Wave Forces Research Articles

Hydrodynamic Characteristics of Offshore Wind Turbine Pile Foundations Under Combined Focusing Wave-Current Conditions

In extreme marine environments, the interaction between offshore wind turbine pile foundations (OWTPFs) is critical, and the associated hydrodynamic loads are complex. This study focused on fixed OWTPFs and used computational fluid dynamics (CFD) to numerically simulate the flow field around pile foundations under the combined action of focusing waves and current. The objective was to investigate the influence of different focusing wave and current parameters on the hydrodynamic properties of the pile foundations. The findings indicate the following: (1) When the wave and current directions are opposite, the maximum wave force on the pile foundations is greater than when they are aligned. (2) Large-amplitude focusing waves around pile foundations generate secondary loads, which are nonlinear and lead to a rapid increase in the wave force. These secondary loads are short-lived and particularly prominent near the front row of pile foundations. (3) The influence of the group pile effect diminishes under high-amplitude waves, where the wave component dominates the generation of the dimensionless wave force, and the impact of the current on this force decreases.

The Summer North Atlantic Oscillation, Arctic sea ice, and Arctic jet Rossby wave forcing.

We use Coupled Model Intercomparison Project Phase 6 (CMIP6) coupled and Atmospheric Model Intercomparison Project (AMIP) climate models, dynamical analyses, and observations to investigate interactions between summer Arctic sea ice concentration (SIC) variations and the Summer North Atlantic Oscillation (SNAO). Observations suggest that SIC-SNAO relationships mainly come from the East Siberian to Arctic Canada (ESAC) region where a weak atmospheric jet stream exists in summer. Twelve CMIP6 models with the most realistic atmospheric climatologies over the North Atlantic and Europe agree well with reanalyses on relationships between SIC and Northern Hemisphere atmospheric circulation. CMIP6 model data indicate that ESAC SIC influences the SNAO with a lead time of several weeks. However, AMIP simulations do not reproduce the observed atmospheric circulation when observed sea ice is prescribed. Rossby wave analyses do though support observed ESAC SIC influences on the SNAO. We conclude that ESAC Arctic SIC modestly influences the SNAO, and such investigations require the use of coupled models.

Experimental Investigation of Nonlinear Forces on a Monopile Offshore Wind Turbine Foundation Under Directionally Spread Waves

Abstract Accurate prediction of nonlinear wave loading is crucial for designing marine and offshore structures, yet it remains a challenging task. Prior research has primarily focused on uni-directional extreme sea states, revealing that linear loading cannot accurately represent the total wave forces acting on offshore wind turbine foundations, with significant contributions from high-order harmonics. This study broadens the scope to include multi-directional and bi-directional wave interactions with monopile offshore wind turbine foundations. We use a phase-based harmonic separation method to isolate harmonic components in the presence of complex wave scenarios. This approach allows for the clear delineation of individual harmonics from the total wave force by controlling the phase of incident focused waves. Remarkably, this method shown effective even with multi-directional and bi-directional spreading. The clean separation of individual harmonics enables the estimation of contributions from each harmonic. Our findings are in line with previous research, showing that nonlinear loading can constitute up to 40% of the total under certain wave conditions. We have also observed that wider wave spreading reduces nonlinear high-order harmonics, and uni-directional waves induce the most severe nonlinear forces. These insights emphasise the importance of accounting for high-order nonlinear wave loading in offshore structure design.

Design and Research of Dual-Mode Power Generation Device Based on Improved Oscillating Buoy

In response to the national “dual-carbon” strategic goals, a dual-mode ocean energy generation device was researched. First, improvements were made to the power generation system and mechanical structure of an oscillating buoy with a radius of 2.5 m, designing a power generation device that utilizes both wave energy and tidal energy. Subsequently, wave generation was carried out using the Realizable k-ε turbulence model, and the buoy’s strength was analyzed using the Ansys Fluent simulation platform with finite element analysis, with simulation results indicating a rational design. Then, the Froude–Krylov hypothesis method and the oscillating buoy body decomposition method were used to calculate the combined force in the vertical direction of the buoy, and combined with other forces, the maximum wave force on the buoy was determined. It was verified that the buoyancy of the buoy met the requirements of the hydraulic system. Finally, the hydraulic power generation system model was simulated and analyzed using AMEsim, yielding a power generation of 55.2284 kW. Using a formula, the maximum power generation of a single buoy was calculated to be approximately 15.5 kW, and the ideal maximum power generation of the entire device was able to reach 101.7284 kW.

