Numerical Wave Tank Research Articles

Data Assimilation and Parameter Identification for Water Waves Using the Nonlinear Schrödinger Equation and Physics-Informed Neural Networks

The measurement of deep water gravity wave elevations using in situ devices, such as wave gauges, typically yields spatially sparse data due to the deployment of a limited number of costly devices. This sparsity complicates the reconstruction of the spatio-temporal extent of surface elevation and presents an ill-posed data assimilation problem, which is challenging to solve with conventional numerical techniques. To address this issue, we propose the application of a physics-informed neural network (PINN) to reconstruct physically consistent wave fields between two elevation time series measured at distinct locations within a numerical wave tank. Our method ensures this physical consistency by integrating residuals of the hydrodynamic nonlinear Schrödinger equation (NLSE) into the PINN’s loss function. We first showcase a data assimilation task by employing constant NLSE coefficients predetermined from spectral wave properties. However, due to the relatively short duration of these measurements and their possible deviation from the narrow-band assumptions inherent in the NLSE, using constant coefficients occasionally leads to poor reconstructions. To enhance this reconstruction quality, we introduce the base variables of frequency and wavenumber, from which the NLSE coefficients are determined, as additional neural network parameters that are fine tuned during PINN training. Overall, the results demonstrate the potential for real-world applications of the PINN method and represent a step toward improving the initialization of deterministic wave prediction methods.

Hydrodynamic modulation instability triggered by a two-wave system.

The modulation instability (MI) is responsible for the disintegration of a regular nonlinear wave train and can lead to strong localizations in the form of rogue waves. This mechanism has been studied in a variety of nonlinear dispersive media, such as hydrodynamics, optics, plasma, mechanical systems, electric transmission lines, and Bose-Einstein condensates, while its impact on applied sciences is steadily growing. It is well-known that the classical MI dynamics can be triggered when a pair of small-amplitude sidebands are excited within a particular frequency range around the main peak frequency. That is, a three-wave system, consisting of the carrier wave together with a pair of unstable sidebands, is usually adopted to initiate the wave focusing process in a numerical or laboratory experiment. Breather solutions of the nonlinear Schrödinger equation (NLSE) revealed that MI can generate much more complex localized structures, beyond the three-wave system initialization approach or by means of a continuous spectrum. In this work, we report an experimental study for deep-water surface gravity waves asserting that a MI process can be triggered by a single unstable sideband only, and thus, initialized from a two-wave process when including the contribution of the peak frequency. The experimental data are validated against fully nonlinear hydrodynamic numerical wave tank simulations and show very good agreement. The long-term evolution of such unstable wave trains shows a distinct shift in the recurrent Fermi-Pasta-Ulam-Tsingou focusing cycles, which are captured by the NLSE and fully nonlinear hydrodynamic simulations with some distinctions.

Effects of gap entrance configuration on gap resonances between two free-heaving barges: Higher-order harmonics

The hydrodynamic characteristics of linear and nonlinear gap resonances between two identical side-by-side free-heaving barges are investigated in a numerical wave tank based on the constrained interpolation profile method. This study focuses on the influence of the gap entrance configuration on key hydrodynamic parameters during gap resonances, comparing conditions of round and square edges. Additionally, the effects of incident wave height and the barge's heave responses are examined. The distributions of the first four harmonic components of the key parameters are illustrated, including the wave elevation at the gap, wave run-up on each barge, and wave forces. Numerical results reveal that the gap entrance configuration influences more on the linear gap resonance rather than the nonlinear gap resonances. The higher-order components of the wave elevation at the gap are more sensitive to the incident wave height rather than the edge shape. The influences of the edge shape on the wave forces are mainly manifested in the magnitude of the wave forces rather than in their tendencies. Furthermore, the response time during the development stage of gap resonance is analyzed. The findings indicate that gap resonance develops more quickly with square edges or when the incident wave height increases.

Generation of nonlinear gravity waves based on the harmonic polynomial cell method incorporated with a mass source

A nonlinear numerical wave tank is established using the Harmonic Polynomial Cell (HPC) method, which is incorporated with a mass source. The numerical wave tank consists of the mass source wave generation region and the working region, with sponge layers at both ends for wave absorption. In the mass source region, a generalized HPC method is applied to solve the inhomogeneous elliptic boundary value problems. The Poisson equation's special solution is represented by a bi-quadratic function. In the remaining domains, the HPC method is employed with harmonic polynomials to solve the problems governed by the Laplace equation in each grid cell. The free surface is tackled by the immersed boundary method (IB-HPC), and the kinematic and dynamic conditions of the free surface are described using a semi-Lagrangian approach. A variety of waves propagation are simulated, including Second-order Stokes wave, fifth-order Stokes wave, solitary wave, fifth-order Fenton stream function wave, random wave and the interaction with a straight vertical wall. The numerical solutions are compared with theoretical solutions. The numerical simulation results demonstrate that the present method can generate arbitrary two-dimensional wave fields by specifying an appropriate source function. Additionally, the reflected waves can propagate through the wave generation region, ensuring that the process of wave generation is not affected by the reflections.

