Wave Surface Research Articles

Wave-in-deck loads induced by regular wave impact: The role of compressible air entrainment

During the process of wave-in-deck when waves impacting a horizontal platform deck from below, large air cavity entrainment would be generated between the free wave surface and the deck. The air entrainments are compressed and expanded during the process of wave impacts. As the momentum and energy exchange medium in the interactions between waves and the structure, air entrainments conversely influence the forces on the deck, risking structural safety. The key to dealing with the air entrainment is the combination of the mass source wave method and pressure-based compressible technique in capturing the cavity volume variation. In this work, the advanced compressible two-phase model is first developed with our in-house solver to simulate a regular wave impacting a fixed flat plate. The air cavity kinematics/dynamics and their relationship with wave impact features in the process of wave-in-deck impacting are discussed, and the mechanism of the compression/expansion effect is carefully analysed. Two distinct impacting types, direct water impact and entrained-air impact, are identified in this work, and the larger wave impacting pressures in the latter situation with compressible air layer is demonstrated. The good comparison of the numerical results and laboratory data on pressure features reveals that the proposed model is capable of reproducing the nonlinear entrained-air wave impacts and accurate oscillating pressures on a flat deck for applications.

Solitary wave scattering by segmented arc-shaped breakwater

An analytical solution is presented to study a plane solitary wave propagating past a concentric segmented arc-shaped breakwater using the matched eigenfunction and separation of variable methods. The undetermined potential coefficients are obtained based on matching conditions. The numerical results of this study are found to agree well with previous calculation results. The major factors (including the number of arc-shaped breakwaters, opening angle, incident angle, and gap width) that affecting the hydrodynamic loads and diffracted wave surface are discussed. The results indicate that the shielding effect of a segmented two-arc breakwater with a small gap width is better than that of an unsegmented arc-shaped breakwater. However, the arrangement of the segmented arc impacts the sheltering effect. Numerical results provide a valuable reference for the hydrodynamic analyses and structural design of segmented arc-shaped breakwaters.

The Influence of the Hardness of the Tested Material and the Surface Preparation Method on the Results of Ultrasonic Testing

Non-destructive ultrasonic testing can be used to assess the properties and condition of real machine elements during their operation, with limited (one-sided) access to these elements. A methodological question then arises concerning the influence of the material properties of such elements and the condition of their surfaces on the result of ultrasonic testing. This paper attempts to estimate the influence of material hardness and surface roughness on the result of such testing study area testing machine or plant components of unknown exact thickness. Ultrasonic testing was carried out on specially prepared steel samples. These samples had varying surface roughness (Ra from 0.34 to 250.73 µm) of the reflection surface of the longitudinal ultrasonic wave (the so-called reflectors) and hardness (32 and 57 HRC). The ultrasonic measures were the attenuation of the wave, estimated by the decibel drop in the gain of its pulses, and the propagation velocity of the longitudinal ultrasonic wave. Ultrasonic transducers (probes) of varying frequencies (from 2 to 20 MHz), excited by a laboratory and industrial defectoscope were used as the source of such a wave. The results of our research provide a basis for the recommendation of two considered ultrasonic quantities for assessing the material properties of the tested element. This is of particular importance when testing machines or plant components of unknown exact thickness and unknown roughness of inaccessible surfaces, which are the reflectors of the longitudinal ultrasonic wave used for testing. It has been demonstrated that by using the ultrasonic echo technique, it is possible to evaluate the roughness and hardness of the tested elements.

Numerical study on the behaviors of coastal bridges with box girder under the action of extreme waves

This study presents an in-depth investigation of the wave-girder interaction by considering the Fluid-Structure Interaction (FSI) effect. Firstly, a 2D FSI model is developed based on the overset mesh method. The model's validity is confirmed through comparisons with analytical wave surface and relevant experimental data. Subsequently, the model is employed to examine the girder behaviors under extreme wave action, including wave forces on the girder, dynamic response, and forces on bridge bearings. Moreover, parametric studies are carried out to assess how variations in girder dimensions affect the girder's behaviors. The numerical results indicate that the girder dynamic response effectively reduces the maximum wave forces on the girder, but simultaneously increases the horizontal bearing force. During the extreme wave action process, the seaward bearing experiences both tension and compression forces, whereas the landward bearing experiences only compression force. The deck thickness of the girder significantly influences its behaviors, necessitating an optimization design to minimize the failure risk of coastal bridges. This study provides valuable insights into the behaviors of coastal bridges under extreme wave conditions and offers references for designing and enhancing coastal bridges.

