Wave Crest Research Articles

Abstract The directional spreading is an important characteristic of a sea state. For example, the probability of extreme wave crests occurring within the sea state and the loading on offshore structures are both dependent on the amount of spreading. Accordingly, field measurements of waves that allow quantification of directional spreading provide valuable insight into the directional characteristics of sea states and consequently into wave crest and wave load modelling. Wave buoys that measure three orthogonal component of surface displacement permit directional spreading to be estimated; the Datawell Directional Waverider buoy and the Sofar Spotter buoy are two examples. The Directional Waverider is a 90 cm diameter buoy and has seen widespread use since its introduction some 35 years ago. The Spotter is a recent development, and due its small size, with a diameter of 38 cm, and relatively low-cost, it has become popular solution for wave measurements, particularly in remote regions of the ocean. The Directional Waverider wave measurements are based on its own acceleration measured with onboard accelerometers, whereas the Spotter wave measurements are based on its own velocity measured with GPS. In this paper we compare the relative performance of the Directional Waverider and the Spotter buoys, with particular focus on the directional spreading, using parallel data sets from measurements made at a near shore, 17 m water depth, location in the US Army Corps of Engineer's field research facility at DUCK, on the east coast of USA.

Tip streaming enables flow transitions from the millimeter scale to the microscale and even nanoscale, generating tiny droplets with broad applications in precision 3D printing, nanomaterial fabrication, and drug delivery. In these applications, high-frequency jetting is required to improve efficiency. However, understanding and controlling high-frequency tip streaming remain challenging. Here, a series of dancing electrohydrodynamic (EHD) tip streaming phenomena is reported, characterized by subharmonic ejection modes under high-frequency electric fields. The underlying mechanism of this intriguing phenomenon is elucidated, which stems from global meniscus oscillations induced by Faraday instability, followed by jetting at the Faraday wave crests due to local interfacial instability. It is shown that the optimal excitation frequencies of these ejections are governed by the natural frequencies of Faraday instability, and introduce a maximum electric Bond number comparing electric and capillary effects to determine the ejection voltage threshold, thus enabling precise control of high-frequency EHD tip streaming. Owing to the high excitation frequency and multi-directional jetting feature, the dancing EHD tip streaming demonstrates enhanced throughput and multi-path delivery, opening new and exciting prospects for various drop-on-demand technologies.

Abstract The sea surface height budget, obtained by integrating hydrostatic balance over the water column, relates sea surface height variations to variations of the seafloor pressure, density in the water column, and atmospheric surface pressure. This budget is crucial for calibrating and interpreting satellite altimetry measurements. It only holds once nonhydrostatic surface gravity waves are averaged out, however, which complicates an observational closure of the budget. Using data from the California Current System, this study demonstrates that the budget closes to within understood uncertainties if GPS buoy measurements of surface height are interpreted as Lagrangian measurements. The buoy largely follows wave motion and spends slightly more time near wave crests than troughs. The associated Stokes offset, which reaches a maximum of 16 cm in these observations, must be accounted for in the Eulerian sea surface height budget.

A novel adaptive time-window method for detecting slow wave-spindle coupling: Comparison of temporal co-occurrence and phase-amplitude coupling approaches.

Double submerged breakwaters play a vital role in coastal protection by dissipating wave energy and mitigating shoreline erosion. Traditional grid-based numerical methods often struggle in capturing the complex, nonlinear wave process around such structures. In this study, a smoothed particle hydrodynamics (SPH) approach is used to simulate nonlinear wave propagation and transformation over double submerged breakwaters. Model validations against extensive experimental data demonstrated excellent agreement in the wave elevations and velocity fields. Results showed that the double submerged breakwater configuration significantly reduces wave crests, enhances wave dispersion, and increases energy dissipation. Analysis of fluid fields revealed strong turbulence and localized vortices behind the structures, providing insight into the energy dissipation mechanisms. The results confirm the effectiveness of the SPH method for simulating wave–structure interactions and offer valuable guidance for the design and application of submerged breakwaters.