Nonlinear hydrodynamic assessment of a floating solar double-hull substructure using viscous numerical wave tank

This paper assesses a viscous numerical solver for hydrodynamic simulations of floating double-hull substructures supporting solar panels, critical for advancing floating solar technologies. Using the OpenFOAM repository, the study develops a model based on the Finite Volume method and Volume of Fluid approach, focusing on a range of wave frequencies, from weakly to strongly nonlinear, at intermediate depths. A free decay test calibrated the mesh morphology of the control volume, enabling comparative analysis of single and double-cylinder structures exposed to Stokes second-order nonlinear waves, alongside nonlinear potential models and experimental data. Spectral analysis of these solutions quantifies the nonlinearities' influence on structural responses and high-order dynamic prediction accuracy. The key findings demonstrate that the viscous model accurately predicted heave and surge responses, outperforming the potential model under steep waves. The gap distance between the cylinder in the double-cylinder platforms significantly affects fluid flow and stability, especially under shorter waves. Accurate wave-body simulations require appropriate mesh resolution and tailored wavemaker functions for nonlinear waves. These findings highlight the need to incorporate viscous effects in floating solar platform design to enhance stability and performance in real-world environments.

Structural Design and Horizontal Wave Force Estimation of a Wall-Climbing Robot for the Underwater Cleaning of Jackets

Currently, divers face significant safety risks when cleaning marine organisms from the steel structures of offshore underwater platform jackets. Consequently, utilizing robots instead of divers to carry out underwater biofouling removal operations will be an important development direction for the underwater maintenance of offshore platforms in the future. In this study, a wall-climbing robot was designed to clean marine organisms from the underwater surface of a platform jacket leg. The overall structure of the underwater cleaning wall-climbing robot is introduced, including the cleaning actuator and the variable curvature-adapted connecting rod mechanism. The corresponding relationship between the variable curvature-adapted connecting rod mechanism and the jacket leg is analyzed in detail. The variable curvature-adapted connecting rod mechanism was optimized using a genetic algorithm to ensure that the underwater cleaning wall-climbing robot can adapt to a minimum diameter of 1 m for the jacket leg. By drawing on Airy wave theory and random wave theory, the Airy wave parameters for waves were analyzed under different sea conditions, considering practical application scenarios. By using Fluent software 2022, a 2D numerical wave tank was constructed to simulate waves under various sea conditions, and the wave surface shapes for different sea states were determined. By building on the Morison equation, a method for calculating the horizontal wave forces on the underwater cleaning wall-climbing robot using the equivalent area and equivalent volume is proposed. By using the two aforementioned methods, the horizontal wave forces on the underwater cleaning wall-climbing robot under specific sea states were determined. The horizontal wave forces of the underwater cleaning wall-climbing robot under different sea conditions were analyzed and simulated in a 3D numerical wave tank. By comparing the theoretical analysis results with the numerical simulation results, where the maximum difference at the extreme points is approximately 11%, the feasibility of the proposed horizontal wave force estimation method was verified.

A p-Multigrid Hybrid-Spectral Model for Nonlinear Water Waves

AbstractTo improve both scale and fidelity of numerical water wave simulations to study the evolution of wave fields within offshore engineering, it is of key practical interest to achieve high numerical efficiency. We propose a p-multigrid accelerated time-domain scheme for efficient and $${\mathcal {O}}(n \log n)$$ O ( n log n ) -scalable solution of a hybrid-spectral model for the simulation of highly nonlinear and highly dispersive water waves, the accurate calculation of wave kinematics and taking into account varying water depth. To achieve low numerical dispersive and dissipate errors, a high-order hybrid-spectral collocation scheme is implemented to solve the fully nonlinear potential flow (FNPF) equations, and utilizing a p-multigrid iterative solver scheme for solving the Laplace problem. Hereby, the numerical scheme combines the high accuracy of spectral methods, high efficiency of the fast Fourier transform (FFT) algorithm, and multigrid methods. Numerical analysis is performed to evaluate the performance and confirm the spectral accuracy of the scheme. Numerical experiments are considered for steady nonlinear wave propagation. A Fourier-continuation technique is used to extend the scheme from a periodic domain setup to perform benchmarks in a finite domain setup for numerical wave tanks utilizing conventional techniques for wave generation and absorption, and with results in excellent agreement with experimental measurements.