On the development of a generalized atmospheric boundary layer velocity profile for offshore engineering applications considering wind–wave interaction

Within industrial standards, effects due to wind–wave interaction on the marine atmospheric boundary layer (ABL) may be included via the Charnock sea-surface roughness parameter for open-sea and near-coastal waters. This roughness parameter does not accommodate the wide variety of wave states possible, nor does it modify the ABL to include speed-up effects resulting from an undulating wave profile. In an attempt to provide an updated definition of the general ABL profile for offshore wind engineering applications, an experimental and numerical study is performed to assess the interaction of the ABL on a fixed wave geometry. By extracting the mean velocity field during the wind–wave interaction, bespoke values of the velocity profile power exponent and wind risk factor can be obtained. A range of wave heights and wave lengths are considered from which a Kriging surrogate model is trained to supply the relevant wind profile parameters depending on the wave state. These newly garnered parameters enable the practitioner to define a reference wind velocity, and then adjust the velocity profile characteristics to contain the influence of the wave. This approach provides a new inlet velocity condition that can be used within computational wind engineering investigations without the need to explicitly model the wave surface, as well as flexibility in specifying the underlying wave conditions. Application of the re-calibrated velocity profile shows that wind forces are significantly greater throughout an offshore wind turbine (OWT) swept blade area when large (H= 15 m) and small (H= 1.5 m) wave heights are compared.

Application of the NSGA-II Algorithm and Kriging Model to Optimise the Process Parameters for the Improvement of the Quality of Fresnel Lenses.

The Fresnel lens is an optical system consisting of a series of concentric diamond grooves. One surface of the lens is smooth, while the other is engraved with concentric circles of increasing size. Optical interference, diffraction, and sensitivity to the angle of incidence are used to design the microstructure on the lens surface. The imaging of the optical surface depends on its curvature. By reducing the thickness of the lens, light can still be focused at the same focal point as with a thicker lens. Previously, lenses, including Fresnel lenses, were made of glass due to material limitations. However, the traditional grinding and polishing methods for making Fresnel lenses were not only time-consuming, but also labour-intensive. As a result, costs were high. Later, a thermal pressing process using metal moulds was invented. However, the high surface tension of glass caused some detailed parts to be deformed during the pressing process, resulting in unsatisfactory Fresnel lens performance. In addition, the complex manufacturing process and unstable processing accuracy hindered mass production. This resulted in high prices and limited applications for Fresnel lenses. These factors prevented the widespread use of early Fresnel lenses. In contrast, polymer materials offer advantages, such as low density, light weight, high strength-to-weight ratios, and corrosion resistance. They are also cost effective and available in a wide range of grades. Polymer materials have gradually replaced optical glass and other materials in the manufacture of micro-optical lenses and other miniaturised devices. Therefore, this study focuses on investigating the manufacturing parameters of Fresnel lenses in the injection moulding process. We compare the quality of products obtained by two-stage injection moulding, injection compression moulding, and IMD (in-mould decoration) techniques. The results show that the optimal method is IMD, which reduces the nodal displacement on the Fresnel lens surface and improves the transmission performance. To achieve this, we first establish a Kriging model to correlate the process parameters with optimisation objectives, mapping the design parameters and optimisation objectives. Based on the Kriging model, we integrate the NSGA-II algorithm with the predictive model to obtain the Pareto optimal solutions. By analysing the Pareto frontier, we identify the best process parameters. Finally, it is determined that the average nodal displacement on the Fresnel surface is 0.393 mm, at a holding pressure of 320.35 MPa and a melt temperature of 251.40 °C. Combined with IMD technology, product testing shows a transmittance of 95.43% and an optimisation rate of 59.64%.

