Wave Elevation Research Articles

Phase-resolved wave prediction with linear wave theory and physics-informed neural networks

Deterministic wave elevation prediction is crucial for improving the power generation efficiency of offshore energy structures (OESs). Although phase-resolved wave models may predict deterministic wave information, a comprehensive understanding of wave theory and mathematics is necessary to guarantee their accuracy. Inspired by the capability of physics-informed neural networks (PINNs) in solving physical equations, we propose an irregular long-crested wave prediction model named LWT-PINN that combines the linear wave theory (LWT) with PINNs. To the best of our knowledge, this is the first time that PINNs are used to predict waves. Five sets of wave elevation time series with steepness ranging from 0.0174 to 0.0349 are generated in a wave basin to optimize and evaluate the LWT-PINN. The computing time for LWT-PINN is 0.13 s, close to real-time. When predicting downstream wave elevation, the LWT-PINN significantly outperforms the linear wave prediction (LWP) model in terms of accuracy and prediction length. Specifically, the LWT-PINN achieves satisfactory accuracy with only 100 s upstream wave elevation, whereas the LWP requires 175 s; LWT-PINN’s high-precision prediction duration is 13.7 s, which is 2.5 times longer than that of LWP (5.5 s). Moreover, LWT-PINN can provide wave autoregressive predictions of around 5 s without the aid of statistical methods, which offers a new direction for developing wave autoregressive prediction methods. The excellent performance of the proposed model can substantially assist the stable operation of OESs.

Prediction of left ventricular thrombus after STEMI based on readily available clinical, echocardiographic and ECG variables

Abstract Background Left ventricular thrombus (LVTh) is an uncommon yet serious complication after ST-segment elevation myocardial infarction (STEMI). LVTh can be accurately detected in late gadolinium enhancement (LGE) sequences in cardiac magnetic resonance (CMR). However, selection of patients who should undergo this imaging technique for LVTh detection is not defined yet. Purpose We aim to stratify the risk of LVTh occurrence after STEMI by clinical, echocardiographic and ECG variables during admission and help select patients who should undergo CMR for LVTh detection. Methods Our registry comprised reperfused STEMI patients who underwent early (1-week) and late (6-month) CMR for clinical indication. LGE sequences were used to analyze the presence of LVTh. Baseline clinical characteristics were recorded. Echocardiography (Echo) was performed before discharge and left ventricular (LV) ejection fraction (LVEF, in %), LV end-diastolic and end-systolic diameters (in mm), tricuspid annular plane systolic excursion (TAPSE, in mm), E and A waves velocities (in m/s) and left auricular antero-posterior diameter (in mm) were measured. ECG during admission were analyzed and maximum and minimum ST-segment elevation, resolution of ST-segment (in %) and the number of leads with Q wave and ST-segment elevation >1mm (Q-STE) were recorded. Univariate and multivariate comparisons were performed to check for an association with LVTh in the first 6 months after STEMI (by CMR). A p<0.05 was considered statistically significant. Results The final cohort comprised 377 STEMI patients (mean age 58.51±11.64 years, 82% male). LVTh was detected in 29 (7.7%) patients by CMR during the first 6 months after STEMI. Predictors of LVTh on multivariate analysis were anterior infarction (HR 4.57 [1.28-16.29], p=0.02), Echo-LVEF (HR 0.97 [0.93-0.99] per %, p=0.04) and Q-STE (HR 1.33 [1.06-1.67] per lead, p=0.01). Echo-LVEF (best cut-off: ≤48%) and Q-STE (best cut-off: >3 leads) were dichotomized and several risk categories for LVTh were defined. In patients with zero or one risk factor the prevalence of LVTh ranged from 1.6% to 5.2% (if anterior infarction and no other risk factors). Patients with anterior infarction and any other risk factor had a 14.3% prevalence of LVTh. However, the highest prevalence was found in patients with concomitantly anterior infarction, Echo-LVEF ≤48% and Q-STE in >3 leads - in this subgroup (n=34, 9% of the cohort) LVTh was found in 26.5% of patients. Conclusions Left ventricular thrombus occurrence in the first 6 months after STEMI can be predicted by readily available clinical (anterior infarction), echocardiographic (LVEF) and ECG (Q-STE) variables before discharge. More than a quarter of patients with anterior infarction, Echo-LVEF≤48% and Q-STE in >3 leads depict LVTh. This could help select patients who should undergo CMR after infarction for LVTh detection.Central Figure.