Offshore wind turbine foundations are subjected to highly complex cyclic ocean loads in real marine environments. Engineering experience indicates that the horizontal resultant forces of these external loads, as well as the pressure acting on the cap region, are the primary causes of structural damage to offshore wind foundations. Compared to onshore support structures, offshore foundations face more complex and severe loading conditions, among which large cyclic wave loads may lead to destructive damage. Therefore, investigating the cyclic wave loads acting on offshore wind foundations is of great significance for guiding structural design and extending the service life of wind turbines operating in marine environments. In this study, a numerical wave flume was constructed to simulate wave–structure interactions, incorporating oceanographic and hydrological data from a domestic offshore wind farm and a cap-supported pile group structure. The hydrodynamic characteristics of wave action on the pile group were analyzed, and the effects of still water depth and incident wave height on the wave loads were systematically investigated. The results show that the pile located at 135° in the quartering downstream region of the cap, relative to the wave heading direction (pile #4), experiences the largest horizontal wave load, while pile #3 (90°, port side) is subjected to the highest vertical load, both of which are closely related to the position and orientation of the piles. When a wave trough acts on the structure, the vertical wave load on the pile group becomes negative. As the still water depth increases, both the horizontal and vertical wave loads on the pile group increase, with a more significant growth observed in the vertical direction. The vertical wave load on piles #1 through #5 shows a progressively increasing trend with depth. As the incident wave height increases, the horizontal wave loads on piles #1 and #2 slightly decrease, while those on piles #3, #4, and #5 increase. The vertical wave loads on all five piles generally increase with wave height, although the growth rate varies among the piles.

Abstract The purpose of this study is to present the first estimates of the breaking strength parameter, , for individual oceanic whitecaps. This is achieved by combining the estimates of the dissipation rate per unit breaking crest length for these whitecaps reported in Callaghan et al. (2024, https://doi.org/10.1029/2023jc020193) with a measure of the whitecap breaking wave speed to implement the Duncan (1981, https://doi.org/10.1098/rspa.1981.0127) relationship. The resulting values of span the range of previously reported laboratory values. Moreover, average values of are in excellent agreement with previous field‐derived average values using different approaches. The results suggest that making routine estimates of for individual whitecaps is now possible. This opens up new possibilities for how the fifth moment of Phillips' distribution of breaking wave crests can be better constrained to estimate the total dissipation rate of energy by oceanic whitecaps.

Understanding the water entry in waves is crucial for the structural safety and stability of vehicles. This study numerically investigates the dynamics of the high-speed water entry of a slender, truncated-cone-shaped projectile under varying wave conditions. The numerical model employs the Reynolds-averaged Navier–Stokes method with an overlapping grid. The focus is put on the influence of the wave phases, speeds, and entry angles on the motion trajectory and associated flow field evolution. Wave presence significantly affects cavity formation compared with static water, with pronounced asymmetry observed during vertical water entry at zero-crossing points, leading to asymmetric hydrodynamic forces and pitch deviations. Substantial transient radial forces are generated, raising concerns regarding the structural integrity under adverse sea conditions. At wave crests or troughs, increased wave forces result in higher peak drag forces, particularly during the crest entry. The entry angle significantly influences hydrodynamic performance. A larger entry angle generally increases the drag and alters the lift, thereby affecting the stability and trajectory of the projectile. As the entry angle increased, a greater asymmetry between the left and right cavities appeared, particularly at 25°, where the left cavity was smaller. Moreover, higher entry angles often resulted in increased surface splashing and spray generation. This can affect the aerodynamic characteristics of the projectile and lead to additional drag forces that should be considered in the design. The results can help understand the dynamic loads of vehicles under wave conditions, thereby enhancing their trajectory stability and optimizing the structural design.

