, investigating the effects of vertical wave amplitudes (ψm). The vortex dynamics analysis unveiled alterations in leading-edge vortices formation within the midplane due to changes in the effective angle of attack resulting from vertical bending, directly influencing lift generation. Our findings highlighted peak lift production atψm=2.5∘and the highest lift-to-drag ratio (L/D) atψm=5∘, with aerodynamic performance declining beyond this threshold. Subsequently, we studied the effects of the dorsal-ventral bending amplitude (ψDV), showing that the tail-up/down body posture can result in different fore-aft body interactions. Compared to the baseline configuration, the lift generation is observed to increase by 17.3% atψDV= 5°, while a preferable L/D is found atψDV= -5°. This study explains the flow dynamics associated with vertical bending and uncovers fundamental mechanisms governing body-body interaction, contributing to the enhancement of lift production and efficiency of aerial undulation in snake-inspired gliding.

Study on the influence of submergence depth on the hydrodynamic and wave load characteristics of semi-submersible structures induced by a solitary wave

The submergence depth directly affects the safety of semi-submersible marine structures due to that the submergence depth significantly impacts on the hydrodynamic characteristics and wave loads of structures excited by extreme wave. This paper studies the influence of submergence depth on the hydrodynamic and wave load characteristics of semi-submersible structures by establishing a numerical model of the interaction between solitary waves and semi-submersible structures based on the SPH model and Rayleigh theory. Furthermore, equations for transmission coefficient, reflection coefficient, and wave load are fitted. The calculated wave heights of solitary wave propagation test case are in good agreement with the theoretical values. The maximum relative error of the wave peak is 8.4%. The calculated wave loads of submerged horizontal plates test case has a consistent trend with the experimental data. The maximum relative error of wave load peak and valley is 54% (absolute error 0.37 N). Furthermore, the interaction between solitary waves and structures with different submergence depths is investigated by using the meshless numerical model. It is found that the reflection coefficient first increases and then decreases with increasing submergence depth, and reaching a maximum value of 0.39 at the submergence depth equal to 0.0 m. On the contrary, the transmission coefficient decreases first and then increases with the increase of submergence depth. The minimum value of transmission coefficient is 0.36 with the submergence depth of 0.3 m. As the submergence depth increased, the horizontal wave load peak of the structure gradually increases, and the maximum value of 0.13 is obtained at the submergence depth of 0.7 m. The peak of vertical wave load rapidly increases with the increase of submergence depth and then gradually decreases while the trough gradually decreases with increasing submergence depth.

A scalable, symmetric atom interferometer for infrasound gravitational wave detection

We propose a terrestrial detector for gravitational waves with frequencies between 0.3 and 5 Hz based on atom interferometry. As key elements, we discuss two symmetric matter-wave interferometers, the first one with a single loop and the second one featuring a folded triple-loop geometry. The latter eliminates the need for atomic ensembles at femtokelvin energies imposed by the Sagnac effect in other atom interferometric detectors. The folded triple-loop geometry also combines several advantages of current vertical and horizontal matter wave antennas and enhances the scalability in order to achieve a peak strain sensitivity of 2×10−21/Hz.

Physical Sensors Based on Lamb Wave Resonators

A Lamb wave is a guided wave that propagates within plate-like structures, with its vibration mode resulting from the coupling of a longitudinal wave and a shear vertical wave, which can be applied in sensors, filters, and frequency control devices. The working principle of Lamb wave sensors relies on the excitation and propagation of this guided wave within piezoelectric material. Lamb wave sensors exhibit significant advantages in various sensing applications due to their unique wave characteristics and design flexibility. Compared to traditional surface acoustic wave (SAW) and bulk acoustic wave (BAW) sensors, Lamb wave sensors can not only achieve higher frequencies and quality factors in smaller dimensions but also exhibit superior integration and multifunctionality. In this paper, we briefly introduce Lamb wave sensors, summarizing methods for enhancing their sensitivity through optimizing electrode configurations and adjusting piezoelectric thin plate structures. Furthermore, this paper systematically explores the development of Lamb wave sensors in various sensing applications and provides new insights into their future development.