Feasibility of Co-locating wave energy converters with offshore aquaculture: The Pioneering case study of China's Penghu platform

As the aquaculture industry moves further offshore, there is an increasing prospect of co-locating wave energy converters (WECs) with offshore aquaculture. In China, the multi-use of wave energy and offshore aquaculture has already been implemented and demonstrated commercially. A thorough analysis of the power performance and dynamic and structural responses on the Penghu platform is performed in this paper to improve the understanding of the co-locating potential. The analysis is based on the potential flow theory, multi-body constrained dynamics equations, and quasi-static finite element analysis (FEA) method. It is found that powering offshore aquaculture operations is possible using wave energy paired with solar energy. In addition, the inclusion of WECs can, to some extent, reduce the platform motion, making visits to the aquaculture site more feasible. The inner pool wave elevation is slightly reduced compared to the free surface elevation outside Penghu, which is conducive to aquaculture operations. It is also shown that the structural design of the Penghu platform is very safe. Still, the hinge points must be seriously considered because of the possibility of fatigue fracture. Overall, co-locating WECs and offshore aquaculture is demonstrated as a feasible solution to the power supply problems of offshore aquaculture.

Wave overtopping of a vertical seawall in a surf zone: A joint analysis of numerical and laboratory data

This research uses physical and numerical experiments to investigate the wave overtopping of a vertical seawall in an uneven surf zone. The numerical experiments exploit two approaches, which differ in vertical resolution and computational time: CFD-RANS and SWASH. The tests were conducted with and without the wall, allowing the analysis of the spectral evolution in shallow water and its relationships with wave overtopping. The study assesses the performance of numerical models with different levels of complexity and uses laboratory and numerical data to understand the key variables that control the phenomena under study. The results indicate that while CFD-RANS is quantitatively in line with the laboratory measurements, SWASH overestimates the spectral moments and underpredicts the overtopping rate by a factor of 2. However, the numerical tools satisfactorily reproduce the physics of the processes, allowing us to focus on some aspects of engineering relevance. Laboratory and numerical data indicate that the overtopping rate depends not on the wave spectrum shape but on the high percentiles of the wave elevation distribution. This outcome clarifies that wave setup is a critical variable for prediction purposes.Finally, the article highlights that the surf zone’s spectral moments are correlated. The correlation structure is such that the mean spectral periods became proportional to the local wave energy despite these quantities being independent in deeper water. We warn that this phenomenon could result in spurious, unphysical relationships between mean spectral periods and overtopping rates. The analysis of further literature data corroborates this conclusion.

Comparison of prediction methods for added power and propeller revolution for a 1,800 TEU container ship using resistance tests in regular and irregular waves

This paper predicts the added power and propeller revolution due to irregular head waves for a 1,800 TEU container ship. Resistance tests were conducted with 11 regular waves and irregular waves at SS = 5. Time series (TS) and autocovariance analysis methods were applied to estimate statistical variables and uncertainties. The paper investigated the statistical convergence times of measured data. The wave elevation, heave and pitch motions obtained from the TS agree well with those from spectral analysis in regular and irregular waves. The added resistance from the TS is larger than that from spectral analysis using a regular wave test by 6.1%. The characteristics of response operators and spectra of the added (or reduced) propulsion performances and overload factors are discussed. The power and propeller revolution were evaluated with a variety of methods: SA(LVM-W), LVM-IR, DPM, and RTIM.