When a high-speed projectile navigates underwater near the surface, the unsteady free surface changes the surrounding flow velocity and pressure distribution, which affects the supercavitating flow pattern and hydrodynamic characteristics. Therefore, the three-dimensional underwater supercavitating projectiles near the unsteady surface are numerically investigated using the inflow velocity boundary wave-generation method. The effects of wave height, length, and immersion depth are analyzed, and the coupling mechanism between the unsteady free surface and supercavitating flow is revealed. Under the influence of a wavy surface, the cavity near the surface enlarges and fluctuates opposite to the wave period. Consequently, the supercavity presents an asymmetry that is convex up and flat down. This is because the vapor in the cavity expands, and the water below the cavity is more difficult to displace than the surface connecting the atmosphere, which suppresses the downward expansion of the cavity. Thus, the wave arches upward, and the arching of the trough is stronger than that of the wave crest. The projectile accordingly suffers from an upward viscous lift force, which also fluctuates periodically with waves. As wave heights increase, the fluctuations of cavity shapes and hydrodynamic forces are enhanced. As the immersion depth decreases, the interaction between the water surface and the cavity is augmented. The upper cavity further enlarges and fluctuates more violently, leading to a reduction in drag and an enhancement of lift. When the immersion depth is further reduced, the supercavity connects with the free surface, which results in the shrinkage of the cavity and a significant fluctuation of hydrodynamic forces.

Gamma oscillations play a crucial role in core cognitive functions such as memory processes. Enhancing gamma oscillatory activity, which is reduced in Alzheimer’s Disease, may have therapeutic potential, but effective interventions remain to be determined. Previous studies have shown that phase-synchronized electric and magnetic stimulation boosts brain oscillatory activities at theta, alpha, and delta frequency bands in different ways. The high-frequency gamma frequency band remains to be investigated. This study applies novel noninvasive brain stimulation techniques, namely phase-locked 40-Hz intermittent theta-burst stimulation (iTBS) and transcranial alternating current stimulation (tACS), and explores gamma oscillation changes in the brain. Thirty healthy young participants randomly underwent 40-Hz tACS (1), 40-Hz iTBS (2), two combined interventions (phase-locked iTBS to tACS peak sine wave or tACS trough sine wave) (3–4), and a sham condition (5). The target regions were the left and right dorsolateral prefrontal cortex and were stimulated by simultaneous tACS and iTBS. Gamma oscillatory activities (for 2 hours after intervention) were monitored following each intervention. Our results show that all stimulation protocols enhanced 40-Hz oscillatory power. The iTBS-tACS Peak shows the most significant and stable increase in gamma oscillatory activities (up to 2 hours), followed by 40-Hz tACS and 40-Hz iTBS. 40-Hz tACS and 40-Hz iTBS had the strongest acute effects (up to 30 minutes) on induced gamma oscillations, while 40-Hz tACS most consistently induced gamma oscillations for up to 2 hours in overall resting EEG data. Phase-synchronizing iTBS with tACS at 40 Hz and the very 40 Hz tACS alone targeting the dorsolateral prefrontal cortex may be a viable approach for inducing and stabilizing gamma oscillatory activity, particularly in conditions where endogenous gamma oscillations are attenuated, such as Alzheimer’s Disease.

In the present study, the lattice Boltzmann method coupled with the multipseudopotential interaction interparticle force model is employed to investigate the vertical falling film phenomenon. Utilization of this method enables the presentation of various study cases and the adjustment of dimensionless Reynolds and Kapitza numbers within the range of 5.1<Re<35 and 14<Ka<85 simultaneously with reduced computational costs. Waves are induced by sinusoidal excitation at the inlet, and the domain length is chosen to ensure the development of fully developed waves. Numerical results pertaining to wave peak thickness, wave trough thickness, and wave speed are compared with experimental results, which exhibit good agreement. Influential factors affecting velocity profile deviation within waves from the semiparabolic state, including wavy regime and the presence of capillary ripples, are investigated. The current numerical model has the capability to observe vortices resulting from the recirculation phenomenon at the wave peak and can concurrently model flow conditions regarding negative shear stress and proximity to flow reversal in line with experimental findings. Wave peak height and flow rate at Ka=25 are studied as functions of Reynolds number variations, revealing that at the second critical Reynolds number equal to 25, the wave peak height and maximum flow rate reach their highest values, coinciding with the occurrence of the recirculation phenomenon.

