Wave Crest Research Articles

Nonlinear random wave fields within a Boussinesq system

The dynamics of nonlinear random fields is important for understanding wave turbulence. In this work, we use a Boussinesq system to examine the distinctions between unidirectional and bidirectional waves. Our study demonstrates that in both scenarios, the wave spectra reach a stationary state. Moreover, we show that the occurrence of rogue waves is more probable in the unidirectional case. In the unidirectional case, the probability distribution of wave crests exceeds the one predicted by the Rayleigh distribution once the spectra reach the stationary state. Conversely, in the bidirectional case, the opposite trend is observed. The discovery of various types of rogue waves, including massive wave trains commonly known in the literature as “two sisters” and “three sisters” are found.

Rogue curves in the Davey-Stewartson I equation.

We report new rogue wave patterns whose wave crests form closed or open curves in the spatial plane, which we call rogue curves, in the Davey-Stewartson I equation. These rogue curves come in various striking shapes, such as rings, double rings, and many others. They emerge from a uniform background (possibly with a few lumps on it), reach high amplitude in such striking shapes, and then disappear into the same background again. We reveal that these rogue curves would arise when an internal parameter in bilinear expressions of the rogue waves is real and large. Analytically, we show that these rogue curves are predicted by root curves of certain types of double-real-variable polynomials. We compare analytical predictions of rogue curves to true solutions and demonstrate good agreement between them.

Experimental study on wave-induced loads and nonlinear effects for pier-pile group foundations of sea-crossing bridges: Wave slamming and suction effect

Strong nonlinear effects, such as wave slamming, suction effects, and wave overtopping, may be induced during wave-bridge interaction. However, an accurate understanding of these nonlinear effects is still insufficient. This study comprehensively investigates the wave slamming and suction effects on pier-pile group foundations of sea-crossing bridges in a 1:50 scale laboratory experiment. Random and regular waves with different strengths are generated based on wave conditions at the bridge site. Five water depths with a 2 cm spacing are designed to simulate varying pile cap clearances. Various pile arrangements are also set up to explore the influence of piles. Results show that wave slamming is low-aeration and is triggered mainly on the cap bottom wall, whereas the wave action on the vertical wall of the pile cap is quasi-static. The suction effect is generally recorded in the quasi-static phase of pressures and depends on the water exit process and the wave crest height. Moreover, the pressure oscillation after the impact phase results from the flow separation and rotation at structure corners. The wave slamming enhances with the increasing wave frequency when the impact area is constant, otherwise, it depends on the impact area. On the cap bottom wall, the wave slamming on inter-pile areas is enhanced, but the suction effect is less affected by pile arrangements. The increase in pile cap clearances reduces vertical forces but has less effect on horizontal forces. Additionally, a sustained increase in the wave crest height may reduce the slamming force. An empirical method for predicting wave forces is finally proposed based on the water entry theory and experimental findings. This work enhances the physical understanding of nonlinear effects during wave-bridge interaction and aims to support the design of substructures for sea-crossing bridges.

Machine learning approach to predict flow fields induced by internal solitary waves acting on mid-water structures based on particle image velocimetry experiments

Mid-water structures (MWSs) have important applications in the ocean to minimize the effects of environmental factors in the surface ocean and to avoid the effects of high pressure on the seabed. However, their operational positions are vulnerable to internal solitary waves (ISWs), which poses a significant challenge to the safe functioning of MWSs. Consequently, there is a pressing need to explore the flow field characteristics surrounding MWSs under the action of ISWs to establish a reliable foundation for structural design. In this study, experimental investigations were conducted to analyze the flow fields induced by ISWs acting on MWSs, employing the particle image velocimetry (PIV) method. The intricate details of the flow fields around the structure were thoroughly analyzed, and the impact of the structure's submerged depth on the ISW-induced flow fields was discussed. A machine learning approach is utilized to develop an Artificial Neural Network (ANN) model aimed at predicting the flow fields of ISWs. The experimental results are compared and analyzed alongside the predicted outcomes, focusing on the anomaly region, the tail field region, and the occluded region. The results show that the presence of the structure complicates the flow characteristics in the tail flow regions, and the flow patterns are constantly changing. The characteristics of the ISW flow fields around the structure vary with the different submerged depths of the MWS. Positioning the MWS above the wave trough results in an ascending trend followed by a descending trend in the strength of the surrounding flow field with increasing submerged depth. The ANN predictions for different types of regions of the flow fields show satisfactory accuracy. The model closely matches the PIV results in predicting the extremes and positions of horizontal velocities in the tail flow fields at different stages of ISW trough propagation. The ANN model can be recommended for predicting the flow fields of ISWs acting on MWSs. This study offers comprehensive insights into the characteristics of the flow fields induced by ISWs acting on MWSs, emphasizing the valuable contribution of machine learning methods to the field of fluid dynamics.