Effect of the drag coefficient on the performance of vertical porous baffles in a sloshing tank

Purpose The present work involves analytical and experimental investigation of sloshing in a two-dimensional rectangular tank including the effect of porous baffles to control and/or reduce the wave motion in the sloshing tank. The purpose of this study is to assess the analytical solutions of the drag coefficient effect on porous baffles performance to track free surface motion variation in the sloshing tank by comparison with experimental shake table tests under a range of sway excitation. Design/methodology/approach The linear second-order ordinary differential equations for liquid sloshing in the rectangular tank were solved using Newmark’s beta method and obtained the analytical solutions for liquid sloshing with dual vertical porous baffles of full submergence depths in a sway-oscillated rectangular tank following the methodology similar to Warnitchai and Pinkaew (1998) and Tait (2008). Findings The porous baffles significantly reduce wave elevation in the varying filled levels of the tank compared to the baffle-free tank under the range of excitation frequencies. It is observed that the Reynolds number-dependent drag coefficient for porous baffles in the tank can significantly reduce the sloshing elevations and is found to be effective to achieve higher damping compared to the porosity-dependent drag coefficient for porous baffles in the sloshing tank. The analytical model’s response to free surface elevation variations in the sloshing tank was compared with the experiment’s test results. The analytical results matched with shake table test results with a quantitative difference near the first resonant frequency. Research limitations/implications The scope of the study is limited to porous baffles performance under range sway motion and three different filling levels in the tank. The porous baffle performance includes Reynolds number dependent drag coefficient to explore the damping effect in the sloshing tank. Originality/value The porous baffles with low-level porosities in the sloshing tank have many engineering applications where the first resonant mode of sloshing in the tank is more important. The porous baffle drag coefficient is an important parameter to study the baffle’s damping effect in sloshing tanks. Hence, obtained analytical solution for liquid sloshing in the rectangular tank with Reynolds number as well as porosity-dependent drag coefficient (model 1) and porosity-dependent drag coefficient porous baffles (model 2) performance is discussed. The model’s test results were validated using a series of shake table sloshing experiments for three fill levels in the tank with sway motion at various excitation frequencies covering the first four sloshing resonant modes.

Stereo vision-based measurement of wave evolution around square column in laboratory

The spatial-temporal measurement of complex wave evolution is significant in studying wave-structure interactions. Current methods, such as that using wave probes, have shown limitations in measuring the wave evolution around structures in laboratories. In this study, an improved stereo imaging method is proposed for measuring the wave evolution around a fixed structure. Regular wave tests were conducted on a fixed surface-piercing square column in a wave flume to validate the reliability and accuracy of the proposed method. A flexible marker-net made of foam particles was arranged around the column to provide Lambertian features for the water surface. Two synchronized stereo imaging systems covered all the surrounding areas of the column and provided stereo pair sequences for wave evolution. Subsequently, image segmentation techniques were used to mask the low-confidence disparities in stereo matching, and finally, three-dimensional (3D) wave surfaces were reconstructed in the time sequence. The time histories of the wave elevations at particular locations were extracted and agreed well with the measurements of wave probes with an average bias of 2.4 %. Subsequently, the reconstructed 3D wave field was sliced, exhibiting the instantaneous profiles that agreed with the measurements of wave probes. Moreover, the wave run-up height ratios were consistent with those of a previous study, thereby verifying the method's accuracy from the perspective of spatial evolution. The results demonstrated that the proposed method was capable of precisely measuring the spatial-temporal evolution of the wave field around the square column and displayed potential for application in more studies on wave-structure interactions.

Analysis of the blade aeroelastic effect on the floating offshore wind turbine wake in a focusing wave with a hybrid model

With the recent trend toward larger floating offshore wind turbines (FOWT), the influence of blade deformation becomes more obvious. Modelling this fully coupled fluid-structure interaction (FSI) system, especially at extreme sea level with large-scale motion of the entire system, is an essential challenge. A hybrid numerical model integrating the potential-viscous flow model (qaleFOAM), the unstable actuator line method (UALM), the Legendre spectral finite element model (BeamDyn), and the Lumped Mass Mooring Model (MoorDyn) is employed in the current research. This model is capable of effortlessly and accurately reflecting the blade aeroelastic effect on the dynamics of a FOWT system under the circumstances of a focused wave and uniform wind. The result reveals that the aeroelastic impacts have been identified to not only increase the fatigue damage on the turbine blades but also affect the wake field distribution. Based on the temporal and spatial distribution of the velocity fields, it is found that the coupled effects of the large wave elevation and the FOWT high-frequency motions will disturb the velocity in the wake region. The slight variation of the wind speed in the wake region will be exacerbated by about 0.21% to 18.6%, and it transforms the shape of the wake region when the blade aeroelastic effect participates in the coupled effect. This phenomenon may further affect the downstream FOWT system features through the upstream FOWT wake field.

