This paper explores the spatial evolution of the short-term statistical distributions of zero-crossing crest heights of waves propagating over various sloping bathymetries. The analysis is based on laboratory data obtained from long random wave simulations in realistic sea-state conditions. The experiments were specifically designed to isolate the contributions of key metocean parameters, such as sea-state wave steepness, effective water depth and seabed slope. The crest height distributions are assessed against some of the most widely-applied statistical models in engineering practice. Their range of applicability is investigated, and key deviations are observed. Taken together, the results presented herein offer important insights for improving extreme crest height prediction, and thus provide significant practical implications for and the design of coastal structures.

The understanding of coastal waves is vital in the design of coastal infrastructure and marine renewables. However, the complexity of interacting physical effects including nonlinear wave amplification, wave breaking, and the influence of bathymetry presents significant challenges in modelling waves in the coastal zone. This has catalysed the development of several numerical models that seek to replicate wave propagation observed in real seas by encapsulating these effects. The present study investigates the performance of Simulating WAves till SHore (SWASH), a non-hydrostatic model based on the solution of the nonlinear shallow water equations (Zijlema et al., 2011), at modelling random waves over a range of bathymetries. The accuracy of the numerical model at capturing the evolution of wave heights is evaluated by comparing numerical predictions to equivalent sea-states generated experimentally. The broad range of sea-states and bed slopes explored in this study establishes a wide scope for the findings of this work.

ABSTRACT Jacket platforms are often fitted with sacrificial anodes to prevent marine corrosion. These anodes are attached to the surface of the tubular members of the jacket, increasing the hydrodynamic loads. Industry typically accounts for this using empirical global factors. The study aims to assess the increase in wave loads caused by the presence of anodes using a 1:20 scale model of a representative jacket. Experiments were conducted for two cases: a bare jacket and a jacket fitted with anodes. Regular and random waves were generated and hydrodynamic loads on these jackets were measured for three different angles of wave attack – 0°, 45° and 90°. Comparisons of wave loads from the different sets of experiments were made and salient conclusions are drawn. For the limited cases undertaken, it was found that the jacket with anode contributed significant increase in the wave loads (maximum case) to an extent around 2.5% for regular waves (wave period = 1–3 s) and 17% for random waves (peak wave period = 3 s).

In recent years, the twin-barge float-over method has been widely used in offshore installations. This paper conducts numerical simulation and experimental research on the twin-barge float-over installation of offshore wind turbines (TBFOI-OWTs), focusing primarily on seakeeping performance, and also explores the influence of the gap distance on the hydrodynamic behavior of TBFOI-OWTs. Model tests are conducted in the ocean basin at Tsinghua Shenzhen International Graduate School. A physical model with a scale ratio of 1:50 is designed and fabricated, comprising two barges, a truss carriage frame, two small wind turbines, and a spread catenary mooring system. A series of model tests, including free decay tests, regular wave tests, and random wave tests, are carried out to investigate the hydrodynamics of TBFOI-OWTs. The experimental results and the numerical results are in good agreement, thereby validating the accuracy of the numerical simulation method. The motion RAOs of TBFOI-OWTs are small, demonstrating their good seakeeping performance. Compared with the regular wave situation, the surge and sway motions in random waves have greater ranges and amplitudes. This reveals that the mooring analysis cannot depend on regular waves only, and more importantly, that the random nature of realistic waves is less favorable for float-over installations. The responses in random waves are primarily controlled by motions’ natural frequencies and incident wave frequency. It is also revealed that the distance between two barges has a significant influence on the motion RAOs in beam seas. Within a certain range of incident wave periods (10.00 s < T < 15.00 s), increasing the gap distance reduces the sway RAO and roll RAO due to the energy dissipated by the damping pool of the barge gap. For installation safety within an operating window, it is meaningful but challenging to have accurate predictions of the forthcoming motions. For this, this study employs the Whale Optimization Algorithm (WOA) to optimize the Long Short-Term Memory (LSTM) neural network. Both the stepwise iterative model and the direct multi-step model of LSTM achieve a high accuracy of predicted heave motions. This study, to some extent, affirms the feasibility of float-over installation in the offshore wind power industry and provides a useful scheme for short-term predictions of motions.