Internal solitary wave in the Lombok Strait: Satellite-observed spatiotemporal characteristics and their propagations modulated by the Indonesian Throughflow

The Lombok Strait shows active large-amplitude internal solitary waves (ISWs) and is also a primary gateway for the Indonesian Throughflow (ITF), which is a critical ocean current affecting the ocean ecosystem. This study collected 858 satellite images from 2018 to 2022, and ISW wave crests were extracted. Analysis shows that ISW 5-year cumulative occurrences reached the highest/ lowest of 136/28 days, with a 29 %/6 % frequency in October/ June. Satellite and reanalysis data revealed that ISW occurrence and propagation speed correlate to ITF variations. Enhanced southward ITF corresponds to less ISW occurrence and decreased/increased northward/southward ISW propagation speed. To understand how ITF modulates ISWs, three-dimensional MITgcm simulations were employed. Results show that when southward ITF decreases, ISWs tend to generate earlier/later, thus leading to a longer/shorter propagation distance for ISWs in the north/ south direction, revealing a suppressive effect on northward ISW generation.

Investigation of Crack Propagation and Failure of Liquid-Filled Cylindrical Shells Damaged in High-Pressure Environments

Cylindrical shell structures have excellent structural properties and load-bearing capacities in fields such as aerospace, marine engineering, and nuclear power. However, under high-pressure conditions, cylindrical shells are prone to cracking due to impact, corrosion, and fatigue, leading to a reduction in structural strength or failure. This paper proposes a static modeling method for damaged liquid-filled cylindrical shells based on the extended finite element method (XFEM). It investigated the impact of different initial crack angles on the crack propagation path and failure process of liquid-filled cylindrical shells, overcoming the difficulties of accurately simulating stress concentration at crack tips and discontinuities in the propagation path encountered in traditional finite element methods. Additionally, based on fluid-structure interaction theory, a dynamic model for damaged liquid-filled cylindrical shells was established, analyzing the changes in pressure and flow state of the fluid during crack propagation. Experimental results showed that although the initial crack angle had a slight effect on the crack propagation path, the crack ultimately extended along both sides of the main axis of the cylindrical shell. When the initial crack angle was 0°, the crack propagation path was more likely to form a through-crack, with the highest penetration rate, whereas when the initial crack angle was 75°, the crack propagation speed was slower. After fluid entered the cylindrical shell, it spurted along the crack propagation path, forming a wave crest at the initial ejection position.

The Impact of the new DMS-1030 Stability Standard on the Future Design of Navy Ships

In 2022, the German BAAINBw launched a revised issue of their 1030-1 stability regulations for Navy surface vessels. The improvements of the revised code concerned (inter alia) a new stability criterion for minimizing the effect of parametric rolling combined with pure loss of stability on the wave crest and revised damage stability calculation assumptions, which mainly focus on the submergence of openings and a special treatment of watertight doors. The improvements of the code were found to be necessary to keep track of recent developments in IMO for commercial ships and to update the safety level represented by the code. At the same time, the revised code gives more freedom to the ship designer, a fact which may allow novel and more cost effective concepts of Navy Ships in the near future, provided, the evaluation of the stability according to the code takes place immediately during the very early design phase of the ship. The present paper gives insight into the important updates of the code and it demonstrates at the same time how the design of Navy Ships may benefit from the revised code, if it is applied throughout the very first design phase of the ship. The paper will further present an improved design regime for the early design stage.