Non-linear dynamics of cantilevered circular cylindrical shells with thickness stretch, containing quiescent fluid with small-amplitude sloshing

Studies on nonlinear vibrations of circular cylindrical shells containing fluid are mostly limited to thin simply supported shells, such that no results regarding the behavior of thick cantilevered shells with shear and thickness deformations can be found in the literature. In this article, for the first time, thin and thick circular cylindrical shells with clamped-free boundary conditions are modeled according to the third-order shear deformation theory with thickness stretch. The contained liquid satisfies the Laplace equation and linearized boundary conditions are imposed at the free surface and at the contact with the shell. Using Lagrange equations, the governing differential equations of the system in terms of shell-fluid interaction are derived. In linear free vibration analysis, it was found that increasing the fluid level inside the shell and decreasing the shell thickness, cause a significant rise in the fluid free-surface wave elevation. This increase is such that limits the application of linear sloshing theory. It was observed that the fluid presence can change the nonlinear behavior from softening to hardening type and intensifies the shell thickness deformation. In addition, the presence of contained liquid reduces the circumferential dynamic contraction of the shell caused by large amplitude vibrations.

Physical model comparison of gray and green mitigation alternatives for flooding and wave force reduction in an idealized urban coastal environment

A 1:16 scaled physical model was constructed to investigate the effectiveness of a seawall, a submerged breakwater, and mangrove forests to mitigate overland flooding and forces on structures in an idealized urban coastal environment. The experiment was performed using tsunami-like waves at different water levels, wave amplitudes, and time scales to simulate long-wave dynamics. The baseline condition (no mitigation), seawall, submerged breakwater, and mangrove forest were tested individually, and the seawall and submerged breakwater were also tested in combination. Wave gauges, acoustic Doppler velocimeters, loadcells, and pressure gauges were used to measure wave elevations, velocities, forces, and pressures on coastal structures, respectively. The performance of these hard structures and mangroves was compared through their effects on wave elevation, particle velocity, and force reduction. Experimental results showed that each protecting structure reduced the horizontal wave forces and inland flow hydrodynamics in the low-water-level case, with a similar performance by the individual seawall, submerged breakwater, and four rows of mangroves. The combined configuration, when the seawall and submerged breakwater were installed simultaneously, caused the most significant maximum force percent reduction by approximately 50%, while mangrove forests arranged in eight rows resulted in a force reduction of 46% in the first building array. However, in the high-water-level cases, the impulsive force measured with the presence of the submerged breakwater was larger than in the baseline case; thus, the submerged breakwater may amplify the impulsive force on the vertical building rows for certain incident wave conditions. Generally, the combined hard structures induced the lowest force reduction factor measured in almost every building row compared to the seawall, submerged breakwater, and mangroves considered separately for all wave conditions and water levels. That means this multi-tiered configuration showed better performance than individual alternatives in reducing horizontal forces inland than the individual alternatives considered separately.

Stereo Reconstruction Method for 3D Surface Wave Fields around a Floating Body Using a Marker Net in a Wave Tank

Spatial wave fields around floating bodies are important for the understanding of hydrodynamics, and particularly the wave drift forces, of floating bodies in waves; however, experimental measurement of these fields is challenging. This paper presents a stereo reconstruction method for three-dimensional (3D) surface wave fields around floating bodies in a wave tank. Styrofoam markers were attached to a flexible net in a regular grid, called a marker net, and were placed on the water surface to be used as targets for stereo cameras (SCs). A thin plate spline was applied to the markers detected by the SCs to reconstruct the 3D surface wave profile around a floating body model. The proposed method was validated by measuring the wave field around a cylindrical floating body with a footing at its bottom. These experiments were conducted under regular wave incidence conditions. A wave elevation time series measured using a servo-controlled wave gauge was used as the benchmark data. The 3D surface wave field reconstruction method was applied under three different conditions: without the model, with a fixed model, and with a freely oscillating model. The results showed reliable reconstructions of the scattering and radiation waves. The marker net’s effects on the floating body’s motion and the surrounding wave fields were shown to be negligible by comparing the results acquired with and without the marker net.