Verification and validation of a numerical wave tank with momentum source wave generation

Verification and validation of a numerical wave tank with momentum source wave generation

Characteristics of wave loading and viscous energy loss of a bottom-sitting U-OWC wave energy device: A validated numerical perspective

This study involves numerical simulations of regular waves interacting with a bottom-sitting circular OWC wave energy converter with a U-shaped duct (circular U-OWC). A numerical wave tank is built based on the RANS equation and is validated against experiments. The effect of water depth and the height of the outer tube of the U-shaped duct on capture efficiency, wave loading, and viscous energy loss is investigated numerically. Results show that the height of the outer tube of the U-shaped duct has a significant effect on the capture efficiency of the device. Wave loading analysis reveals a critical mode of stability that may threaten the operation safety of the device. It is found that increasing the height of the U-shaped duct opening increases the viscous energy loss inside the U-shaped duct. A semi-theoretical model between work done by waves to the device and the viscous energy loss in the U-shaped duct is established, numerical data indicates that a significant amount of work done by waves to the device is lost in viscous effects. This suggests that certain optimization for reducing wave loading could possibly also reduce viscous energy loss, thus improving the overall efficiency of the device.

Numerical investigation of triadic interactions during wave propagation over a submerged bar using a fully nonlinear numerical wave tank

This study models wave propagation over a submerged trapezoidal bar problem with a Higher Order Boundary Element Method (HOBEM) based on a two-dimensional fully nonlinear numerical wave tank (NWT). A Mixed Eulerian-Lagrangian technique is implemented, and the NWT is validated using the experimental results available from the existing literature. A numerical investigation is conducted on the individual wave harmonics as it propagates across the numerical wave tank over the submerged bar. The amplitude spectrum is obtained from the time histories of wave elevation across the tank at various locations over the trapezoidal bar and compared with the experimental results. The redistribution of the energy spectrum across the domain is recorded as the regular long wave propagates and undergoes deformations because of shoaling followed by de-shoaling. This phenomenon is investigated using a higher-order statistical analysis method viz. Bispectrum. The mechanics of the redistribution of energy among the harmonics is quantified through bispectrum analysis. Further, regular and irregular wave propagation over the submerged bar in the presence of the following and opposing currents is simulated. The effect of current is studied using the amplitude spectrum and the harmonic interaction for each case is compared using bispectrum analysis.

Hydrodynamics of fluid resonance in a narrow gap between two boxes with different breadths

Violent fluid oscillations occur inside narrow gaps between closely side-by-side structures, threating the safety of the operations. In the current study, fluid resonance in the gap between two side-by-side different boxes is investigated by a two-dimensional viscous-flow numerical wave tank, which can simultaneously predict the viscous damping and free-surface nonlinearity. The accuracy of the established numerical model is fore validated by the published experimental data. The upstream box keeps fixed and has six varied breadths, the downstream box heaves freely under wave actions and remains a constant breadth. The current work aims to study the effects of the breadth ratio and heave motion of the lee-side box on the hydrodynamics of gap resonance. The wave amplification in the gap, the heave motions of the lee-side box, the reflection, transmission, and energy loss coefficients, and the response time and damping time are concerned. Results show that the gap resonance frequency is insensitive to the variation of the breadth ratio. As the breadth ratio increases from 0.4 to 1.4. The maximum wave height amplification in the gap reduces more than 25%. The maximum response time of the fluid resonance occurs when two boxes have equal breadth.

