Wave Surface Research Articles

Model anisotropic materials with ellipsoidal wave surfaces and their application to determination of elastic constants by acoustical methods

A new class of elastic materials with orthorhombic symmetry is introduced. For such materials, group velocity surfaces of quasi-longitudinal waves have ellipsoidal shapes. Relations between elastic constants that guaranty ellipsoidal shapes of the group velocity surfaces are indicated. The model materials are used for approximate determination of effective elastic constants of heterogeneous materials by acoustical methods. Examples of reconstruction of elastic constants from acoustical data are presented, and possible errors of the reconstructions are discussed.

Research on a Measurement Method for the Ocean Wave Field Based on Stereo Vision

The wave parameter is an important environmental input condition. Traditional contact wave measurement methods are unable to meet the requirements of high precision, non-contact, and ship wave field assessment. Alternatively, stereo vision technology can realize a non-contact and mobile form of measurement. However, this technology suffers from poor timeliness and adaptability. This paper proposes a comprehensive wave measurement method that is based on stereo vision, wherein the gridding of siftGPU is used to achieve the fast matching of large images. The whole algorithm can be run within 6 s and it guarantees more than 20,000 feature-matching logarithms. Furthermore, by utilizing the least squares method and sea surface wave surface theory, the sea surface base level can be calculated without control points, along with the inversion of the sea wave parameters (wave height, period, and wave direction) and error point fitting. The rationality and superiority of the algorithm were verified through multiple comparison experiments. Compared with the Richard Brancker Research (RBR) wave height meter, the measurement error of the wave height is less than 10%, the period error is less than 0.5 s, and the wave direction error is less than 10° with the proposed method.

Microdisk array based Weyl semimetal nanofilm terahertz detector.

High-performance terahertz wave detectors at room temperature are still urgently required for a wide range of applications. The available technologies, however, are plagued by low sensitivity, narrow spectral bandwidth, complicated structure, and high noise equivalent power (NEP). Here, we have demonstrated a Weyl semimetal surface plasmon-enhanced high-performance terahertz wave detectors which are based on microdisk array deposited WTe2 nanofilm epitaxially grown on GaN substrate for room temperature operation. With the microdisk array combined the WTe2 layer, strong terahertz wave surface plasmon polaritons can be generated at the WTe2-air interfaces, which results in significant improvement in detecting performance. For the 40μm diameter microdisk array, a detectivity (D *) of 5.52 × 1012cmHz1/2 pW-1 at 0.1THz is achieved at room temperature. In addition, the responsivity (R A) of 8.78AW-1 is also obtained. Such high-performance millimeter and terahertz wave photodetectors are useful for wide applications such as high capacity communications, walk-through security, biological diagnosis, spectroscopy, and remote sensing.

Measuring free surface elevation of shoaling waves with pressure transducers

An assessment of formulas to recover wave surface elevation from pressure measurements was carried out in the present study. The investigation focused on the formulas’ performance in the shoaling region, i.e. where the wave nonlinearity gradually increases as the wave travels towards shallower waters. Formulas based on linear wave theory alongside nonlinear reconstructions were considered. Experiments in a large-scale wave flume provided with a concrete beach profile were performed, in which regular waves were generated and surface elevation was measured with acoustic, resistive and pressure gauges. The considered formulas require the application of a cutoff frequency to the wave signal in order to avoid high frequencies amplification that progressively arise as wave shoaling occur. A simple but effective method to obtain a reference cutoff frequency is proposed in the present work; the method is based on a polynomial fitting of the unfiltered wave energy spectrum. A sensitivity analysis of each formula to the variation of this cutoff frequency was carried out. Results showed that all the investigated formulas recover wave elevation fairly well for low-nonlinearity waves, whereas overestimating wave crest height as nonlinearity increases. Wave reconstruction of the linear formulation performance was comparable to nonlinear formulations in terms of wave crest height reconstruction, although tending to amplify frequencies in the wave trough. Moreover, the performance of the formulas to correctly recover the asymmetry and flatness of the surface elevation distribution was assessed by analysing third- and fourth-order moment statistics. In this sense, nonlinear reconstruction formulas performed better in recovering the asymmetric distribution of the wave elevation, with the formula based on linear wave theory underestimating skewness and kurtosis for large nonlinearity waves.