Highly switchable photonic spin hall effect in vanadium dioxide grating structure

The enhancement and manipulation of the photonic spin Hall effects are essential for the spin photonic applications. The emergence of the phase transition material, vanadium dioxide (VO2), presents a unique chance to explore its conductivity dependent optical properties. However, the explorations on the PSHEs in VO2 based microstructures are quite rare. Here, we report the enhanced and controllable reflected photonic spin Hall effects under the horizontal or vertical polarized wave by establishing the VO2 grating structure. It can be found that associated with the phase transition of VO2, its changed conductivity not only tunes the magnitude of the reflected spin shift but also changes its sign, which even results in a dramatic modulation of the reflected spin shift from the negative maximum value under the vertical polarized wave to the positive maximum value under the horizontal polarized wave at the specific wavelength. Such features can be attributed to the dramatic changes of the reflectances in the VO2 grating structure under different polarizations induced by the changed conductivity of VO2. Our results allow the actively alternative phase transition material based configurations capable of dramatic manipulation of the reflected spin shifts and it constitutes a significant step toward highly switchable spin photonic devices.

The effect of porous non-metallic balls on detonation propagation in hydrogen–oxygen mixtures

In this study, the influence of porous non-metallic balls on the dynamics of detonation propagation in hydrogen–oxygen mixtures is studied in stainless steel tubes with square cross-sections. The effect of the length and thickness of the balls is considered in detail. Four pressure transducers are used to record the detonation time-of-arrival, and the average velocity of detonation propagation is calculate. The smoked foil technique is performed to register the detonation cellular structures. The results indicate that increasing the filling length and thickness of the balls leads to a significant increase in velocity loss, critical pressure, and re-initiation distance during detonation propagation. Two propagation modes are observed near the critical pressure. In sub-critical mode, the detonation wave is attenuated and failed eventually, propagating to the end of the tube in the form of a low-speed deflagration wave. In super-critical mode, the detonation propagation can be promoted by inducing a vertical transverse wave generated by the detonation wave passing through a group of small balls. It is worth noting that the increase in filling thickness of the small balls leads to a greater velocity loss compared to the increase in filling length. However, an increase in the filling length will cause the detonation wave to undergo a longer and more sustained weakening process as it passes through the small balls, thereby resulting in a longer re-initiation distance and a lower average velocity over a short distance after re-initiation. By increasing the filling length of the small balls to 312 mm, the transition of the detonation wave from multi-head detonation to double-head detonation can be observed, and then successfully turns into stable detonation. However, when filling double-layer small balls, even in super-critical conditions, the attenuated detonation wave cannot achieve re-initiation over a short distance.

Experimental study on plunging breaking waves impacting a vertical cylinder with three different model scales

Scale effects, which can influence the reliability and effectiveness of experimental results, are often unavoidable but seldom explored, particularly in the context of plunging waves. To investigate the scale effects of plunging wave impacts on a vertical cylinder, experiments were conducted in a wave flume at model scales of 1:20, 1:30 and 1:40. The wavemaker movements were scaled based on the Froude-similarity law and the pressures on the front surface of the cylinder were analyzed. The results indicated that plunging waves were generated across these three scales, with fine agreement in overall wave elevations and a local waveform similarity of 80–90%. The analysis of pressures showed that the distribution of peak pressures on the cylinders remained consistent across different scales; however, scale effects were closely related to the intensity of wave impacts. Specifically, in cases of relatively weak impact, such as when the wavefront struck the cylinder before breaking or even after an intense wave breaking with intense gas-liquid mixtures, the pressure discrepancies were less than 20% among these different scales. This discrepancy can exceed 50% near the wave peaks during the vertical wave front or early jet formation stages with strong impacts.

Extreme Wave-Induced Pressure Distribution and Wave Forces on Tandem Pile Groups: An Experimental Study

As the foundation of marine infrastructure, pile groups are subjected to extreme wave loads. Existing research primarily focuses on regular waves and wave forces. There is limited research on the pressure distribution of pile bodies under extreme waves. This paper describes a wave flume experiment where waves of a self-proposed extreme wave type were generated. The experiment considers three water depths (25/35/45 cm), three wave-pushing velocities (20/30/40 cm/s), and two clear distances (D, 2D). A total of 216 measuring points equipped with digital pressure sensors captured the vertical and circumferential pressure distribution and wave positive force. The results show that (1) the vertical and circumferential pressure distribution patterns of each component pile and the single pile are similar in various loading scenarios and clear distances. (2) The measuring point pressure, pressure after circumferential integration, and wave positive force are positively correlated with wave-pushing velocity. (3) The wave pressure is positively correlated with the water depth, while the pressure after circumferential integration is negatively correlated with the water depth. (4) When the clear distance is D, the wave positive force coefficient of each component pile is less than 1.0.