Modeling Ocean Swell and Overtopping Waves: Understanding Wave Shoaling with Varying Seafloor Topographies

One risk posed by hurricanes and typhoons is local inundation as ocean swell and storm surge bring a tremendous amount of energy and water flux to the shore. Numerical wave tanks are developed to understand the dynamics computationally. The three-dimensional equations of motion are solved by the software ‘Open Field Operation And Manipulation’ v2206. The ‘Large Eddy Simulation’ scheme is adopted as the turbulence model. A fifth-order Stokes wave is taken as the inlet condition. Breaking, ‘run-up’, and overtopping waves are studied for concave, convex, and straight-line seafloors for a fixed ocean depth. For small angles of inclination (<10°), a convex seafloor displays wave breaking sooner than a straight-line one and thus actually delivers a smaller volume flux to the shore. Physically, a convex floor exhibits a greater rate of depth reduction (on first encounter with the sloping seafloor) than a straight-line one. Long waves with a speed proportional to the square root of the depth thus experience a larger deceleration. Nonlinear (or ‘piling up’) effects occur earlier than in the straight-line case. All these scenarios and reasoning are reversed for a concave seafloor. For large angles of inclination (>30°), impingement, reflection, and deflection are the relevant processes. Empirical dependence for the setup and swash values for a convex seafloor is established. The reflection coefficient for waves reflected from the seafloor is explored through Fourier analysis, and a set of empirical formulas is developed for various seafloor topographies. Understanding these dynamical factors will help facilitate the more efficient designing and construction of coastal defense mechanisms against severe weather.

Hybrid intelligent and numerical methods to estimate the transmission coefficients of rectangular floating breakwaters

ABSTRACT Breakwaters are used to reduce incoming wave energy at harbors and shorelines. This paper presents a comparison of novel two-dimensional hybrid intelligent models for the idealization of the effects of waves on the performance of moored rectangular floating breakwaters (FBs). Fluid structure interactions (FSIs) were idealized by airy-type monochromatic regular waves generated in a numerical wave tank. The coupled Volume of Fluid-Fast Fictitious Domain (VOF-FFD) interpolation method was used to evaluate FB motions. Different forms of Least Squares Support Vector Machine Methods (LSSVMs) that utilized 183 data streams were used to model FB performance for different wave height-to-water depth ratios, dimensional aspect ratios, and specific length-to-water depth ratios. Of those, 80% were used to train the model and 20% to test it. Parametric studies have shown that during training a Least Squares Support Vector Machine Method-Bat Algorithm (LSSVM-BA) with R2 = 0.8725, MAE = 0.0276, and RMSE = 0.0488 presents the most appropriate model for the evaluation of FB performance. Notwithstanding this, during testing a Least Squares Support Vector Machine Method-Cuckoo Search (LSSVM-CS) Algorithm with corresponding values of 0.6841, 0.0519, and 0.0708 performs better.

Performance of dual‐chamber oscillating water column device under irregular incident waves using Reynolds averaged Navier–Stokes model

AbstractThe purpose of this study is to analyze the hydrodynamic performance and efficiency of a dual‐chamber oscillating water column (OWC) device. For the Joint North Sea Wave Project (JONSWAP) incident waves spectrum, a two dimensional numerical wave tank is employed with nonlinear Reynolds averaged Navier–Stokes equations model along with the standard turbulence model. The free surface elevation is measured using the volume of fluid method. The numerical simulation demonstrates the streamline and velocity vector profiles throughout an entire pressure fluctuation cycle inside the chambers of the given OWC device. Further, investigation is carried out to analyze the impact of pressure drop and air flow rate through the orifice of the dual‐chamber OWC device on the power generation. Moreover, the power spectral density analysis of the free surface elevation is provided to know the variation of the parameters in the frequency domain. These results demonstrate that the effectiveness of the dual‐chamber OWC device is more near the significant wave height m.

Study on the Active Wave Absorption Methods in Lattice Boltzmann Numerical Wave Tank

The active wave absorption method has been widely employed in numerical wave tanks. The wave absorption performance of active wave absorption methods is investigated within a numerical wave tank based on a lattice Boltzmann method. Specifically, two active wave absorption methods—the classical shallow water method and the extended range method—are compared. By analyzing the contributions of free and bound components in the harmonics of the reflected wave to the reflection coefficient, we found that the extended-range method is more effective than the shallow-water method in absorbing the reflection of the primary harmonic. Moreover, a wave absorption performance index is proposed to carry out rapid evaluation of active wave absorption method performance without resorting to numerical simulations. Our findings indicate that the performance index ratio of two active wave absorption methods closely mirrored their reflection coefficient ratio. Notably, the extended-range method significantly reduces the performance index in both shallow and deep waters, exhibiting superior active absorption performance within the lattice Boltzmann method-based numerical wave tank context compared to the shallow-water method.