On the forcing and collapsing properties of a nonlinear random two-dimensional Schrödinger model in applied physics

This paper experimentally investigates the wave pressure and pore pressure within a sandy seabed around two pipelines under the action of random waves (currents). The experiments revealed that when the random wave plus current cases are compared with the random wave-only case, the forward current promotes wave propagation, whereas the reversed backward current inhibits wave propagation. Furthermore, the wave pressure on the downstream pipeline decreases as the relative spacing ratio increases and increases as the diameter increases. However, alterations in the relative spacing ratio or dimensions of the downstream pipeline exert a negligible influence on the wave pressure of the upstream pipeline. Moreover, the relative spacing ratio between the pipelines and the dimensions of the pipelines considerably influence the pore pressure in the sand bed. When the relative spacing ratio remains constant, increasing the downstream pipeline diameter will increase the pore-water pressure of the soil below the downstream pipeline.

Near-surface floating kelp farms constitute a Nature-Based Solution (NBS) capable of damping incident wind-generated waves, which might be beneficial to reduce wave overtopping on maritime structures. As the global mean sea level rises, the mean wave overtopping discharge is expected to increase. The incorporation of this NBS, as a green–grey solution, might be beneficial to mitigate this effect. Physical modelling experiments with random waves have been conducted to assess the ability of this NBS to reduce the mean wave overtopping discharge on a rubble mound breakwater. Results show that while the mean wave overtopping discharge was reduced by 47% with a kelp farm length of 50 m (prototype scale), a kelp farm of 200 m achieved a reduction of 93% for the tested conditions. This reduction is mainly a function of the ratio between floating kelp farm length and incident wavelength. An idealized case study at the Port of Leixões breakwater suggests that, under storm wave conditions with return period of 2 and 5 years, floating kelp farms could maintain mean wave overtopping discharges below present levels until 2070. Thus, this study highlights the relevance of incorporating NBS with existing coastal and port defence structures as an adaptation measure to mitigate climate change effects.

The number of services on the internet has experienced explosive growth, and the rapid and accurate discovery of required services among a vast array of similarly functioning services with differing degrees of quality has become a critical and challenging aspect of service computing. In this paper, we propose a trusted service discovery algorithm based on an ant colony system (TSDA-ACS). The algorithm integrates a credibility-based trust model with the ant colony search algorithm to facilitate the discovery of trusted web services. During the evaluation process, the trust model employs a pseudo-stochastic proportion to select nodes, where nodes with higher reputation have a greater probability of being chosen. The ant colony uses a voting method to calculate the credibility of service nodes, factoring in both credibility and non-credibility from the query node’s perspective. The algorithm employs an information acquisition strategy, a trust information merging strategy, a routing strategy, and a random wave strategy to guide ant search. To evaluate the effectiveness of the TSDA-ACS, this paper introduces the random walk search algorithm (RW), the classic max–min ant colony algorithm (MMAS), and a trustworthy service discovery based on a modified ant colony algorithm (TSDMACS) for comparison with the TSDA-ACS algorithm. The experiments demonstrate that this method can achieve the discovery of trusted web services with high recall and precision rates. Finally, the efficacy of the proposed algorithm is validated through comparison experiments across various network environments.

Study on mechanism of propagation and deformation of random waves over a complex uneven coral reefs

This study explores the application of the smoothed particle hydrodynamics (SPH) method in simulating Bragg resonant reflection of surface waves to enhance coastal protection strategies. Using the DualSPHysics model, the research investigates the hydrodynamic characteristics of wave interactions with periodic and island reef topographies. The results demonstrate that periodic topographies exhibit stronger wave reflection capabilities compared to island reefs, particularly under resonant conditions, leading to significantly reduced wave heights and impact pressures. This study underscores the potential of SPH, as a comprehensive particle-based model, in advancing coastal engineering and ecological protection. The assessment is based on regular wave conditions in a controlled setting. To improve the accuracy and applicability, future research should consider random wave conditions and diverse marine climate scenarios.