Large eddy simulation of the combined effect of heat fluxes and wave forcing of summer monsoon on a diurnal ocean mixed layer in the north Arabian Sea

Large eddy simulation of the combined effect of heat fluxes and wave forcing of summer monsoon on a diurnal ocean mixed layer in the north Arabian Sea

Dynamic response analysis of a floating bridge structure under combined actions from seismic loading and waves at different incident angles

Abstract This paper investigates the complex coupled response of a cross-sea floating bridge under the combined actions of seismic loading and wave at different incident angles. The bridge structure is modeled using the finite element method, considering the interaction between the girder, pier, pontoon, and mooring chains. Wave forces are calculated based on potential theory, and an added mass approach is applied to simulate the hydrodynamic forces induced by the earthquake. Simulations were conducted using a one-year random wave at three different incident angles of 0o, 45o, and 90o, combined with three-dimensional seismic loading of varying magnitudes: 0.3 g, 0.5 g, and 1 g. The simulation results indicate that the direction of the incident wave significantly influences the bridge's response. The coupling effect between wave and seismic forces on the floating bridge's response is not simply additive. Generally, when the earthquake magnitude is low, the wave loading significantly impacts the bridge's dynamics. However, as the earthquake magnitude increases, the bridge's response becomes dominated by the seismic forces, rendering the influence of wave forces negligible.

A probabilistic coral rubble mechanical instability model applied with field observations from the Great Barrier Reef

Unstable coral rubble hinders coral recruitment and recovery of coral reefs after damage from cyclones and bleaching events. If coral rubble remains unstable under typical everyday environmental conditions, areas of coral rubble will not be able to recover. Evaluating the probability of rubble instability over regional scale reef systems can assist the optimization of coral reef restoration efforts. Currently, robust and verified models for such applications do not exist. This paper presents a comprehensive assessment method to predict the probability of coral rubble instability, which combines a fluid-structural interaction approach with a statistical regional wave climate model. The hydrodynamic model employs non-linear wave theory to determine near-bed velocity, pressure gradients, and the corresponding drag and inertia forces acting on the coral rubble. The instability model assesses when overturning or sliding forces exceed resisting forces, considering thousands of combinations of different coral sizes and densities to calculate the proportion of instability under a given wave forcing. The model was calibrated and validated using prior laboratory experiments as reported by Kenyon et al. (2023b). The hydrodynamic and instability models use an extensive dataset of non-cyclonic wave climates (hindcast from over 30 years of wind measurements) specific to the region around Heron Reef, Great Barrier Reef, Australia, enabling a comprehensive evaluation of the probability of rubble instability in this area. Results indicate that the overall probability of rubble instability reaches 0.74 in water depths less than 2 meters (typical of reef crests or reef flats), while it declines to below 0.21 at a depth of 12 meters (typical deeper parts of the fore reef). Coral rubble on reef crests near Heron Reef, which are sheltered by surrounding formations, demonstrates low probability of instability. Thus, coral rubble instability is influenced by both its specific location within the reef and the position of the reef relative to other nearby reefs. By integrating the rubble instability model with non-cyclonic wave climate data, a map of the probability of rubble instability was generated for eight reefs in the Capricorn and Bunker Group (CBG). This map provides valuable guidance for coral reef restoration efforts, significantly reducing the need for extensive field-based data.

Numerical study of internal solitary wave loads on a submerged slender body with multi-parameter coupling

This study investigates the destabilizing loads exerted on submarines by large-amplitude internal solitary waves (ISWs), which significantly increase the risk of a phenomenon known as “falling deep.” Using numerical simulations and theoretical analysis, the research explores the multi-parameter coupling effects of ISWs on a slender body in a two-layer fluid system. A numerical wave generation method for large-amplitude ISWs, based on the strongly nonlinear adjusted high-order unidirectional (aHOU) model, is proposed. A corresponding numerical model is also developed to simulate the interaction between ISWs and a submerged slender body, with validation against experimental data confirming its accuracy and reliability. The study further examines how wave amplitude, submergence depth, and wave incidence angle affect the load characteristics induced by ISWs. Theoretical analysis identifies the components of ISW-induced loads, revealing a linear relationship between horizontal load and wave amplitude, as well as the influence of submergence depth on the duration of vertical forces. The primary contributor to the horizontal force is identified as the pressure-gradient force generated by the ISW's flow field, while the vertical force is primarily driven by the reduced gravity force due to density stratification and wave forces, which are well-approximated by Morison's formula. Additionally, the peak values of horizontal and vertical forces are significantly affected by wave incidence angle and wave amplitude, respectively. These findings provide a theoretical foundation for understanding the “falling deep” phenomenon encountered by submarines under the influence of ISWs.