Interaction of gravitational waves with permeable breakwater

A method for calculating the parameters of gravitational waves that interact with vertical permeable breakwaters, based on potential theory, has been developed and presented. The wave motion of a fluid was described by the velocity potential that satisfies the Laplace equation. The shape of the wave surface and the components of the velocity vector were determined. Numerical analysis of the influence of permeability of the vertical wall on wave energy adsorption was carried out. The propagation of surface gravitational waves in the linear formulation of problems in a channel with a vertical permeable obstacle was analyzed. The dependence of the wave reflection coefficient as a function of the wave transmission coefficient in accordance with the law of energy conservation was given. Experimental studies have been conducted to determine the features of the hydrodynamic interaction of sea waves and coastal protection structures of the permeable type. The experiments were performed in the laboratory in a wave channel with models of vertical slotted walls of different permeability. Visual and instrumental studies have shown the features of the interaction of the wave field with permeable breakwaters, the formation of reflection and transmission waves through the breakwater. It is established that vertical slotted walls, depending on the permeability, significantly affect the wave field, generate reflected waves and waves passing through the breakwater, as well as lead to a significant dissipation of wave energy. The dependences of the reflection and transmission coefficients of the wave, as well as the dissipation coefficient of the wave energy depending on the permeability of the slotted breakwater and the relative depth of the water area were given. It is shown that with increasing permeability of the breakwater the wave reflection coefficient decreased, and the wave transmission coefficient on the contrary increased. It was found that the reflection coefficient of the wave was increased with increasing relative depth, and the coefficient of wave propagation was decreased. The dissipation coefficient of the wave energy had the maximum value, which was observed for greater permeability of the breakwater, when the relative depth compared to the wavelength was increased.

Investigation of Vortex Structure Modulation by Spume Droplets in the Marine Atmospheric Boundary Layer by Numerical Simulation

Direct numerical simulation (DNS) of a droplet-laden, turbulent Couette airflow over a waved water surface is performed modeling the marine atmospheric boundary (MABL) layer carrying idealized spume droplets. Both the instantaneous and mean flow properties, the characteristics of the vortex structures and the momentum exchange between air turbulence and waved water surface and droplet-mediated momentum transfer are investigated. A Eulerian–Lagrangian approach is employed in DNS where full, 3D Navier–Stokes equations for the carrier air are solved in a Eulerian frame, and the trajectories of individual droplets are simultaneously tracked in a Lagrangian frame. The impact of the droplets on the carrier air flow is modeled via a point force approximation. The droplets size is considered in the range of spume droplet sizes observed in MABL. Various water surface roughness and droplet injection scenarios are considered, and both instantaneous and phase-averaged flow fields, the Reynolds stresses and the eigenvalues of the local air velocity gradient tensor are evaluated in DNS. Numerical results show a strong dependence of the droplet-mediated airflow modification on-the-droplet injection mechanism. Droplets injected with the surrounding air velocity effectively mitigate the vortex structures by reducing their swirling strength and suppress the momentum flux from air turbulence to water surface by weakening both ejections and sweeping events, and thus accelerating the mean flow as compared to the droplet-free flow. On the other hand, droplets injected with the velocities of the Lagrangian particles of the water surface enhance both the swirling strength of the vortex structures and air-flow turbulent stresses and decelerate the mean wind. The results also show that these effects of droplet-mediated flow modification become less pronounced as the water surface wave steepness increases.