With the increasing global emphasis on sustainable energy, wave energy has gained recognition as a significant renewable marine resource, drawing substantial research attention. However, the efficient conversion of low-frequency, random, and low-energy wave motion into electrical power remains a considerable challenge. In this study, an advanced hybrid generator design is introduced which enhances wave energy harvesting by optimizing wave–body coupling characteristics and incorporating both a triboelectric nanogenerator (TENG) and an electromagnetic generator (EMG) within the shell. The optimized asymmetric trapezoidal shell (ATS) improves output frequency and energy harvesting efficiency in marine environments. Experimental findings under simulated water wave excitation indicate that the accelerations in the x, y, and z directions for the ATS are 1.9 m·s−2, 0.5 m·s−2, and 1.4 m·s−2, respectively, representing 1.2, 5.5, and 2.3 times those observed in the cubic shell. Under real ocean conditions, a single TENG unit embedded in the ATS achieves a maximum transferred charge of 1.54 μC, a short-circuit current of 103 μA, and an open-circuit voltage of 363 V, surpassing the cubic shell by factors of 1.21, 1.24, and 2.13, respectively. These performance metrics closely align with those obtained under six-degree-of-freedom platform oscillation (0.4 Hz, swing angle range of ±6°), exceeding the results observed in laboratory-simulated waves. Notably, the most probable output frequency of the ATS along the x-axis reaches 0.94 Hz in ocean trials, which is 1.94 times the significant wave frequency of ambient sea waves. The integrated hybrid generator efficiently captures low-quality wave energy to power water quality sensors in marine environments. This study highlights the potential of combining synergistic geometric shell design and generator integration to achieve high-performance wave energy harvesting through improved wave–body coupling.

In this work, we investigate the mixing of active scalars in two dimensions by the stirring action of stochastically generated weak shock waves. We use Fourier pseudospectral direct numerical simulations of the interaction of shock waves with two non-reacting species to analyse the mixing dynamics for different Atwood numbers ( At ). Unlike passive scalars, the presence of density gradients in active scalars alters the molecular diffusion term and makes the species diffusion nonlinear, introducing a concentration gradient-driven term and a density gradient-driven nonlinear dissipation term in the concentration evolution equation. We show that the direction of concentration gradient causes the interface across which molecular diffusion occurs to expand outwards or inwards, even without any stirring action. Shock waves enhance the mixing process by increasing the perimeter of the interface and by sustaining concentration gradients. Negative Atwood number mixtures sustain concentration gradients for a longer time than positive Atwood number mixtures due to the so-called nonlinear dissipation terms. We estimate the time until that when the action of stirring is dominant over molecular mixing. We also highlight the role of baroclinicity in increasing the interface perimeter in the stirring dominant regime. We compare the stirring effect of shock waves on mixing of passive scalars with active scalars and show that the vorticity generated by baroclinicity is responsible for the folding and stretching of the interface in the case of active scalars. We conclude by showing that lighter mixtures with denser inhomogeneities ( $At\lt 0$ ) take a longer time to homogenise than the denser mixtures with lighter inhomogeneities ( $At\gt 0$ ).

When the XBeach model is used to simulate beach profiles, the selection of four sensitive parameters—facua, gammax, eps, and gamma—is crucial. Among these, the two key parameters, facua and gamma, are particularly sensitive. However, the XBeach model does not specify the exact choice of these four key parameters, offering only a broad range for each one. In this paper, we investigate the applicability of tuning these four parameters within the XBeach model. We employ Generalized Likelihood Uncertainty Estimation (GLUE) to optimize the model settings. The Brier Skill Score (BSS) for each parameter combination is calculated to quantify the likelihood probability distribution of each parameter. The optimal parameter set (facua = 0.20, gamma = 0.50) was ultimately determined. Here, the facua parameter represents the degree of influence of wave skewness and asymmetry on the direction of sediment transport, while the gamma parameter represents the equivalent random wave in the wave dissipation model and is used to calculate the probability of wave breaking. Six profiles of the southern beach on Chudao Island are selected to validate the results, establishing the XBeach model based on profile measurement data before and after Typhoon “Lekima”. The results indicate that after parameter optimization, the simulation accuracy of XBeach is significantly improved, with the BSS increasing from 0.3 and 0.17 to 0.68 and 0.79 in P1 and P6 profiles, respectively. This paper provides a recommended range for parameter values for future research.

Abstract On compact Riemannian manifolds with chaotic geometries, specifically those exhibiting the random wave model conjectured by Berry, we derive heuristically a homogeneous kinetic wave equation that is universal for all such manifolds.