The strong nonlinearity of shallow-water waves significantly affects the dynamic response of floating offshore wind turbines (FOWTs), introducing additional complexity in motion behavior. This study presents a series of 1:80-scale experiments conducted on a 5 MW FOWT at a 50 m water depth, under regular, irregular, and focused wave conditions. The tests were conducted under regular, irregular, and focused wave conditions. The results show that, under both regular and irregular wave conditions, the platform’s motion and mooring tension increased as the wave period became longer, indicating a greater energy transfer and stronger coupling effects at lower wave frequencies. Specifically, in irregular seas, mooring tension increased by 16% between moderate and high sea states, with pronounced surge–pitch coupling near the natural frequency. Under focused wave conditions, the platform experienced significant surge displacement due to the impact of large wave crests, followed by free-decay behavior. Meanwhile, the pitch amplitude increased by up to 27%, and mooring line tension rose by 16% as the wave steepness intensified. These findings provide valuable insights for the design and optimization of FOWTs in complex marine environments, particularly under extreme wave conditions. Additionally, they contribute to the refinement of relevant numerical simulation methods.

The results of direct numerical simulation of plane-symmetric turbulence of water waves for potential flows within the framework of conformal variables taking into account low-frequency pumping and high-frequency viscous dissipation are presented. In this model, for a wide range of pumping amplitudes, the weak turbulence regime was not detected. It is shown that for typical turbulence parameters, the main effects are the processes of wave breaking, the formation of cusps on wave crests, which make the main contribution to the turbulence spectra with a dependence on frequency and wavenumber with the same exponent equal to –4. In this strongly nonlinear regime, the probability density of wave steepness at large deviations has power-law tails responsible for the intermittency of turbulence.

Abstract. Wave extreme values, such as significant wave height, peak period, and crest height, are central to design and operation practices for offshore wind structures. However, the most suitable methods for deriving these extremes, both statistically and from numerical models, are not straightforward. This is especially acute in mixed-type climates, as on the Atlantic coast of the US, where tropical cyclones (hurricanes) and extratropical cyclones (winter storms) occur at the same locations with varying frequency and intensity. Limited guidance is provided in major offshore wind energy standards for the minimum requirements of these ocean models and methods used for determining accurate design and operational metocean conditions for regions with tropical cyclones and mixed-type environments. This study investigates the representation of extreme significant wave heights on the US Atlantic coast generated by mixed storm types, as represented in numerical simulations and univariate extreme value analysis. Notable differences between N-year design values are found, as projected by the two different modeled conditions with both block maxima and peaks-over-threshold methods. Attributing factors include hindcast duration, proximity of design location to storm track centers, and single analysis of mixed-type distributions. This paper is the first of its kind to propose a methodology for defining extreme significant wave heights due to tropical cyclones for offshore wind design and operation in mid-Atlantic and North Atlantic waters. Recommendations for achieving accurate and representative extreme values for offshore design on the US Atlantic coast are provided.

The eastern North Pacific Ocean coastline (from the Salish Sea to the western Aleutian Islands) is highly glaciated with relic sediment deposits scattered throughout a highly contoured and variable bathymetry. Oceanographic conditions feature strong currents and tidal exchange. Sand wave fields are prominent features within these glaciated shorelines and provide critical habitat to sand lance (Ammodytes spp.). Despite an awareness of the importance of these benthic habitats, attributes related to their structure and characteristics remain undocumented. We explored the micro-bathymetric morphology of a subtidal sand wave field known to be a consistent habitat for sand lance. We calculated geomorphic attributes of the bedform habitat, analyzed sediment composition, and measured oceanographic properties of the associated water column. This feature has a streamlined teardrop form, tapered in the direction of the predominant tidal current. Consistent flow paths along the long axis contribute to well-defined and maintained bedform morphology and margin. Distinct patterns in amplitude and period of sand waves were documented. Strong tidal exchange has resulted in well-sorted medium-to-coarse-grained sediments with coarser sediments, including gravel and cobble, within wave troughs. Extensive mixing related to tidal currents results in a highly oxygenated water column, even to depths of 80 m. Our analysis provides unique insights into the physical characteristics that define high-quality habitat for these fish. Further work is needed to identify, enumerate, and map the presence and relative quality of these benthic habitats and to characterize the oceanographic properties that maintain these benthic habitats over time.