Investigation on the turbulent structures in combined wave-current boundary layers

The problem of turbulent vortices and vortex dynamics under the influence of ocean waves is a subject of continuing research in the field of wave-current interaction. Thus, this study investigates the evolution of turbulence structures and vortex interactions in combined wave-current boundary layers, where water waves propagate with currents. Experiments were performed in two glass-walled laboratory channels with water depths of 160 and 400 mm. A two-dimensional two-component (2D2C) Particle Image Velocimetry (PIV) system was used to measure the velocities. Periodic variations in turbulence are observed for combined wave-current flows. Pairs of counter-rotating vortices are identified in the outer region when the combined flow is reversed, leading to destructive vortex interactions. This process leads to a reduction in the turbulent kinetic energy (TKE) and TKE production and dissipation during the passage of the wave trough. A conceptual model of hairpin vortices in combined wave-current flows is proposed in this study. The results of this study provide novel insights into the hydrodynamics of combined wave-current flows.

Extreme wave impacts on a suspended box above free surface

A systematic approach incorporating precision-controlled experiments and high-fidelity numerical simulations has been employed to delve deeper into the physics of extreme wave impact pressures. Using a suite of high-speed imaging and high-resolution pressure sensing techniques that are accurately synchronized with the wave generation, a consistent and well-correlated set of data providing details of the focusing incident wave front, flow velocities, and impact pressure time histories has been successfully obtained. The numerical simulations using a validated incompressible smoothed particle hydrodynamics (ISPH) provided further details that were not tractable in the experiments. Based on the results obtained, there were five broad impact scenarios identified, ranging from focusing crest impacts to plunging jet impacts with varying entrapped air. Among these impact types, the highest impact pressures were those associated with a focusing wave crest. It has been found that high impact pressures were correlated with a convergence of the horizontally impinging overturning crest and the vertical surge of the wall boundary water mass, but with the overturning crest impingement just ahead of the arrival of the wall boundary water mass, which in essence amounted to the impingement of a focusing wave front. Depending on the relative arrival times of the impinging crest and the wall boundary upsurge, the impact scenarios could vary from an up-slosh to a jet impingement with a clear entrapped air pocket, followed by a flip-through of the incident crest. For the scenario with the highest impact pressures, broadly classified as type II impact in this paper, the peak pressures could reach as high as 85ρC2, an order of magnitude higher than impact scenarios without the focusing effect, such as the scenario with a plunging jet impact with entrapped air (classified as types III and IV impact in this study). As the volume of entrapped air for this scenario was relatively small, the one-phase ISPH model used in this study was able to capture the peak pressure characteristics, including the peak pressure amplitudes. However, in scenarios with significantly highly entrapped air during impact, a two-phase model would be necessary.

Experimental Study Of The Wave Field Around A Monopile Due To Moderate Steepness Irregular Incident Waves

Most offshore wind turbine foundations are of monopile type and need regular marine operations to be conducted nearby during the lifetime of the turbine. Proper wave estimation around the monopile is needed to assure the safety of the operations. The trend of increasing monopile's diameter also adds the need to investigate the wave field around the increased monopile diameter for the marine operation analysis. Experimental campaigns of wave field around a monopile in irregular incident waves with different steepness are reported in this study to extend the available experiments which focused mostly on the runup of cylindrical structures. The wave field at two radial positions and six angular positions around the monopile is investigated. The results are processed to obtain the Linear Transfer Function of the wave field around the monopile and the Exceedance Probability of the wave height and crest of the waves around the monopile. For the tested conditions, the linear solution accurately captures the frequency domain characteristics and the exceedance probability of wave height but fails to predict the crest exceedance probability.