The adhesion of viscoelastic bodies with slightly wave surfaces

Adhesive contact of viscoelastic bodies is a challenging problem due to its rate-dependent nature. In this work, we formulate a theoretical model to describe the pulling process of a slightly wavy indenter from a soft medium, comparing predictions with numerical simulations. A cohesive approach is adopted to formulate the theory based on the assumption that viscoelastic dissipation is confined to a small region around the contact edge. The resulting increase in surface energy is related to the quasi-static work of adhesion through the creep compliance. Theoretical findings match quite good numerical results. However, when separation arises from complete contact, the pull-off force can be estimated only if a small flaw is postulated at the interface.

A Computation Method for the Typhoon Waves Using the Field Wave Spectrum

Wave features and propagation characteristics during typhoons are the key factors to study the dynamic response of ocean engineering and coastal disaster prevention and mitigation under extreme climate. Based on the Longuet-Higgins theory, the method of the field spectrum during the typhoon was used to compute the typhoon waves. And the directional spectrum, the formulas of wave surface, the velocity of water particles, and the acceleration of water particles were investigated. The results showed that the interpolated field wave spectrum combined with the SWOP direction spectrum could accurately simulate the three-dimensional typhoon waves. The significant wave height and the average period of the simulated wave surface at fixed point were statistically evaluated by the upward zero-crossing method, and the relative errors were ± 5% and ± 15%, respectively. The typhoon wave surface computed by a dual peak spectrum had small periodic waves, and the velocity and acceleration of water particles differed considerably from the JONSWAP spectrum. Finally, a fastened slender cylinder was simulated under action of the typhoon waves, which proved the applicability of the computation method. This study aims at providing a basis for the simulation of the dynamic response of marine structures under the typhoon waves action.

Highly porous Fe2O3-SiO2 layer for acoustic wave based H2S sensing: mass loading or elastic loading effects?

A highly porous Fe2O3-SiO2 layer prepared using sol-gel and spin-coating methods was applied on the surface of a surface acoustic wave (SAW) device for H2S sensing. SiO2 in this sensing layer serves as a porous support for dispersing Fe2O3 nanoparticles, and Fe2O3 nanoparticles can effectively adsorb and react with H2S molecules. By changing the Fe/Si molar ratio in this Fe2O3-SiO2 layer, its pore volume, pore distribution and H2S adsorption capacity can be adjusted, the contribution of mass loading effect and the elastic loading effect toward the frequency response of the sensor can be controlled, and the sensing performance of the sensor can be optimized. The optimized sensing response is − 4.4 kHz toward 100 ppm H2S, with a good selectivity and reproducibility operated at room temperature (25 ℃).

Numerical investigation on movement of triple points on oblique detonation surfaces

A normal detonation wave in a gaseous mixture is a transient, multidimensional structure containing triple points (TPs) that collide in pairs and then propagate oppositely. However, the TPs on an oblique detonation wave (ODW) almost propagate along the same direction in most studies. In this study, the reactive Euler equations coupled with a two-step induction–reaction kinetic model are used to solve a two-dimensional wedge-induced ODW. Two novel movement patterns are observed in most cases. Results show that the TPs of the ODW can propagate upstream and even stand on the wave surface. The movement patterns of TPs include downstream, upstream, and steady according to their propagation direction relative to the wedge. We find that the ratio of the post-ODW flow speed Uτ to the transverse wave speed UT dominates the TP movement types. When the speed ratio Uτ/UT is approximately equal to 1, the TPs can stand on the wave surface. Above unity, downstream TPs form, and upstream TPs correspond to a value smaller than 1. Furthermore, the inflow Mach number has little influence on UT, while Uτ changes significantly. This is largely due to the high sensitivity of the ODW angle to the inflow. The high heat release rate benefits upstream TPs, and steady TPs form under a large wedge angle. The results are confirmed by varying the inflow Mach number, wedge angle, and chemical parameters.