Abstract This study demonstrates the impact of mountain width on the occurrence of downslope windstorms by deriving a solution for 2-D flow past an idealized mountain range, including non-hydrostatic effects. Additionally, idealized numerical simulations were conducted to validate the solution. The novel solution revealed physical process of the mountain width effect after wave breaking. As the mountain width decreased, more wave crests appeared per unit horizontal distance, indicating an increase in the horizontal wavenumber of mountain waves. A higher horizontal wavenumber leads to a lower vertical wavenumber, resulting in a longer vertical wavelength. As the vertical wavelength increased, the non-dimensional mountain height normalized using this wavelength decreased. A reduced non-dimensional mountain height inhibits the occurrence of downslope winds after wave breaking. The solution extends the local hydraulic theory to non-hydrostatic conditions and advances local wind studies. The idealized numerical simulations yielded similar results as from the proposed analytical solution. The simulations showed that narrow mountain ranges required higher heights than wide ones to generate downslope winds. Specifically, no downslope winds occurred after the wave broke in the simulation within the narrow mountain range of a particular height. In contrast, downslope winds occurred after the wave broke in the simulation with a wide mountain range of the same height. Moreover, wave breaking did not occur when the mountain height was sufficiently low. Mountain waves propagate upward and downstream within narrow mountain ranges. In contrast, mountain waves propagate upward only over wide mountain ranges. When the mountain height was sufficiently high, downslope winds occurred after the wave broke regardless of the mountain width.

Hydrodynamic modulation of short ocean surface waves by longer ambient waves significantly influences remote sensing, interpretation of in situ wave measurements and numerical wave forecasting. This paper revisits the wave crest and action conservation laws and derives steady, nonlinear, analytical solutions for the change of short-wave wavenumber, action and gravitational acceleration due to the presence of longer waves. We validate the analytical solutions with numerical solutions of the full crest and action conservation equations. The nonlinear analytical solutions of short-wave wavenumber, amplitude and steepness modulation significantly deviate from the linear analytical solutions of Longuet-Higgins &amp; Stewart (1960 J. Fluid Mech. vol. 8, no. 4, pp. 565–583) and are similar to the nonlinear numerical solutions by Longuet-Higgins (1987 J. Fluid Mech. vol. 177, pp. 293–306) and Zhang &amp; Melville (1990 J. Fluid Mech. vol. 214, pp. 321–346). The short-wave steepness modulation is attributed 5/8 to wavenumber, 1/4 due to wave action and 1/8 due to effective gravity. Examining the homogeneity and stationarity requirements for the conservation of wave action reveals that stationarity is a stronger requirement and is generally not satisfied for very steep long waves. We examine the results of Peureux et al. (2021 J. Geophys. Res.: Oceans vol. 126, no. 1, e2020JC016735) who found through numerical simulations that the short-wave modulation grows unsteadily with each long-wave passage. We show that this unsteady growth only occurs for homogeneous initial conditions as a special case and not generally. The proposed steady solutions are a good approximation of the nonlinear crest-action conservation solutions in long-wave steepness $\lesssim 0.2$ . Except for a subset of initial conditions, the solutions to the nonlinearised crest-action conservation equations are mostly steady in the reference frame of the long waves.