Large eddy simulation of wind turbulence over non-breaking and breaking waves

Wind-wave interaction affects the wind-wave fields and the combined loading on structures. This study aims to characterize turbulent airflow over non-breaking and breaking waves using a high-fidelity two-phase model in OpenFOAM. The volume of fluid method is utilized to model the complex air–water interface. Wind turbulence is considered via prescribing it at the inlet boundary. The model is validated against experimental data, and a numerical case study is conducted to simulate extreme wind and wave-plunging conditions. Results reveal that non-breaking waves induce wind turbulence and affect averaged wind velocity. For wave steepness exceeding 0.35, extreme wind forces amplify the turbulence by over 100% at wave crests. The amplified turbulence region extends to about 0.6λ in height. When waves plunge, an overturning jet propels the wind forward, generates a counterclockwise vortex, and enhances wind turbulence. Averaged wind speeds increase by over 20% above wave crests, with the enhanced region extending to a height of around 0.2λ for old waves. Maximum turbulence kinetic energy transiently increases by around 0.1Cp2 and maximum kinematic energy of wave-coherent velocity increases and subsequently decreases during wave plunging.

The Propagation Velocity and Influences of Environmental Factors of Deterministic Sea Wave Prediction in the Long Crest Wave

Ocean waves are one of the leading environmental factors that cause motion of the ocean’s structure. Wave prediction is of great significance for the safety of marine structures. The deterministic sea wave prediction (DSWP) has been focused on because it provided an accurate temporal wave surface. The propagation velocity of wave components is one of the critical problems in DSWP. In this paper, the research of propagation velocity is focused on. The Taylor expansion to wave number is used to prove that the group velocity is the propagation velocity of wave components. The simulated irregular long crest wave data is generated. Utilizing the simulated data, the calculated wave surfaces based on group velocity are consistent with the simulated results. Meanwhile, the comparisons of calculated results based on the group velocity and phase velocity are given. Then, a tank experiment is set to verify the prediction results. To further investigate the prediction performance under different conditions, the influences of environmental factors, including the wind speed, water depth and sea state are analyzed in this paper.

Dynamic responses and interactive failure mechanisms of carbon fiber composite face sheets/double-layer corrugated core sandwich structures under low-velocity impacts loading

A single-layer and double-layer corrugated core sandwich structure consisting of carbon fibre–reinforced polymer (CFRP) panels and aluminium alloy core layers was designed. Numerical simulations were carried out in HyperMesh/LsDyna, and the simulation results of single-layer and double-layer corrugated sandwich structure were compared with the experimental results to verify the reliability of the proposed numerical model. Compared with the results of single-layer and double-layer corrugated sandwich structure, the superiority of a double-layer corrugated sandwich structure in anti-collision performance is verified. Considering the effects of impact energy and impact position on impact force, energy absorption capacity, and failure mode, a series of low-velocity impact finite element simulations was carried out. It was found that the main failure mode of composite laminates included fibre damage, matrix damage and delamination, and core buckling. At the same impact position, the higher the impact energy, the greater the initial slopes of the contact force-time and absorbed energy-time curves, the higher the peak force, and the larger the energy absorption capacity. Under the same impact energy, when the impactor hit the wave crest of the sandwich structure, the damage to the structure was small; however, the maximum impact force on the structure was large (∼8 kN).

Investigating a defect width identification based on half-peak width for LDC-based eddy current testing

ABSTRACT The eddy current testing (ECT) technology based on the Inductance-to-Digital Converter (LDC) has the advantages of low power consumption and simple signal conditioning circuitry, which contributes to the miniaturisation of the instrument and low power consumption design. Existing defect identification methods primarily focus on the conventional Analog-to-Digital Converter (ADC)-based ECT. These methods rely on complex analytical models to analyze the phase and amplitude information of voltage signal. However, these approaches do not apply to the LDC-based ECT. The paper proposes a method to identify defects employing the R p -Inductance 2D plane, and use the half-peak width of the inductance signal to evaluate the defect width for symmetric slots. Using finite element simulation and experimental verification, the half-peak widths of the inductive signal wave crests at the defects are the same for the four slots with 1 mm width and different depths on the aluminum specimen; for four wire-cut slots with 4 mm depth and different widths, the half-peak widths are positively correlated with the defect widths. These experimental results demonstrate that the relationship between crack width, wave crest, and half-peak width can serve as the foundation for width identification and classification. This also offers a fresh perspective for further quantifying crack widths.