Experimental study on hydrodynamic performance and structural forces of curved and vertical front face pile-supported permeable breakwaters

This paper presents an experimental study on the hydrodynamic characteristics and structural forces of pile-supported permeable breakwaters under regular wave conditions. The study evaluates three distinct configurations: one featuring a vertical superstructure, another with a permeable curved superstructure, and a third that combines a permeable curved superstructure incorporating a perforated diaphragm. Experiments were conducted under regulated wave conditions, focusing on pressures, forces, and hydrodynamic scattering coefficients associated with each structural form. Results from the experiments indicate that, under the conditions tested in this study, the curved permeable superstructure significantly reduces wave reflection coefficients and forces acting on critical elements. The curved permeable superstructure maintains reflection coefficients below 0.3 while ensuring low transmission coefficients. Moreover, the study explores dynamic water pressure on an inclined perforated plate and identifies an asymmetric double-peak phenomenon in the pressure time series, signifying the transition from regular waves to breaking waves. The critical wave steepness for the occurrence of double peaks was found to be lower than the breaking limit steepness. Filter analysis elucidates the generation mechanism and evolution pattern of this double-peak phenomenon, revealing the influence of relative water depth, with second-order harmonics dominating near the bottom and second- and third-order harmonics prevalent at the free water surface. This research contributes to the understanding of the hydrodynamic performance of pile-supported permeable breakwaters and underscores the benefits of the curved permeable superstructure design in reducing wave reflection and structural forces. The findings provide valuable insight for the further development and application of pile-supported breakwater structures.

Transient resonant triads: An examination of turbulent patches injected into finite-width internal wave fields

This article presents an experimental investigation into the interaction of a freely evolving turbulent structure with a steadily forced, finite-width internal gravity wave beam. Specifically, a vortex ring is used as the simplified prototype for a propagating turbulent structure and we present an exploration into how it's passage affects the linear stability of the imposed (or forced) wave field. We use the term "vortex ring" to describe an initially axisymmetric, toroidal fluid structure with azimuthal vorticity. We first examine both the vortex ring and the imposed internal gravity wave beam separately and present how they develop in a quiescent, stratified environment. In the absence of any vortex ring, we find—in agreement with many previous studies—there is an amplitude threshold that the wave beam must surpass before it becomes linearly unstable by a process known as triadic resonance instability (TRI). In the absence of an imposed wave field, we present the propagation and collapse of a coherent vortex ring into a turbulent patch, and measure the transient spectrum of internal waves produced. We then combine these two phenomena and investigate how each impacts the other. While we find that the preexisting internal wave beam has no significant influence on the evolution of the incident vortex ring, we do find that the propagation and subsequent collapse of the ring provokes a response from the internal wave beam. This response allows us to demonstrate two key findings relating to the internal wave beams pathway to triadic resonance. First, the passage of a vortex ring propagating through a forced wave field can provide a nonlinear trigger for the transition to a triadic state when the amplitude of the imposed wave field is itself too small for the spontaneous growth of such a triadic state through TRI. Second, we find that in some cases the triadic states induced by this interaction are not self-sustaining and eventually decay, prompting the terminology "transient triads." These surprising findings are further confirmed by the unintentional release of trapped air arising from under our "magic carpet" wavemaker. These air bubbles turbulently propagate vertically through the imposed beam and, in some cases, induce similar triadic state transitions to those of the vortex ring. Our analysis leads to a discussion on the beam's pathway to instability and to question the structure of the underlying dynamical system arising from the distribution of spectral power in a finite-width beam. Published by the American Physical Society 2024

The effect of a 120 kg pontoon mass on the wave energy converter device due to heaving