Current Loads on a Horizontal Floating Flexible Membrane in a 3D Channel

A 3D analytical model is formulated based on linearised small-amplitude wave theory to analyse the behaviour of a horizontal, flexible membrane subject to wave–current interaction. The membrane is connected to spring moorings for stability. Green’s function approach is used to obtain the dispersion relation and is utilised in the solution by applying the velocity decomposition method. On the other hand, a brief description of the experiment is presented. The accuracy level of the analytical results is checked by comparing the results of reflection and the transmission coefficients against experimental data sets. Several numerical results on the displacements of the membrane and the vertical forces are studied thoroughly to examine the impact of current loads, spring stiffness, membrane tension, modes of oscillations, and water depths. It is observed that as the value of the current speed (CS) rises, the deflection also increases, whereas it declines in deeper water. On the other hand, the spring stiffness has minimal effect on the vibrations of the flexible membrane. When vertical force is considered, higher oscillation modes increase the vertical loads on the membrane, and for a mid-range wavelength, the vertical wave loads on the membrane grow as the CS increases. Further, the influence of the phase and group velocities are presented. The influences of CS and comparisons between them in terms of water depth are presented and analysed. This analysis will inform the design of membrane-based wave energy converters and breakwaters by clarifying how current loads affect the dynamics of floating membranes at various water depths.

Profilometry: a non-intrusive active stereo-vision technique for wave-profile measurements in large hydrodynamic laboratories

Profilometry is proposed as a novel non-intrusive image-based technique to capture the profile of the air–water interface as a dense point cloud. It can be classified as an active stereo-vision method applied to the study of gravity-driven water waves and specifically developed to be used in large hydrodynamic laboratories. As an active vision technique, it relies on the use of light sources, and as a stereo technique, it requires one or more high-speed camera pairs for imaging the same scene synchronously. To enhance the visibility of the laser lights on the wave profile, the water surface is sprayed with water droplets. Profilometry, compared to standard wave probes, can be considered as an alternative source of information that can augment spatial resolution to the identification of the air–water interface to capture nonlinear wave-evolution mechanisms and violent wave–body interactions. Its feasibility and accuracy are examined preliminarily in a small-scale flume and then in a large-scale towing tank using long-crested wave scenarios, including regular, irregular, and focused gravity-driven waves, without the presence of a structure. The values of the wave steepness examined were various and included also quite steep cases with nearly vertical wave fronts. Role played by parameters of the technique, as well as of its setup in capturing the wave features are also analysed, with the aim to provide a useful guidance for other researchers that intent to use and develop further this approach.

Numerical solution of the boundary value problem for inertia-gravity internal waves

This paper presents a numerical calculation of the boundary value problem for the equation of free internal inertia-gravity waves in an unbounded basin of constant depth in the Boussinesq approximation and the presence of a two-dimensional vertically inhomogeneous flow. The boundary value problem for the vertical velocity amplitude has complex coefficients and is solved both numerically and by perturbation theory. Using the example of calculating the decrement of attenuation of internal waves and momentum wave flows, it is shown that the exact numerical calculation gives significantly better estimates in comparison with the perturbation method. In particular, at minimum divergence in the dispersion curves for both calculation methods, the imaginary part of the wave frequency, interpreted as the decrement of attenuation, can differ by two or three orders of magnitude. Vertical wave momentum fluxes are comparable to turbulent ones and may exceed them, with results obtained by the numerical method being almost an order of magnitude smaller than those calculated by the perturbation theory method.

Experimental study of wave diffraction loads on a vertical circular cylinder with heave plates at deep and shallow drafts

This study focuses on wave diffraction loads influenced by heave plates at deep and shallow submerged depths. An extensive experimental campaign is conducted on a fixed vertical and free-surface piercing circular cylinder with five different circular plates, including a perforated plate. The horizontal and vertical wave forces are studied in monochromatic and bichromatic waves. The results show that the heave plate significantly influences the forces varying in time and representative harmonics, including sum- and difference-frequency components. The study found that wave steepness and submerged depth of the plate contribute to the nonlinearity of the loads and that the porous plate reduces the loads compared to the solid plate. Corresponding results from a boundary element method (BEM) solver, HydroStar, provide a reasonable prediction of the harmonics. However, the first harmonic of the vertical force is underpredicted at low frequencies, specifically where the BEM results indicate the cancellation of the forces. Dedicated computational fluid dynamics (CFD) simulations are carried out to investigate the discrepancy, and it is observed that flow separation occurs around the edge of the plate. A simplified approach based on Morison’s equation is employed to model the flow separation effects using a quadratic drag force calculated with a constant drag coefficient. The approach shows that viscous drag is the dominant contributor to vertical wave forces on the heave plate in the low-frequency regime.