Coarse Sand Transport Processes in the Ripple Vortex Regime Under Asymmetric Nearshore Waves

AbstractLarge‐scale wave flume experiments are conducted in the ripple vortex regime to study near bed coarse sand transport processes below asymmetric surface waves typical of the coastal nearshore region. For this purpose, a set of complementary acoustic instruments were deployed under regular nearshore wave conditions. Time‐resolved velocity, sand concentration and sand flux profiles are measured across both the dense bedload and dilute suspension layers with an Acoustic Concentration and Velocity Profiler. The equilibrium 2D suborbital ripples are in good agreement in terms of dimensions, shape and onshore migration rate with Wang and Yuan (2018, https://doi.org/10.1029/2018jc013810, 2020, https://doi.org/10.1016/j.coastaleng.2019.103583). Stoss ripple vortex entrainment around the trough‐to‐crest flow reversal (FR+) is found to be more energetic in terms of sand pick‐up into suspension compared to the counter rotating lee side vortex around the FR‐ flow reversal, as a consequence of the onshore skewed wave acceleration. Ripple vortex driven nearbed velocity phase leads around both flow reversals exceed typical bed friction induced values found in turbulent Wave Boundary Layers. Intrawave sand erosion events can be distinguished locally at the two ripple vortex positions around the flow reversals and two events more uniformly distributed along the ripple profile at wave crest and trough. Spatial fields of sand flux reveal the origin of the net onshore directed suspended and bedload transport. Good agreement is found with the mechanism identified under asymmetric oscillatory flows in Wang and Yuan (2020, https://doi.org/10.1016/j.coastaleng.2019.103583). Differences with ripple vortex regime under skewed shoaling waves and symmetric oscillatory flows are highlighted.

Location Dictates Snow Aerodynamic Roughness

We conducted an experiment comparing wind speeds and aerodynamic roughness length (z0) values over three snow surface conditions, including a flat smooth surface, a wavy smooth surface, and a wavy surface with fresh snow added, using the wind simulation tunnel at the Shinjo Cryospheric Laboratory in Shinjo, Japan. The results indicate that the measurement location impacts the computed z0 values up to a certain measurement height. When we created small (4 cm high) snow bedforms as waves with a 50 cm period, the computed z0 values varied by up to 35% based on the horizontal sampling location over the wave (furrow versus trough). These computed z0 values for the smooth snow waves were not significantly different than those for the smooth flat snow surface. Fresh snow was then blown over the snow waves. Here, for three of four horizontal sampling locations, the computed z0 values were significantly different over the fresh snow-covered waves as compared to those over the smooth snow waves. Since meteorological stations are usually established over flat land surfaces, a smooth snow surface texture may seem to be an appropriate assumption when calculating z0, but the snowpack surface can vary substantially in space and time. Therefore, the nature of the snow surface geometry should be considered variable when estimating a z0 value, especially for modeling purposes.

The smallest structures in Saturn’s rings from UVIS stellar occultations

On the largest scales Saturn’s rings are often thought of as axisymmetric annuli varying only radially in optical depth with exceptions of spiral waves and eccentric ringlets. But on scales smaller than a few tens of km yet still larger than the largest common ring particles, the assumption of azimuthal symmetry breaks down. Structures such as “straw” in the troughs of density waves, partial gaps around propeller moonlets, and ephemeral particle aggregates such as self-gravity wakes are responsible for the predominant variations in optical depth. During the 13 year Cassini mission, the Ultraviolet Imaging Spectrograph (UVIS) high speed photometer (HSP) measured 80 stellar chord occultations of Saturn’s main rings. In the vicinity of the minimum ring plane radius of each chord, the occultation line-of-sight slewed across the ring plane tangent to the Keplerian motion of the ring particles. These occultations measured ultraviolet light in the wavelength range 110–190 nm with 1- or 2-ms ms integration times, providing optical depth measurements with resolution comparable to the Fresnel scale of ∼10 m in the frame co-moving with the local Keplerian speed. These high-resolution chord occultations reach their minimum ring radii over a broad range of radial locations within Saturn’s main rings and resolve non-axisymmetric structures in a wide variety of ring regions. We measure the azimuthal length scales and optical depth profiles of “ghosts”, or azimuthally limited gaps with radial scales less than 30 m (Baillié et al., 2013), in the C ring plateaus. We measure the length scale of transparent gaps and self-gravity wakes in the peaks and troughs of spiral density waves. We present optical depth profiles which resolve axisymmetric waves in the A and B rings and constrain the azimuthal length scale over which the waves remain axisymmetric to ∼1000 km. We combine autocorrelation length scales from stellar occultations which cut across the minimum ring radius of a chord occultation with line-of-sight trajectories from other occultations which are not tangent to the rings to constrain the morphology of the azimuthally and temporally averaged mesoscale structures at that ring radius. 2D autocorrelation profiles from stellar occultations show self-gravity wakes and axisymmetric waves often coexisting.