ANALYSIS OF THE ERRORS OF DETERMINING THE EQUIVALENT SIZE AND ORIENTATION OF A PLANE DEFECT UNDER MANUAL ULTRASONIC CONTROL

The article reviews and analyzes the method of defect identification for determining the angle of inclination of a planar point defect to the input surface of an ultrasonic wave and its equivalent size during manual ultrasonic testing by the echo-pulse method. The method is most widely used in ultrasonic control of parts obtained by plastic deformation (forging, hot and cold stamping, rolling). This is due to the fact that defects in such parts are predominantly planar in nature. The method of ultrasonic defect identification is based on the use of a combined transducer P131-2.5-0i18-VO-04 containing two piezoelectric transducers in one housing with a normal input of a longitudinal ultrasonic wave and an input angle of 18º. The article presents a mathematical apparatus for the implementation of this method. Also presented is a software product that allows you to automate calculations when using this method of defect identification. The article carried out experimental studies of this method of ultrasonic defect identification, which showed its low error and high efficiency. The average value of the relative error in determining the angle of inclination of a planar point defect to the input surface of an ultrasonic wave was 1.525 %. The average value of the relative error in determining the equivalent size of a planar point defect located at an angle to the ultrasonic wave input surface was 1.192 %.

Multiple rogue wave solutions of a generalized (3+1)-dimensional variable-coefficient Kadomtsev--Petviashvili equation

Abstract Kadomtsev–Petviashvili equation is used for describing the long water wave and small amplitude surface wave with weak nonlinearity, weak dispersion, and weak perturbation in fluid mechanics. Based on the modified symbolic computation approach, the multiple rogue wave solutions of a generalized (3+1)-dimensional variable-coefficient Kadomtsev–Petviashvili equation are investigated. When the variable coefficient selects different functions, the dynamic properties of the derived solutions are displayed and analyzed by different three-dimensional graphics and contour graphics.

Thermal Modeling of Ultrasound Diathermy in Tissues with a Circular Inclusion near a Curved Interface

The influences of implants on the temperature field in tissues during ultrasound diathermy is controversial. In addition, most previous studies have focused on plate implants, and the effects of irregular implants and bones are seldom discussed. In this study, a hybrid computational framework per se is proposed to investigate the effects of double circular inclusions on the temperature distribution during ultrasound diathermy. The tissue–inclusion–bone structure is simplified as a two-dimensional bilayer composite model consisting of soft tissue and bone with a circular inclusion imbedded in the soft tissue. The interface between the bone layer and the soft-tissue layer is assumed as a convex surface for the incident ultrasonic waves. Multiply scattered waves originate between the two acoustic scatterers, i.e., the circular inclusion and the convex bone. The proposed computational framework consists of two kernels tackling ultrasound propagation and heat conduction problems, respectively. Making use of theoretical solutions of pressure fields, the transformed heat sources are efficiently obtained in the first kernel without sacrificing much computational burden. Temperature distributions in the composite media under ultrasound diathermy are evaluated via finite element numerical simulations in the second kernel. Numerical results indicate that the temperature distributions in the composite system obviously change when the bone layer changes from flat to convex. In addition, the inclusion size, location, material, and ultrasound operation frequency will also affect the temperature distribution and peak temperature during ultrasound diathermy. Pertinent findings could serve as a guide for clinical innovations in therapeutic ultrasounds.

Experimental investigations of secondary load cycle formation in wave force on a circular cylinder under steep regular waves