Random Scattering Effect of SV Waves by a 3D Sedimentary Basin Considering Geotechnical Parameter Uncertainty

ABSTRACT This study investigated the random scattering effect in sedimentary basins with uncertain geotechnical parameters under vertical SV waves using multiplicative dimensional reduction method. The influence of the depth-to-radius ratio of basins and variability of geotechnical parameters on the random scattering effect was explored. The results indicate that the scattering in sedimentary basins significantly amplifies the uncertainty. The variability of displacement amplitude factors of basins is significantly affected by the depth-to-radius ratio of basins, providing a 2- or 3-time difference under high-frequency waves. The coefficient of variations of displacement amplitude factors has a nonlinear amplification relationship with those of geotechnical parameters.

A two‐layered, analytically‐tractable, atmospheric model applied to Earth, Mars, and Titan with sources

AbstractThis work utilizes an analytic expression for a model of acoustic propagation in a two‐layered, inhomogeneous atmosphere developed by the authors. The model is used to study the atmospheres of Earth, Mars, and Titan. In particular, vertical wave propagation in these atmospheres is studied. The effect(s) of a two‐layered, inhomogeneous atmosphere on vertical, acoustic propagation due to a time‐harmonic, point source are examined. An adiabatic atmosphere is used for the bottom layer (troposphere) and an isothermal one for the top (stratosphere). The derived, analytic solution is expressed in terms of the acoustic pressure fluctuations. For the adiabatic layers, the solutions satisfy Bessel's equation for orders of , and for Earth, Mars, and Titan, respectively. The Bessel function's argument is , where and are dimensionless frequency and height, respectively. For the isothermal layer, the solution represents a damped, harmonic oscillator with a cutoff value of . Only values greater than are considered. The analysis and results are reported for combinations of single‐ and double‐layer atmospheres in the presence of a source on given boundaries. Acoustic propagation and transmission loss results are shown and discussed for all three planetary bodies: Earth, Mars, and Titan.

Numerical Study of Hydrodynamic Characteristics of a Three-Dimensional Oscillating Water Column Wave-Power Device

The impact of wave-induced forces on the integrity of stationary oscillating water column (OWC) devices is essential for ensuring their structural safety. In our study, we built a three-dimensional numerical model of an OWC device using the computational fluid dynamics (CFDs) software OpenFOAM-v1912. Subsequently, the hydrodynamic performance of the numerical model is comprehensively validated. Finally, the hydrodynamic performance data are analyzed in detail to obtain meaningful conclusions. Results indicate that the horizontal wave force applied to the OWC device is approximately 6.6 to 7.9 times greater than the vertical wave force, whereas the lateral wave force is relatively small. Both the horizontal and vertical wave forces decrease as the relative water depth increases under a constant wave period and height. In addition, the highest dynamic water pressure is observed at the interface between the water surface and device, both within and outside the front wall of the gas chamber. The dynamic water pressure at different locations on the front chamber increases and subsequently decreases as the wave frequency increases.

Dynamic response of a permafrost railway subgrade with 3D train-track-subgrade-ground model simulations

Studying train-induced response characteristics is essential for safely operating permafrost railway subgrades. A three-dimensional thermal-mechanical coupling nonlinear dynamic model of train-track-subgrade-ground relationships was established to analyse the train-induced dynamic stress, acceleration and stress path characteristics of a permafrost railway subgrade, and field monitoring data were used to verify this model. The differences between the 2D and 3D models are also discussed, along with the seasonal changes, train speed, axle load, and train type affecting permafrost subgrades. The main results are as follows. First, the vibration load significantly impacts the subgrade 6 m below the sleeper, producing distinct vertical dynamic stress waves due to the wheels and bogies. Dynamic compression stress dominates the subgrade and is influenced by the train structure, speed, and sleeper spacing. While the 2D model tends to underestimate the dynamic stress in shallower layers, it concurs with the 3D model in deeper subgrade dynamics within a 10% margin of error. Then, the principal stress axis of the subgrade soil rotates synchronously with train movements, exhibiting regular stress paths in the YZ plane (longitudinal section) with depth-dependent variations in the stress cycles and deviatoric stress. Finally, predominantly originating from sleeper-induced vibrations, the subgrade vibration acceleration varies with the train speed, sleeper spacing, and season and is most pronounced in the vertical direction. This study provides theoretical guidance for the vibration response of permafrost subgrades on the Qinghai-Tibet Railway (QTR).