Nonlinearities of the gap resonance for a free-heaving moonpool: Higher-order harmonics and natural frequency component

The piston-mode gap resonance of a free-heaving moonpool was investigated in a two-dimensional numerical wave tank based on a Constrained Interpolation Profile (CIP) method. The wave elevation at the narrow gap, the moonpool's heave response, and wave loads on the free-heaving moonpool were all specifically examined in the current study, which was primarily focused on the higher-order harmonics of the gap resonance for the free-heaving moonpool against various gap widths and body drafts. The flow pattern around the entrance of the gap of the free-heaving moonpool was identified at the typical resonant frequencies. The frequency range of the beat pattern for the wave elevation at the gap was initially suggested. Furthermore, the natural frequency component (NFC) was observed from the interesting beat patterns, and the NFC-based approach was proposed as a straightforward way to forecast the resonant frequency of the free-heaving moonpool. Numerical studies showed that the quadratic wave excitation (QWE) driven gap resonances were recorded for both the fixed and the free-heaving moonpools versus regular waves. The resonance frequency of the free-heaving moonpool can be directly, precisely, and rapidly estimated using the suggested NFC-based approach. Finally, four frequency zones were proposed to differentiate the various gap resonances for the free-heaving moonpool based on distinct hydrodynamic characteristics of the wave elevation at gap.

Fully coupled aero-hydrodynamic modelling of floating offshore wind turbines in nonlinear waves using a direct time-domain approach

In standard operating conditions, a floating offshore wind turbine (FOWT) suffers from the combined action of nonlinear waves and wind. It is important to explore the effect of higher-order hydrodynamic loads induced by the nonlinear waves on its motion response. In this work, a fully coupled aero-hydrodynamic analysis method for FOWT is developed. The hydrodynamic part is based on the nonlinear potential flow theory and the perturbation approach, using a higher-order boundary element method in the time domain. Blade element momentum theory is applied to evaluate the aerodynamic load on the turbine rotor. The mooring system is modelled by the catenary theory. The developed method is verified against the published data of the NREL's 5-MW baseline wind turbine supported by the DeepCwind semi-submersible platform. The verifications are conducted stepwise in the following ways, including hydrodynamic wave excitation load, free-decay response, the load-displacement relationship of the mooring line, the steady-state response of the wind turbine, and fully coupled aero-hydrodynamic interaction. It is found that the nonlinear effect mainly influences the surge motion. The coupled configuration has little effect on the linear wave force and platform displacement but notably impacts the nonlinear wave force and displacement. The FOWT motion is found to be critical in changing the wave field, the maximum wave elevation position around the platform, and the nonlinear wave force acting on the floating platform. The results illustrate that the traditional indirect time-domain method using the Quadratic Transfer Function (QTF) based on assumed response cannot appropriately evaluate the nonlinear wave force of a FOWT in coupled motions. The results also reveal that nonlinear wave hydrodynamics is necessary to understand the motion response of a fully coupled FOWT.