The traditional steady-state focused wave model is commonly used to assess the quality of focused wave generation in physical/numerical wave flumes. However, it cannot determine whether the given focused wave parameters are suitable for evolving a desired wave profile, often requiring multiple adjustments of the focused parameters. In this study, we develop an analytical transient solution for focused waves using the phase velocity method (FWPV) within the framework of linear potential flow theory. The FWPV method captures all transient features of the free surface elevation during the evolution of focused waves and allows for the extraction of transient characteristics for each individual wave component. Consequently, it can be employed to identify appropriate focused wave parameters. We investigate how the free surface profiles of focused waves are affected by different focused parameters and find that an asymmetry in the wave crests and troughs on either side of the main crest occurs. This asymmetry is attributed to unreasonably focused parameters. Additionally, we compare the transient features of the free surface elevations predicted by the FWPV with the results from computational fluid dynamics (CFD) simulations and the high-order spectral (HOS) model. Our findings show that the theoretical results closely match the results of CFD and HOS when wave nonlinearity is weak.

Abstract This study investigates sediment resuspension by internal wave processes on the shallow California shelf, using high-resolution field observations collected by the Naval Research Laboratory during the 2017 Inner-Shelf Dynamics Experiment. High-resolution observations of pressure, flow velocity profiles, temperature stratification, and acoustic backscatter intensity collected near the 35-m isobath show that California inner shelf is a dynamic environment of coupled multiscale perturbations that include barotropic surface tides, internal tides and waves, and surface gravity waves. Here, we analyze sediment resuspension by an internal wave group event observed on 15 September 2017, using several theoretical formulations of wave–current boundary layer flows. Our analysis indicates that the oscillatory bottom stress induced by surface waves exceeded the mobilization threshold throughout the entire event allowing internal wave/tide currents to easily transport or resuspend the mobilized sediments. The analysis of the acoustic backscatter recorded by a velocity profiler suggests that sediment resuspension by the combined internal tide/waves flows occurred primarily under internal wave crests rather than troughs. We show that resuspension is caused by increased near-bed turbulence due to the phase coupling of internal tide and waves, which skews near-bed flows to the direction of the internal wave propagation. This is consistent with previous results showing increased turbulence during the onshore internal wave phase (Becherer et al. 2020). Because the dominant mechanism of internal wave generation on a shallow shelf is the nonlinear disintegration of the internal tide, the phase relation between the internal tide and internal waves is not random but governed by the history of their nonlinear shoaling evolution. This suggests the possibility that the sediment transport direction is modulated by the phase relation between internal tides and internal waves. Significance Statement This study investigates sediment resuspension under the multiscale turbulence due to surface waves and internal waves and tides on a shallow shelf. Results show that all turbulence scales contribute to sediment resuspension. Surface waves stresses consistently exceed sediment mobilization threshold, while the stresses due to the combined internal tide/waves flow exceed the resuspension threshold when the two oscillations are in phase. The phase relation determines the direction of sediment transport. This effect is significant for shallow shelves, where internal waves are generated by the disintegration of the internal tide, and therefore, their phase relationship is a product of their coupled evolution.

This paper presents the aspects of the formation of multilayer composite material (MCM) consisting of aluminium-magnesium alloy AlMg6, titanium VT1-0 and austenitic stainless steel 12Cr18Ni10Тi during explosive welding. This MCM has promising properties for use in various industries such as shipbuilding and automobile manufacturing. However, the production of this material presents certain difficulties due to different properties of the initial materials. In this paper, the effect of residual stresses occurring in MCM after explosive welding on the continuity of the joint was investigated. Using metallographic studies and electron microscopy, it was found that the high velocity impact process between different materials comprising MCM formed weld interfaces with straight and wavy profiles. There was also evidence of dynamic recrystallisation at the 12Cr18Ni10Ti–VT1-0 weld interface and the formation of vortex zones in wave crests. The microhardness of the layers was also measured. The measurement showed that hardening occurred in MCM layers with the maximum value in the 12Cr18Ni10Ti steel layer. The evaluation of tear strength revealed that the formation of cracks occurred at the interface between the VT1-0–AlMg6 weld interface, with an average strength of 160 MPa. The results of the study may be useful to specialists in materials science, mechanical engineering and other related fields