Construction of a wavefront model for internal solitary waves and its application in the Northern South China Sea

Internal solitary waves (ISWs) play a crucial role in the development of various physical and biological processes, and numerous high-precision two-dimensional or three-dimensional numerical models have been developed to simulate the generation and propagation processes of ISWs. However, these numerical models, especially when simulating the interaction between ISWs and ocean circulation, require substantial computational resources. This burden can make it challenging to apply them in real-time or short-term forecasting scenarios. In this study, we propose a new numerical model for ISWs by combining traditional one-dimensional ISW theory with wave refraction theory. The proposed model resolves the issues of ray crossing and divergence, which are commonly encountered in traditional refraction models, by employing equally spaced grids along the wave crest line. As a result, this model is capable of simulating the far-field propagation of ISWs. This model enables rapid prediction of the vertical structure and wave crest morphology of ISWs in specific current fields and at given time frames, and it is utilized to investigate the characteristics and propagation of ISWs generated by the nonlinear steepening of internal tide (IT) in the South China Sea. Comparative analysis with satellite imagery demonstrates the model's accurate representation of ISW processes and phenomena, such as wave crest line discontinuities, diffraction, and wave‒wave interactions when passing through Dongsha Island. Furthermore, propagation time estimates based on this model have errors of ±0.98 h (1σ) over which the ISWs are observed by a mooring system, and the average time difference is 0.81 h

Phase-lag effect on the instantaneously-liquefied seabed depth under progressive waves: Explicit approximations

Instantaneous liquefaction can be induced by the upward seepage force while waves propagating over a porous seabed. In this study, the instantaneous liquefaction within a non-cohesive seabed under progressive waves is analytically investigated and verified with the existing offshore observations. To characterize the instantaneous liquefaction potential, the vertical gradient of excess pore-pressure is employed, and the explicit solutions for the liquefied soil depth are then derived to reflect the phase-lag effect. Wave scale effect is further examined by comparative analysis of the liquefaction potential between laboratory and field conditions. It is indicated that, due to the phase-lag effect, the maximum liquefaction potential and the maximum liquefied soil depth no longer appear exactly under the wave trough; nevertheless, such phase difference relative to the wave trough wouldn't exceed π/4. Neglecting the phase-lag effects would considerably underestimate the liquefaction potential as well as the liquefaction depth. Moreover, both the liquefaction potential and the corresponding liquefied soil depth are predominantly related to the non-dimensional parameter Ic for characterizing the combined influence of wave and seabed properties.

Application of Radon Transform in in-seam Wave Advanced Detection Technology

In view of the increasingly high degree of mechanization of coal mining and the increasing difficulty of mining, seismic exploration based on ground seismic method is not applicable in coal seams. Therefore, a trough wave seismic detection method of geophysical prospecting method is introduced into coal mine tunneling roadway, which provides a method and means for ascertaining the geological anomalies in front of the tunnel face. Combined with modern geological information, seismic data can be visualized and interpreted by geological personnel, which can identify geological anomalies such as faults, collapse columns, goafs and water inrush areas in the process of coal seam excavation and mining, and reduce the occurrence of disasters and accidents in the mining process.