Numerical study on the force mechanism of the superstructure of offshore box bridge under tsunami actions

This paper presents a beam-pier structure model based on the Reynolds Averaged Navier-Stokes (RANS) equation and offshore box bridges to investigate the effect of tsunami-induced forces on the superstructure of offshore box bridges. The validity of the numerical simulation is substantiated through the comparison with wave surface theoretical solutions and experimental results. Subsequently, the force mechanism acting on the superstructure of offshore box bridges under tsunami actions is analyzed using the proposed model. The research results show that the peak value of horizontal and vertical forces can be divided into fluctuating growth stages and stable stages with different distances between the center of the section beam and the center of the pier. Notably, the vertical force peak is more susceptible to the pier compared to the horizontal force peak, while the overturning moment on the box girder by the pier has a significant influence. This study is of great significance in the realm of bridge failure modes identification and the formulation of measures aimed at disaster reduction and protection.

Third-order aberration analysis of a Fresnel lens

This paper presents expressions for the third-order aberrations of a Fresnel surface (Seidel coefficients). The formulas are derived in a form that allows analytical aberration analysis to be performed at the stage of layout and preliminary design of a system composed of both classical and Fresnel surfaces. In addition to the five major monochromatic Seidel aberrations of the classical surfaces and the line coma which was described for the Fresnel-type surfaces, another aberration, called quadratic astigmatism, is described in this paper. Although the obtained expressions are an approximation for the third-order aberration domain, i.e. higher-order aberrations are ignored, they provide sufficient accuracy in practice, which is also shown in the paper. The derived expressions can be applied to the analysis of aberrations in schemes using a Fresnel lens, which makes it possible to identify the areas of rational use of elements of this type.

Numerical investigation on the initiation of oblique detonation waves in stoichiometric methane–air mixtures

The study investigates the oblique detonation characteristics in a stoichiometric methane–air mixture employing reactive Euler equations coupled with a detailed chemical reaction model. The analysis evaluates the initiation variation for both the inflow Mach number and the wedge angle. The results show that an increase in the Mach number from M0 = 9 to M0 = 12 changes the oblique shock-to-detonation transition from an abrupt to a smooth type. Furthermore, the distinction between high and low Mach numbers is explored through a comparison of the induction length along the wave surface. Additionally, the transition is affected by changes in wedge angle elevation under high Mach numbers, while a large wedge angle generates a second detonation wave surface due to a strong reflection shock downstream under low Mach numbers. Finally, the initiation length is quantitatively compared across varying inflow Mach numbers and wedge angles, which can benefit future investigations of a methane-fueled oblique detonation engine.

Airy-type bichromatic wave pulses on the sea surface and generation of rogue waves

We present a theoretical study of bichromatic weakly non-collinear Airy-type waves propagating with various amplitudes in water of infinite depth. The coupled nonlinear Schrödinger equations are invoked to study the behavior of self- and cross-interacting Airy wave packets. We demonstrate that bichromatic pulses possess the main properties of single Airy wave packets—shape invariance and self-acceleration or self-deceleration—when propagating in a dispersive medium. Accounting for nonlinearity leads to a strong dependence of the structure, stability, and propagation velocity of wave pulses on their amplitude. We show that interacting pulses of Airy-type waves can form giant accelerating and decelerating waves.

Comparative Performance of Radar, Laser, and Waverider Buoy Measurements of Ocean Waves. Part II: Time-Domain Analysis

Abstract Accurate measurements of ocean waves underpin efficient offshore operations and optimal offshore structure design, helping to ensure the offshore industry can operate both safely and economically. Popular instruments used by the offshore industry are the Rosemount WaveRadar (Radar) and the Waverider Buoy. The Optech Laser has been used at some locations for specific studies. Recent reports indicate systematic differences of order 10% among the wave measurements made by these instruments. This paper examines the relative performance of these instruments based upon various time-domain comparisons, including results from a quality control (QC) procedure, capabilities of measuring the wave surface profile (skewness), and crest heights for varying wind sea and swell conditions. The QC check provides good-quality data that can be further investigated with an assurance of error-free data, suggesting that the Waverider produces the best-quality data with the lowest failure rate compared to the Laser and Radar. A significant number of the Waverider surface elevation records have negative skewness, particularly at higher sea states, affecting its crest height measurements, which are lower than those from the Laser and Radar. Additionally, the significant wave height (H1/3) estimates of the Radar are lower than the Laser and Waverider, but its zero-crossing wave periods (TZ), on average, are longer than the Laser and the Waverider. The significant heights (H1/3) of Laser and Waverider are in good agreement for all three datasets, but the Waverider’s zero-crossing wave period (TZ) estimates are significantly longer than the Laser.