Instability analysis of random inhomogeneous gravity waves with depth-uniform current

Active heave compensation for remotely operated vehicle (ROV) recovery operations presents significant challenges due to the system's nonlinear dynamics and the influence of random and uncertain external wave disturbances. This study proposes a control strategy that integrates feedforward model predictive control (MPC) with model reference adaptive control (MRAC) to enhance the robustness and performance of heave compensation systems. The MPC utilizes position feedback from the ROV and system modeling to predict future outputs, enabling proactive control adjustments. A hybrid model, combining high-order dynamic mode decomposition with long short-term memory neural networks, is developed to forecast vessel motion. The MPC mitigates the effects of uncertain wave conditions and system delays by incorporating the prediction. In addition, the MRAC dynamically adjusts the proportional–integral–derivative controller parameters in real time, compensating for variations in rotational inertia and nonlinear characteristics caused by winch cable retractions. A comprehensive system dynamics model is presented, which includes barge motion under random wave excitation, the electric-driven winch model, and umbilical cable dynamics. Numerical simulations demonstrate that the feedforward MPC-MRAC controller outperforms conventional control strategies of heave compensation performance, significantly enhancing the control system's disturbance rejection capabilities and operational stability. The proposed control strategy exhibits stable and superior heave compensation performance across sea conditions. These findings provide valuable insights for improving the safety and efficiency of offshore ROV recovery operations in dynamic marine environments.

The potential advantages of wave-energy converters can be extended beyond their capability to produce clean and safe energy, including wave attenuation using hybrid devices. This study presents an experimental investigation of the power production and wave attenuation capabilities of a floating twin-raft hybrid device. Model tests were performed using different random waves and damping values for a simulated power take-off (PTO) system. The coefficients of wave transmission (Kt), reflection (Kr), dissipation (Kl), and mechanical power conversion efficiencies for the seaside raft (η1) and rear side raft (η2) were estimated. It was observed that varying the peak wave period considerably affects the hydrodynamic characteristics, whereas wave height has a lesser influence. The PTO simulation is an area of uncertainty in wave-energy converters. Moreover, the study of the influence of PTO damping on device performance is new. Varying the PTO damping marginally influenced the Kt, Kr, and Kl, whereas the power conversion efficiencies of both seaside and rear-side rafts varied significantly. η1 and η2 were maximized at low-input wave height conditions. As the wave height increased, η1 and η2 decreased. This occurred due to the significant wave-energy dissipation. Liberal (Kt < 0.5 and η1 or η2 > 0.2) and stringent (Kt < 0.2 and η1 or η2 > 0.4) hydrodynamic performance conditions were used to discuss the effective range of available wave frequencies under different PTO damping conditions. This would help identify the areas where this type of device can be applied. This study validated the concept of a floating twin-body hybrid wave-energy converter. This study belongs to the concept development stage of wave-energy conversion technologies, and the conclusions can help further develop and improve this concept.

Hydromechanical factors influencing erosion and recession of compacted sandy bluffs under random waves actions

Abstract Offshore structures are primarily subjected to wind and wave interactions, which are inherently coupled and mutually influence each other. It is necessary to study the mechanism of extreme wind‐wave combined action on offshore structures especially unstable ones for their safety and performance. Utilizing the theory of random waves, this study examines irregular wave actions, focusing specifically on the maximal double‐cantilever configuration of a continuous rigid frame bridge during construction. The dynamic response of the structure under extreme wind‐wave combinations is analyzed, accounting for the effects of flow velocity and piles‐group interactions. By comparing with the results of regular wave analysis, it was found that under the corresponding combination of load conditions, the maximum displacement effect of the structure obtained by using irregular waves was about 20% greater than that obtained by using regular waves, and the maximum internal force effect was about 10% greater. Therefore, using regular waves for structural dynamic analysis may result in smaller results and underestimate the structural responses.

Abstract A floater is a buoyant apparatus employed to enable a floatplane to remain afloat and operate on the water surface. During its operational period, the floater experiences stress and deformation as a result of hydrodynamic loads. This study primarily focuses on providing a comprehensive examination of the structural strength of the proposed floater design. The determination of the structural integrity is achieved by the use of the finite element approach which is a popular method for numerically solving, and where in the wave-induced loads experienced by the floater structure are utilized as input parameters. The stress intensity in the floater structure is resulted in relation to the wave load parameters, specifically wave height and wave heading angle. The use of a structural reliability approach involves the consideration of the inherent randomness associated with both the load imposed on a structure and its strength. The Monte Carlo method is utilized to generate randomness of in order to determine the Probability Density Function (PDF) of both the structure’s stresses and its strength. The computational findings elucidate that the floater structure exhibits reliability level of 97 % to 71% in a range of wave height between 0.5 to 3 meters and including reliability level of 100 % to 92% in a similar wave height factor, based on construction materials of aluminium and steel, respectively. This reliability level was indicating toughness of floater structure in each wave condition, smaller reliability level means there is high chance of structural failure.