When a large wave interacts with a marine structure, it would lead to a high-frequency structure response, and impose great threats to marine structures. In this paper, wave forces on a vertical cylinder in regular waves with moderate to extreme steepness were measured experimentally. The secondary load cycle phenomenon in wave force time history was observed and its generation mechanism was analyzed. It is found that secondary load cycle strongly depends on wave steepness. When the wave steepness exceeds critical values, the secondary load cycle phenomenon appears in the time history of wave force, and a high frequency response accompanied this phenomenon. Further, a new critical wave steepness kA = 0.3tanh(kh) (A is wave crest height, k is wavenumber and h is water depth) is found to distinguish the secondary load cycle occurrence. Here the wave steepness threshold value is no more a constant value that was proposed before, it varies with water depth and becomes smaller with the decrease of water depth. Moreover, the secondary load cycle and the subsequent high-frequency response are divided from the wave force signal based on the empirical mode decomposition (EMD) method. The results show that the high-frequency response locates in the natural frequency region of cylinders, which is much higher than the high-order wave components. Finally, the generation mechanism of this phenomenon is explained. As a steep wave passes a cylinder, a large wave run-up would be generated on the front side of the cylinder. One part of water body of the run-up swashes down and impacts the wave surface heavily. The other part of wave run-up fills into the cavity on the lee side of the cylinder, and generates violent turbulence. Both processes are found to lead to an instant impact on the structure, and then excite structural high-frequency vibration. This instant impact expresses as secondary load cycle in wave force history. These new findings from experimental studies have provided new insights into the generation mechanism and the associated changes in wave properties during the formation of secondary load cycle.

Numerical simulation of interaction between wave-driven currents and revetment on coral reefs

The stability of a revetment breakwater is vital for the safety of islands and reefs formed with reclaimed sand under the action of a complex marine environment. The interactions in wave-reef-revetment systems are complex and difficult to accurately simulate; in addition, it is difficult to describe the dynamic wave pressures distribution by empirical formula, although these parameters are important for the safety of reefs and revetments; hence, more studies are required. In this study, an investigation of the interaction between the wave-driven current on the reef flat and rear revetment breakwater is performed, and the hydrodynamic pressure on the revetment is discussed. A two-dimensional numerical model is established using the Navier–Stokes equation to explore the interaction and calculate the pressure distribution on the revetment, which is verified by an experiment designed and implemented in a wave flume. The simulation illustrates that the wave-driven current is stratified in the vertical direction, and the velocity at the surface is approximately 2–3 times that of the average value, and the maximum flow velocity can reach 13 m/s. By varying the parameters of the geomorphology of the coral reef, the results suggest that for steeper fore-reef slopes, longer reef flats, and larger relative distances, the peak value of the pressure increases consistently. The detailed and sophisticated hydrodynamic pressure distribution on the revetment is obtained, and the numerical results indicate that the fifth-order polynomial can match the regulation of pulsating pressure at the wave surface with the relative submerged water depth.

Two-Phase Smoothed Particle Hydrodynamics Modelling of Hydrodynamic-Aerodynamic and Wave-Structure Interaction

A two-phase (air and water) smoothed particle hydrodynamics (SPH) method is employed to study the hydrodynamic-aerodynamic and wave interaction with fixed and floating structures in a wave basin. The method is first verified for a classical two-phase dam-breaking. A mirror-open boundary is implemented at the top and left sides of a two-phase wave basin with a piston to generate a second-order regular wave. It is observed that, compared to the single-phase simulation, the two-phase one obtains a smoother water surface and prevents the non-physical water splash when interacting with the sloped dissipative beach. This wave basin is also used to investigate wave-structure problems such as wave interaction with a rigid cantilever beam fixed to the basin bottom and downstream of the wave-maker mechanism and the dynamics of a single floating box and two floating boxes in the waves. A typical wave-structure interaction period is captured and described using pressure contours and velocity vectors at three selected instants for the wave-rigid cantilever beam case. With the increase of the structure’s height, the wave height after the structure decreases, but no evident variation is found when changing its thickness. Besides the hydrodynamics interaction, a periodical collision is observed between the two floating boxes on the wave surface.