The environment is negatively impacted by the use of fossil fuels as a source of electricity. Using sustainable ocean wave energy is one way to replace fossil fuels and maximize the usage of natural energy. Electrical energy is produced from mechanical energy by ocean waves. An apparatus for converting wave energy from the ocean is needed to absorb it. The wave energy converter uses the up-and-down action of a chain on a pontoon to rotate a generator, producing electrical energy. The mass of the pontoon and the force of the ocean waves that excite it both have an impact on its vertical movement. Thus, the impact of pontoon mass on the wave energy converter is examined in this research. Both a planetary gear system and one without were used in the investigation. The voltage and current obtained at a wave height of 35 cm were 2.28 Volts and 0.160 A, respectively, without the planetary gear and 160.41 Volts and 13.95 A, with the planetary gear. Furthermore, an evaluation of the wave energy converter machine's performance was carried out. Using a planetary gear and a wave height of 13 cm, the second experiment's minimum power production was 212.63 Watts, while the sixth experiment's maximum power output was 2237.72 Watts with a wave height of 35 cm. In the second experiment, the generator without a planetary gear produced 0.0327 watts of power with the same wave height, and in the sixth trial, the generator produced a maximum of 0.3648 watts with a 35 cm wave height. As a result, utilizing a generator with a planetary gear is preferable to using one without one

Group interaction effect on breaking wave forces on a vertical pile: Experimental tests and predictive models

Pile groups are extensively utilized as supports for many coastal structures, such as bridges, jetties, and oil production platforms. The problem of understanding the interaction effects within pile groups and predicting the breaking wave forces on them is considered in this paper, using experimental tests and machine learning-based predictive modeling. The restriction of previous studies on this important engineering problem is that the pile group arrangements considered are limited. Prediction methods are therefore developed only for specific pile group arrangements and do not incorporate the effect of the incident wave direction. In this study, to partially overcome this limitation, an extensive experimental investigation is conducted on 70 different pile group arrangements under six breaking wave conditions. Three pile group coefficients, characterized by the total, quasi-static, and dynamic forces, are introduced for a thorough assessment of the interaction effects within the pile group. First, the pile group coefficients for three basic arrangements (tandem, side-by-side, and staggered) are evaluated. The results reveal a sheltering effect in the tandem arrangement and an amplification effect in the side-by-side arrangement. However, the forces on the measured pile in the staggered arrangement resemble those on the isolated pile, with neither significant sheltering nor amplification effects observed. Then, the results for all arrangements highlight the significant effect of wave direction on the pile group coefficients for small inter-pile spacing. Finally, different machine learning algorithms are adopted to develop predictive models for the group coefficients. The XGBoost model demonstrates superior accuracy for predicting the total and quasi-static force coefficients, while the dynamic force coefficient remains challenging to predict accurately due to its stochastic nature.

Predictability of the 2020 Strong Vortex in the Antarctic Stratosphere and the Role of Ozone

AbstractThe Antarctic vortex of October–December 2020 was the strongest on record in the satellite era for the season in the mid‐ to lower stratosphere. However, it was poorly predicted by the Australian Bureau of Meteorology's operational seasonal climate forecast system of that time, ACCESS‐S1, even at a short lead time of a month. Using the current operational forecast system, ACCESS‐S2, we have, therefore, tried to find a primary cause of the limited predictability of this event and conducted forecast sensitivity experiments to understand the potential role of ozone in the event and its associated anomalies of the Southern Annular Mode (SAM) and rainfall over south–eastern Australia and western Patagonia. Here, we show that the 2020 strong vortex event did not follow the canonical dynamical evolution seen in previous strong vortex events in spring but suddenly appeared as a result of the record‐low upward propagating wave activity in September 2020. The ACCESS‐S2 forecasts significantly underestimated the negative wave forcing in September even at zero lead time, irrespective of the ozone configuration, therefore falling short in predicting the record strength of the polar vortex in late spring 2020. Nevertheless, ACCESS‐S2 with prescribed realistic ozone that had large anomalies in the Antarctic stratosphere significantly better predicted the strong vortex and the subsequent positive SAM and related rainfall anomalies over south–eastern Australia and western Patagonia in the austral summer of 2020–21. This highlights the potentially important role of ozone variations for seasonal climate forecasting as a source of long‐lead predictability.