Transient Response of an Unsaturated Single-Layer Seabed Subjected to a Vertical Compressional Wave

Transient Response of an Unsaturated Single-Layer Seabed Subjected to a Vertical Compressional Wave

MS-GWaM: A Three-Dimensional Transient Gravity Wave Parametrization for Atmospheric Models

Abstract Parameterizations for internal gravity waves in atmospheric models are traditionally subject to a number of simplifications. Most notably, they rely on both neglecting wave propagation and advection in the horizontal direction (single-column assumption) and an instantaneous balance in the vertical direction (steady-state assumption). While these simplifications are well justified to cover some essential dynamic effects and keep the computational effort small, it has been shown that both mechanisms are potentially significant. In particular, the recently introduced Multiscale Gravity Wave Model (MS-GWaM) successfully applied ray-tracing methods in a novel type of transient but columnar internal gravity wave parameterization (MS-GWaM-1D). We extend this concept to a three-dimensional version of the parameterization (MS-GWaM-3D) to simulate subgrid-scale nonorographic internal gravity waves. The resulting global wave model—implemented into the weather forecast and climate code Icosahedral Nonhydrostatic (ICON)—contains three-dimensional transient propagation with accurate flux calculations, a latitude-dependent background source, and convectively generated waves. MS-GWaM-3D helps reproduce expected temperature and wind patterns in the mesopause region in the climatological zonal mean state and thus proves a viable internal gravity wave (IGW) parameterization. Analyzing the global wave action budget, we find that horizontal wave propagation is as important as vertical wave propagation. The corresponding wave refraction includes previously missing but well-known effects such as wave refraction into the polar jet streams. On a global scale, three-dimensional wave refraction leads to a horizontal flow-dependent redistribution of waves such that the structures of the zonal mean wave drag and consequently the zonal mean winds are modified.

Contribution to micromechanical modeling of the shear wave propagation in a sand deposit

The object of study is the vertical wave propagation in a sand deposit. This paper is aimed at analyzing the vertical wave propagation in a sand deposit through micromechanical modeling that inherently takes account of intergranular slips during deformation. Such a problem, which is part of the general framework of wave propagation in the soil, has long been analyzed using continuum models based on approximate behavior laws. For this purpose, a 2D Discrete Element Method (DEM) model is developed. The DEM model is based on molecular dynamics with the use of circular shaped elements. The intergranular normal forces at contacts are calculated through a linear viscoelastic law while the tangential forces are calculated through a perfectly plastic viscoelastic model. A model of rolling friction is incorporated in order to account for the damping of the grains rolling motion. Different boundary conditions of the profile have been implemented; a bedrock at the base, a free surface at the top and periodic boundaries in the horizontal direction. The sand deposit is subjected to a harmonic excitation at the base. Using this model, the fundamental and resonance frequencies of the deposit are first determined. The former is determined from the low-amplitude free vibration and the latter by performing a variable-frequency excitation test. It is noted that there is a significant gap between the two frequencies, this gap could be attributed to the degradation of the soil shear modulus in the vicinity of the resonance. Such degradation is well proven in classical soil dynamics. The effects of deposit height and confinement on resonance frequency and free-surface dynamic amplification factor are then investigated. The obtained results highlighted that the resonance frequency is inversely proportional to the deposit’s thickness whereas the dynamic amplification factor Rd increases with the deposit’s thickness. In the other hand, when the confinement increases the deposit becomes stiffer, which results in reducing the amplification. Such result is in accordance with theoretical knowledge which states that the most rigid profiles such as rocks do not amplify seismic movement.

Null-filled high gain airborne antenna with metasurface for emergency communication

This letter presents a null-filled high-gain airborne antenna with metasurface for emergency communication. The proposed antenna consists of a monopole with two metal feeding loops, a metal cylindrical cavity and metasurface radome (MSR). By cutting the corners of the monopole and adding two loops, the aim is to direct vertical radiation electromagnetic waves. The cavity and MSR are used to achieve vertical null-filled radiation performance with high gain. Simulated and measured results exhibit that the antenna has a −10 dB bandwidth of 0.8–1.0 GHz, covering the emergency communication band, with a high gain (5.0–6.7 dBi). Furthermore, the null-filled level of the vertical radiation E-plane of the antenna is higher than −4.6 dB, and the H-plane maintains horizontal omnidirectional 360°radiation. The proposed airborne antenna is a good contender for emergency communication and also provides ideas for the antenna to meet both vertical null-filled and horizontal-omnidirectional radiation.