Diversity of wave structures to the conformable fractional dynamical model

This manuscript examines the recently developed conformable three-dimensional Wazwaz–Benjamin–Bona–Mahony (3D-WBBM) equation’s dynamical behavior in terms of its spatial and temporal variables. The governing equation is stretch for the Korteweg-de-Vries equation that represents the unidirectional propagation of small amplitude long waves on the surface of hydro magnetic and acoustic waves in a channel, especially for shallow water. Solitary wave solutions of various types, such as kink and shock, as well as singleton, combined solitons, and complex solitons, are all retrieved. Additionally, solutions to hyperbolic, exponential, and trigonometric functions are obtained through the use of recently developed methods, namely the Kudryashov method (KM), the modified Kudryashov method (MKM), and the new extended direct algebraic method (NEDAM). The study conducts a comparison of our findings to well-known findings, and concludes that the solutions reached here are novel. Additionally, the earned results are sketched in different shapes to demonstrate their dynamics as a function of parameter selection. We can assert from the obtained results that the applied techniques are simple, vibrant, and quite well, and will be helpful tool for addressing more highly nonlinear issues in various of fields, especially in ocean and coastal engineering. Furthermore, our findings are first step toward understanding the structure and physical behavior of complicated structures. We anticipate that our results will be highly valuable in better understanding the waves that occur in the ocean. We feel that this work is timely and will be of interest to a wide spectrum of experts working on ocean engineering models.

A rapid imaging method of the seismic back‐scattered wavefield for urban road near‐surface anomalous structures

ABSTRACTUrban road near‐surface anomalous structures are buried at shallow depths (≦20 m) and small scale. Current geophysical methods, such as the transient electromagnetic, ground‐penetrating radar and shallow seismic methods with reflection wave, refraction wave and Rayleigh surface wave, do not provide sufficient detection accuracy for near‐surface anomalous structures. Although the back‐scattered method is promising in this task, it still needs improvement. This paper proposes an efficient near‐surface seismic back‐scattered method to realize the rapid lateral imaging of urban road anomalous structures. The proposed method uses a principal component analysis algorithm to directly extract the anomalous structure information. It does not require the knowledge of parameters such as velocity or the seismic wavelet so that the solutions are not affected by these parameters. Moreover, the proposed method retains the high transverse resolution of the back‐scattered wavefield and does not lose the wavefield information. Simulation and experimental operation show that the proposed method is very efficient. Combined with the hardware equipment provided by the towed seismograph, the proposed method can realize rapid detection and data imaging, which has a high engineering application value.

Different approaches to numerical modeling of sea waves

The main approaches in direct modeling of surface waves based on complete equations of dynamics of the inviscid liquid with a free surface are briefly considered. Most of the models are intended for study of the applied and engineering problems. It is assumed that the main model is written in the curvilinear coordinate system where the height is counted off from wave surface. In the two-dimensional periodic formulation, when using a conformal system, the problem is reduced to the system of one-dimensional equations that can be easily solved using Fourier-transform method. For three-dimensional waves such simplifications do not exist, thus, the vertical velocity on the surface is calculated by solving a three-dimensional Poisson equation or using a surface integral method. An approximate scheme based on the two-dimensional equations is considered. The scheme allows reproducing the statistical mode of waves with high accuracy consistent with the similar results obtained from the accurate three-dimensional model.

Coupling characteristics of bubbles with a free surface initially disturbed by water waves

The interactions between bubbles and water waves have important applications in ocean engineering, and their coupling characteristics are strongly associated with the wave phase angle, wavelength, and wave amplitude. Based on the assumption that the liquid is inviscid and incompressible, the coupling characteristics between bubbles and water waves are solved by the Euler equations with the finite volume method, and the bubble surface and water wave surface are tracked by the front tracking method. The accuracy of the numerical method is verified by comparison with a spark-generated bubble experiment. Compared with the bubble near the initially plane free surface, the rising height of the water spike is reduced by water waves in the crest state, where a concave shape forms on the falling water wave during bubble contraction when the wavelength λ≤ 4.00 and the wave amplitude h≥ 0.364. The rising height of the water spike is significantly strengthened by water waves in the trough state with smaller wavelengths and larger wave amplitudes, which produce a thinner and higher water spike. The bubble cycle is shortened by water waves in the crest state with smaller wavelengths and prolonged by water waves in the trough state with smaller wavelengths and larger wave amplitudes. The results presented in this paper provide guidance for the study of underwater explosions in complex water wave environments.