Phase-resolved real-time forecasting of three-dimensional ocean waves via machine learning and wave tank experiments

Accurate prediction of ocean waves plays an essential role in many ocean engineering applications, such as the control of wave energy converters and floating wind turbines. However, existing studies on phase-resolved wave prediction using machine learning mainly focus on two-dimensional wave data, while ocean waves are usually three-dimensional. In this work, we investigate, for the first time, the phase-resolved real-time prediction of three-dimensional waves using machine learning methods. Specifically, the wave prediction is modeled as a supervised learning task aiming at learning mapping relationships between the input historical wave data and the output future wave elevations. Four frequently-used machine learning methods are employed to tackle this task and a novel Dual-Branch Network (DBNet) is proposed for performance improvement. A group of wave basin experiments with nine directional wave spectra under three sea states are first conducted to collect the data of 3D waves. Then the wave data are used for verifying the effectiveness of the machine learning methods. The results demonstrate that the upstream wave data measured by the gauge array can be used for control-oriented wave forecasting with a forecasting horizon of more than 20 s, where the directional information provided by the upstream gauge array is vital for accurately predicting the downstream wave elevations. In addition, further investigations show that by using only local wave data (which can be easily obtained), the very short-term phase-resolved prediction (less than 5 s) can be achieved.

Deep gated recurrent unit networks for time-domain long-term fatigue analysis of mooring lines considering wave directionality

Mooring lines are a crucial component of offshore mooring systems, and long-term fatigue damage assessment is a challenging task in mooring line design and structural health monitoring. Traditional methods require a large number of structural time-domain simulations. Because the sea state varies over time, the variations in wave parameters (e.g., wave heights, periods, and directions) must be considered in long-term fatigue damage assessment. Wave directions have usually been ignored in previous studies, while the wave direction sensitive analysis conducted in this study showed that the wave directions could not be neglected in the long-term fatigue damage assessment of mooring lines. Recent deep neural network (DNN) methods have shown great potential in mooring line/riser response prediction for offshore structures. However, the utilization of float responses as input data in these DNNs restricts their applicability during the structure design phase. To address this issue, a gated recurrent unit (GRU) network is proposed for mooring line tension modeling. The proposed GRU network surrogate models are capable of accurately predicting the mooring line tension using wave elevation components or float motion responses. The rain-flow counting algorithm, T-N approach, and Miner's rule were employed to estimate the structural fatigue damage. The results showed that the proposed method could replace the heavy cost numerical computation, assess the long-term fatigue damage with high accuracy and alleviate the data dependency of DNN methods.

Improved generalization of NARX neural networks for enhanced metamodeling of nonlinear dynamic systems under stochastic excitations

Nonlinear autoregressive networks with exogenous inputs (NARX) are popular in data-driven metamodeling of complex dynamic systems. One practical challenge is the insufficient generalization due to excitation stochasticity. To improve the generalization, three novel schemes are proposed. They are: (1) Advanced NARX (A-NARX), where k-fold cross validation-based ensemble with early stopping is implemented over intact time series samples under concurrent training via data reconstruction; (2) Experienced NARX (E-NARX), built on A-NARX and gaining experience about the underneath dynamic system by series–parallel training before entering the parallel training; and (3) Gaussian Experienced NARX (GE-NARX), which introduces the pseudo-parallel training for network precondition to the Gaussian noise contained in the output feedback of the subsequent real parallel training. The proposed schemes are applied with the plain NARX for reference to simulated data corresponding to a nonlinear simple system and a complex offshore floating system, using wave elevation as the input for predicting structural responses. It is found that both the network capability and the training stability are strengthened by proposed schemes. Hence, improved generalization is achieved with increased complexity in the dynamic system and stochastic excitations. GE-NARX consistently demonstrates superior performance over other schemes.

The dynamic response of a Spar-type floating wind turbine under freak waves with different properties