Numerical estimation of wave breaking forces on seawalls

ABSTRACT This paper presents a computationally efficient numerical scheme to estimate wave forces from plunging breakers on vertical rigid seawalls. The approximated velocity equation, an asymptotical solution of the Green-Naghdi equation in the Camassa-Holm scaling, is utilized to obtain the evolution of the free surface and the depth-averaged horizontal velocity over time, leading to the formation of a plunging breaker. The uniform dynamic pressure along the depth is obtained by utilizing the unsteady Bernoulli equation. The wave forces on seawalls are then determined using Froude-Krylov theory, with adjustments for diffraction effects. The results, while being comparable to some existing formulations, notably differ with some others. This highlights the limitations imposed by the inherent assumptions in the existing empirical formulations and underlines the importance of the proposed methodology that is founded on an accurate modelling of the wave breaking process to estimate wave breaking forces on seawalls.

Fatigue Assessment of Pier Structures Under Dynamic Forces

Pier structures in port and fishing harbor facilities require dynamic analyses during the design phase to account for external dynamic forces because of their high flexibility. Dynamic forces are frequently approximated as equivalent static forces for design purposes in practical engineering applications, but the fluctuational effects induced by these dynamic forces can be neglected. As the frequency range of wave forces acting on pier structures (0.05–1.0 Hz) significantly overlaps with the typical natural frequency range of pier structures (0.25–4.0 Hz), the response of a pier structure can be amplified because of the dynamic effects of the waves. In this study, we conducted a dynamic analysis by applying wave forces—a representative dynamic load—to a pier structure. The results were compared with those from a static analysis. A fatigue life assessment, which is often overlooked in static analyses, was also performed. The findings indicated that the concrete at the connection between the upper pier and steel piles exhibited a fatigue life of 27.3 years. The steel piles exhibited fatigue lives of 27.1 and 8.3 years depending on the weld details, falling short of the expected structural durability. Based on these results, recommendations for pier structures are proposed.

Analysis of Marketing Strategies for Bestselling Books in the Context of Publishing Convergence: A Case Study of The Fugitive Artist

Driven by the dual forces of the digital wave and global trends, the publishing industry is undergoing unprecedented transformation, with publishing convergence becoming the new norm for industry development. In this context, the deep integration of traditional publishing and digital publishing has not only reshaped the methods of content production, distribution, and consumption but has also raised the bar for marketing strategies of international bestsellers. The Fugitive Artist, a fictional literary work that has made a global impact, owes its success not only to its profound literary value and captivating plot but also to its precise and innovative marketing strategies. This provides a valuable case for the market promotion of international bestsellers. This paper aims to analyze the marketing strategies of The Fugitive Artist in the context of publishing convergence, exploring how the book stood out in a complex and ever-changing market environment, and offering insights for the international promotion of similar works from China.

Resonant Forcing by Solar Declination of Rossby Waves at the Tropopause and Implications in Extreme Precipitation Events and Heat Waves—Part 2: Case Studies, Projections in the Context of Climate Change

Based on the properties of Rossby waves at the tropopause resonantly forced by solar declination in harmonic modes, which was the subject of a first article, case studies of heatwaves and extreme precipitation events are presented. They clearly demonstrate that extreme events only form under specific patterns of the amplitude of the speed of modulated airflows of Rossby waves at the tropopause, in particular period ranges. This remains true even if extreme events appear as compound events where chaos and timing are crucial. Extreme events are favored when modulated cold and warm airflows result in a dual cyclone-anticyclone system, i.e., the association of two joint vortices of opposite signs. They reverse over a period of the dominant harmonic mode in spatial and temporal coherence with the modulated airflow speed pattern. This key role could result from a transfer of humid/dry air between the two vortices during the inversion of the dual system. Finally, focusing on the two period ranges 17.1–34.2 and 8.56–17.1 days corresponding to 1/16- and 1/32-year period harmonic modes, projections of the amplitude of wind speed at 250 mb, geopotential height at 500 mb, ground air temperature, and precipitation rate are performed by extrapolating their amplitude observed from January 1979 to March 2024. Projected amplitudes are regionalized on a global scale for warmest and coldest half-years, referring to extratropical latitudes. Causal relationships are established between the projected amplitudes of modulated airflow speed and those of ground air temperature and precipitation rate, whether they increase or decrease. The increase in the amplitude of modulated airflow speed of polar vortices induces their latitudinal extension. This produces a tightening of Rossby waves embedded in the polar and subtropical jet streams. In the context of climate change, this has the effect of increasing the efficiency of the resonant forcing of Rossby waves from the solar declination, the optimum of which is located at mid-latitudes. Hence the increased or decreased vulnerability to heatwaves or extreme precipitation events of some regions. Europe and western Asia are particularly affected, which is due to increased activity of the Arctic polar vortex between longitudes 20° W and 40° E. This is likely a consequence of melting ice and changing albedo, which appears to amplify the amplitude of variation in the period range 17.1–34.2 days of poleward circulation at the tropopause of the Arctic polar cell.