Detecting acoustic chirality with matched metamaterial vortex wave antennas.

Acoustic communications often have limited data rates because of the intrinsically low frequencies. Exploring new spatial modes to increase data bandwidth at fixed frequency is a possible solution to this problem. Here, we demonstrate acoustic wave chirality transmission between two reciprocal metamaterial vortex wave antennas, generating and sensing transmitted acoustic wave chirality through the sub-wavelength geometry of the system. By adding an acoustic leaky wave surface to a ring resonator waveguide, acoustic vortex waves with positive or negative integer mode chirality are independently radiated and detected using a small number of microphones. Through computational simulation and experimental verification, using three-dimensional printed waveguides, we show that the vortex mode chirality can be transferred between two opposing acoustic vortex wave antennas across a small unguided air gap. We also show that emission into an external waveguide can provide long distance data transmission. This demonstrates the first use of metamaterial vortex wave antennas as chiral, mode multi-channel data transceivers.

Sea Surface Roughness Determination from Grazing Angle GPS Ocean Observations and Scatterometry Simulations

Measurements of grazing angle GNSS-R ocean reflections combined with meteorological troposphere data are used for retrieval of ocean wave heights and surface roughness parameters. The observational results are compared to multiphase screen simulations for the same atmosphere conditions. The retrieved data from observations and simulations give equal results within the error bounds of the methods. The obtained ocean mean wave-heights are almost proportional to the square of the wind speed when applying a first-order approximation model to the high-wave-number part of the measured GNSS-R power spectra. The spectral variances from the measurements link directly to the ocean surface roughness, which is also verified by the performed multiple phase-screen wave propagation simulations. Thus, grazing angle GNSS-R techniques are an efficient method for determining the ocean state and the conditions in the boundary layer of the troposphere.

Stable reconstruction of simple Riemannian manifolds from unknown interior sources

Consider the geometric inverse problem: there is a set of delta-sources in spacetime that emit waves travelling at unit speed. If we know all the arrival times at the boundary cylinder of the spacetime, can we reconstruct the space, a Riemannian manifold with boundary? With a finite set of sources we can only hope to get an approximate reconstruction, and we indeed provide a discrete metric approximation to the manifold with explicit data-driven error bounds when the manifold is simple. This is the geometrization of a seismological inverse problem where we measure the arrival times on the surface of waves from an unknown number of unknown interior microseismic events at unknown times. The closeness of two metric spaces with a marked boundary is measured by a labeled Gromov–Hausdorff distance. If measurements are done for infinite time and spatially dense sources, our construction produces the true Riemannian manifold and the finite-time approximations converge to it in the metric sense

New analytical solutions and integrability for the (2 + 1)-dimensional variable coefficients generalized Nizhnik-Novikov-Veselov system arising in the study of fluid dynamics via auto-Backlund transformation approach

Recognising the non-uniformity of boundaries and the inhomogeneities of media, nonlinear evolution equations with variable coefficients may display more realistic scenarios dealing with time-varying environments and inhomogeneous media. In this work, the (2 + 1)-dimensional variable coefficients generalized Nizhnik-Novikov-Veselov system that occurs in the domain of fluid dynamics is investigated. Painlevé analysis technique is used to demonstrate the integrability of the above mentioned system. The governing equations are revealed to be integrable in the Painlevé sense under no specific criterion on the variable-coefficients. To derive numerous analytical solutions, the auto-Bäcklund transformation (ABT) method is taken into account. Consequently, three different analytical solutions are found using the ABT technique, which include linear, exponential, rational, and complex solutions. All the solutions are displayed as 3D plots in which variable coefficients and parameters are varied to produce the desired results. These graphs depict the many aspects of the proposed coupled system in the various forms of periodic waves and complex periodic wave surfaces.