In the present work, the dynamic responses of a Spar-type floating offshore wind turbine (SFWT) under freak waves with different properties are simulated and analyzed. The properties of freak wave are represented by changing different decision parameters a1, a2, a3 and a4, corresponding to the ratios of the wave elevations around the freak wave crest (FWC). The improved phase modulation method is adopted to generate the original freak wave (OFW). On the basis, the freak wave elevation is further modulated to increase the decision parameters with different degrees, and the modulated freak waves (MFWs) are obtained. The SFWT motions under the OFW and MFWs are simulated in the time domain. We firstly investigated the influence of freak wave on the SFWT transient dynamic performances, including the surge, heave, pitch motions, the turbine output power and the mooring tensions. Then, the SFWT dynamic response under different MFWs corresponding to the specific factors were analyzed. The results show that the freak wave fluctuation represented by the factor a1 significantly affects the surge, heave, pitch transient motion, output power and extreme mooring tension of the SFWT. The output power of the SFWT decreases less after the FWC with the wave fluctuation increasing. At the same time, the wave fluctuation significantly affects the mooring tension, which greatly increases both near the focus time and the extreme mooring tension time. The height of the previous wave (PW) related to a2 affects the heave motion at the trough after PW impact, which in turn affects the transient heave. a3 represents the height of the next wave (NW) and has little effect on the dynamic performance. The impact height of freak waves represented by a4 has a particularly significant effect on heave. It not only affects the transient motion at the focus time, but also has a significant effect on heave after the freak wave subsides.

Study on multilayered liquids sloshing tank subjected to sway and roll excitation

Herein, analytical and numerical approaches are used to investigate the interfacial surface elevations by a swaying and rolling tank with multilayered liquids of different densities. The analytical model, formulated using the eigenfunction expansion method based on two-dimensional linear potential theory, incorporates artificial damping to account for energy dissipation due to friction at the walls and bottom. The analytical model is used to predict the wave elevations and hydrodynamic forces on the tank as well as the natural frequencies of multilayered liquids. In parallel, computational fluid dynamics (CFD) is used, which employs quasi-two-dimensional implicit unsteady, incompressible Navier-Stokes equations. The volume of fluids technique is used to track the interfacial surfaces along with high-resolution interface capturing and interface momentum dissipation techniques. The interfacial surface elevations at the tank wall agree well with the analytical and CFD results, with the expected resonant peaks. Fourier analysis estimates added mass and damping coefficients for the three-layered tank from the total force. CFD results for the three-layered liquids exhibit strong nonlinear wave elevations at the interfaces. Power spectral density (PSD) analysis reveals higher harmonics in CFD solutions as tank amplitude increases.

The effect of linear shear current on head-on collision of solitons

Head-on collision of two solitary waves in the presence of linear shear currents is studied by the use of the High-Level Green–Naghdi (HLGN) theory. The finite difference method is used to solve the HLGN model in the time-domain simulation. The initial values are obtained by the steady solution of solitary waves in the presence of linear shear currents. Shear currents with different velocities are considered to assess their effect on the solitary-wave collision. Three aspects of the head-on collision process in the presence of shear current are studied, namely, the wave elevation, velocity field, and particle trajectory. Results show that the background linear shear current significantly affects the wave elevation, velocity field, and particle trajectory during the head-on collision. It is observed that in the presence of the current, the wave elevation is narrower near the maximum surface displacement and is wider near the still-water level. It is also shown that near the seafloor, the horizontal velocity is opposite of the current direction, while it is following the current direction near the free surface. The opposite shear current results in the formation of a vortex in the fluid field. At the point of the collision, the vortex appears at a lower vertical position and shifts upstream of the current direction. Following the particle trajectories in the presence of the shear current, it is observed that the particles do not return to their initial positions after the head-on collisions, and the loop motions of the particles become smaller with larger current velocities.

Comparative study of spread and vertical mooring configuration in floating collar net cage under irregular waves and current

Offshore aquaculture is one of the national strategic programs of the Ministry of Fishery and Ocean Affairs of Indonesia to increase national fish cultivation capacity. One solution is using a simple flexible floating collar net which is suitable for small to medium cage volume. In designing such floating net, its mooring line configuration is vital to maintain fixed position of structural part of the cage volume. The purpose of this study is to compare design aspect of two types of mooring systems, i.e., spread and vertical configuration, by investigating selected parameters: mooring line tension, collar offset, and volume reduction. The mooring configuration and floating collar net cage are analysed through a numerical model based on Morison-force equations, under environmental condition adopted from Kangean field East Java. Load cases from collinearly in-line and between-line directions under extreme waves and current condition are checked against relevant safety factor. The dynamics analysis using the time domain simulation is based on 900 seconds cut-off according to its maximum wave elevation profile to generate the hydrodynamics forces to the mooring systems.