Propagation dynamics of a three-species predator–prey model with non-local dispersal in a shifting habitat

This paper is concerned with the propagation phenomenon of a non-local dispersal predator–prey system involving two preys and one predator in a shifting habitat. Assuming that the growth rate of each prey is moving to the right at a speed of [Formula: see text] and the habitat is suitable for each prey to survive before the shifting edge, while the habitat behind the boundary is not suitable for survival. For any given speed of the shifting habitat edge, we establish four types of forced extinction waves, which describe the conversion from the state of a saturated aboriginal prey with a pair of invading alien predator–prey, two aboriginal co-existent preys with an invading alien predator, a pair of aboriginal co-existent predator–prey and an invading alien prey, and the co-existence of three species to the extinction state, respectively. Meanwhile, we show the non-existence of some forced waves.

Research on Decoupling Duty Cycle Optimization Control Method of a Multiport Converter for Dual-Port Direct Drive Wave Power Generation System

Dual-port direct drive wave energy power generation systems (DP-DDWEPGS) have received widespread attention due to their smooth and zero-free output power, compared to single-port direct drive wave energy power generation systems (SP-DDWEPGS) which have the disadvantage of large out-put power fluctuations. To further enhance the performance of the DP-DDWEPGS, optimal power capture control is proposed to achieve maximum power point tracking. Meanwhile, a multiport converter is applied to the DP-DDWEPGS to solve the problem caused by an excessive number of switching devices in the overall system converter. The multiport converter fulfills all the functional requirements of the DP-DDWEPGS while reducing the number of switching devices. However, switch multiplexing of the multiport converter also introduces coupling relationships between each port and the wave force exhibits time-varying characteristics, necessitating advanced control methods with superior fast-tracking capability. Therefore, in this paper, a decoupling duty cycle optimization model predictive control for DP-DDWEPGS is proposed. Based on the characteristics of switching multiplexing, NSC finite control set model predictive control (FCS-MPC) decouples the current prediction and the cost function, reduces the number of candidate voltage vectors in each operation, and shortens the operation time by 70%. To address the issues of high ripple value and increased error due to decoupling in FCS-MPC, duty cycle optimization control is added, greatly reducing the fluctuations in electromagnetic force and power of the permanent magnet linear generator (PMLG). Based on the established simulation model, the feasibility and superiority of the multiport converter and decoupling duty cycle optimization model predictive current control method are verified.

Coupling dynamic characteristics of installation vessel - Multi buckets jacket foundation lowering system

Precise control of the splash zone lowering process of the multi-bucket jacket foundation for an offshore wind turbine can save time during the entire construction period, thereby reducing construction and installation costs. This paper focuses on the “installation vessel - multi buckets jacket foundation” coupled dynamic system during the lowering process of the multi-bucket jacket foundation. Taking the three-bucket jacket foundation (TBJF) and the four-bucket jacket foundation (FBJF) as the research objects, four different sling layout types were proposed. The influence of the slings layout types on the motion response of the installation vessel and foundation and the slings' tension in this system were comparatively studied through numerical simulation. Research shows that through the lowering of Type 1 conditions, that is, each chord corresponds to a vertical sling and is directly connected to the crane's lifting point, the motion performance of the foundation and installation vessel can be reduced, ensuring the smooth progress of the lowering process of the structure. Under the same conditions, the FBJF has greater motion response due to the large wave force bearing area and large water plane area. Under different conditions, the DAF value and failure factor of the slings of the two structures during the lowering process all meet the specification requirements.