Crustal structure beneath and surrounding the Appalachian Basin region of Eastern North America imaged by joint inversion of P wave receiver functions and surface wave dispersion measurements

SUMMARY To evaluate the plate flexure model for the formation of the Appalachian Basin, we investigate the extent to which crustal structure beneath and surrounding the basin was modified by the Palaeozoic orogenic events that created the basin. We jointly invert receiver functions and surface wave dispersion measurements to obtain 1-D crustal Vs profiles for 261 seismic stations located within and around the basin. The average crustal thickness for the region is 44 km, and the crust gradually thins to the east, consistent with previous studies. Four areas of anomalous crust are identified with respect to the eastward thinning of the crust. An area of thick crust is found along the Grenville Front on the western side of the Appalachian Basin where the crust thickens by ∼5–10 km. Moho depths of up to 54 km in this region likely result from suture-thickening. The crust is thinner beneath the Neoproterozoic Scranton rift by ∼5–7 km, coincident with a ∼40 mGal Bouguer gravity high. Across the Neoproterozoic Rome Trough, the crust thins by ∼4–5 km, coincident with a ∼10 mGal Bouguer gravity high. Density models for these rifts show that the rift-related crustal thinning is sufficient to explain the gravity anomalies. The Vs models obtained for stations in the rifts indicate little, if any, mafic layering in the mid-crust and only a modest amount of mafic layering in the lower crust. In the northwestern portion of the Appalachian Basin in northeastern Ohio and northwestern Pennsylvania within the Elzevir block, another area of anomalously thick crust (50–52 km) is found. This region is not associated with any known tectonic structures or boundaries or a gravity anomaly. The lower ∼5–10 km of the crust in this region is characterized by high (>3.9 km s−1) shear wave velocities and thus appears to be mafic. The origin of anomalous crustal structure in all four areas is best attributed to Precambrian tectonic events that predate the formation of the Appalachian Basin, indicating that the crystalline crust beneath and surrounding the basin was not significantly affected by the Palaeozoic basin-forming orogenic events, a finding which supports the use of plate flexure models for understanding basin formation.

Bidirectional planar absorber with polarization-selective absorption and transmission capabilities.

In this study, we developed a novel planar bidirectional perfect metamaterial absorber (PMA) with polarization-selective absorption and transmission capabilities. The proposed structure can bidirectionally absorb x-polarized incident waves almost perfectly while functioning as a transparent surface for y-polarized incident waves at the same frequency. We discussed the performance and properties of the proposed PMA through simulation results and a theoretical model. We also used the free-space method in experimental tests of a fabricated sample. The results indicated fair consistency between the simulated and measured results, thereby validating the quality of our PMA design.

New Analytic Solutions for Fluid Flow Equations in Higher Dimensions Around an Offshore Structure Describing Bidirectional Wave Surfaces

New Analytic Solutions for Fluid Flow Equations in Higher Dimensions Around an Offshore Structure Describing Bidirectional Wave Surfaces

Numerical Investigation of the Oblique Detonation Waves and Stability in a Super-Detonative Ram Accelerator

This study numerically investigates the effects of diluent gas proportion, the overdrive factor, and throat width on the wave structure and thrust performance of a ram accelerator operating in super-detonative mode. For premixed gas of a high energy density, a typical unstart oblique detonation wave system is observed due to the ignition on the front wedge of the projectile, and the detonation waves move downstream to the shoulder as the energy density decreases. In the start range of the overdrive factor, the wave position also shows a tendency to move downstream as the projectile velocity increases, accompanied by oscillations of the wave surface and thrust. As the throat width increases, the wave standing position changes non-monotonously, with an interval of upstream movement and Mach reflection. The typical wave structure of a ram accelerator in super-detonative mode is identified, as well as the unstart stable wave features and the unstable process for choking, which can provide theoretical guidance for avoiding unstart issues in ram accelerators and optimizing their performance.

Nonlinear fitting based energetic material explosive shock wave pressure action evaluation model

There are many varieties of new developed energetic materials with different capabilities of shock wave pressure action. In order to effectively evaluate the explosive damage power of diverse energetic materials and to make the evaluation model universal, the TNT is used as the basic material, and the evaluation model of the explosive pressure action of energetic materials is established in this paper based on the nonlinear fitting method. Explosion tests of TNT with different charge quantities are carried out under the same test conditions, and the shock wave surface reflection pressure data at different proportional distances are obtained. The evaluation model between the peak pressure of the TNT shock wave and the proportional distances is constructed based on the explosion similarity ratio formula using the nonlinear fitting function. The prediction accuracy of the established model is verified by the typical TNT charge test, and the proposed model is applied to evaluate the explosive pressure effect of energetic materials. Experimental results show that the predication accuracy of the evaluation model for evaluating the explosion shock wave pressure action of energetic materials based on the nonlinear fitting method is higher than 86.5067%, which can meet the requirements of the engineering applications.