Tuning control parameters of underwater vehicle to minimize the influence of internal solitary waves

ISWs (Internal solitary waves) are waves that occur in stratified oceans, generating strong shear near the pycnocline. Encountering ISWs can cause a vehicle to experience the phenomenon of “falling deep”. Therefore, it is quite necessary to exert control on the vehicle in order to effectively avoid this phenomenon. This study establishes a numerical wave tank for ISWs based on the mKdV (modified Korteweg de Vries) theory. Additionally, a PD (Proportional Derivative) control method is developed for vehicles encountering ISWs in stratified fluids. The PD control parameters are designed and tuned, and the vehicle's control effectiveness, motion response and hydrodynamic characteristics, are analysed. The results suggest that this control method can effectively reduce the heave and pitch motions of the vehicle in different submergence depths and wave amplitudes. The pitch angle can be controlled within 0.2 rad for different control parameters. Better control can suppress changes within a range of 0.1 rad. To better evaluate the control effect, a new evaluation parameter σ is proposed, which takes into account both heave and pitch motions. After implementing control, the value of σmax significantly decreases. Optimal control parameters can reduce the value of σmax by about 90% compared to an uncontrolled vehicle.

Hydrodynamic performance of sandglass-type floating body with damping appendages

In the case of sandglass-type floating bodies (STFBs), small water-plan area with low metacentric height may limit their dynamic stability. One strategy to solve this problem is to use damping appendages. Therefore, the main objective of the present paper is to study the effects of the heave damping plate (as a horizontal plate), and flap (as an oblique plate) on the dynamic response of STFBs. To achieve this accomplishment, a STFB is numerically simulated in a numerical wave tank (NWT) in an open-source package of OpenFOAM. CFD results are compared with experimental and other numerical data, an acceptable accuracy is achieved. The main results of the current study show that using damping appendages has significant effects on control of the heave and pitch motions of the STFB. The most acceptable dynamics of this floating structure is also achieved for STFBs using flap with approximately 30% less heave motion and about 20% less pitch motion compared to the original version.

Double-Swing Spring Origami Triboelectric Nanogenerators for Self-Powered Ocean Monitoring

Coastal areas often experience high population density and intense human activity owing to the considerable value of the ocean. Therefore, devices for monitoring marine disasters are crucial for ensuring the safety of human life. Herein, we develop hemispherical spring origami (SO) triboelectric nanogenerators (TENGs) (HSO-TENGs) for self-powered ocean wave monitoring. Optimization is performed using two approaches. First, swing machine experiments are conducted to investigate the monitoring performance of the HSO-TENGs regarding wave height and period with satisfactory accuracy. To increase power generation and monitoring accuracy, the internal inertia and centroid of gravity of the HSO-TENGs are optimized with respect to the structural parameters (i.e., magnet weight, hammer height, and external swing arm length). Second, numerical simulations are performed using the smoothed-particle hydrodynamics (SPH) method to determine the most suitable fixed condition for the HSO-TENGs for sensing wave changes. Subsequently, wave tank experiments are conducted on the HSO-TENGs to determine their ability to sense wave height, period, frequency, and direction. Tests related to supplying other sensors are also conducted. Eventually, the ability of the HSO-TENGs to monitor wave direction and spreading parameters is investigated in a numerical SPH circular wave tank. The results prove that the optimized HSO-TENGs can achieve powering and sensing through the same device.

Experimental and Numerical Investigations for Impact Loading on Platform Decks

Experimental measurement and numerical simulations were carried out for investigating the impact loading behavior of platform decks under regular and irregular wave actions. In the numerical simulation section, a full-scale numerical wave tank was established using STAR-CCM+ software. A decreased tendency can be observed for an increased relative length of platform when the incident wave length is double the deck length. The increased deck height can also decrease impact loading on the platform, which is due to the platform being far away from the incident wave. Impact loading on the deck decreases with the increase in inclination angle, which can be explained by the deck bottom being directly exposed to the incident wave at negative inclination angles. Finally, the variation tendency of impact loading on platform decks under irregular wave actions is similar to that under regular wave actions, including the averaged values and significant values.

Numerical investigation of the response of the hybrid wave energy converter including oscillating water column and horizontal floating cylinder to irregular waves

The main goal of this research is to investigate the effect of some geometrical parameters on an onshore Hybrid Wave Energy Converter (HWEC) including an onshore Oscillating Water Column (OWC) and a Horizontal Floating Cylinder (HFC) under regular and irregular waves. The TMA spectrum is the basis of this study. The wave spectrum is used to generate irregular waves in a numerical wave tank using Ansys-fluent software based on URANS equations. Active wave absorption is used to avoid the effect of reflected waves. Also, the SST k−ω turbulence model and the VOF scheme are used for turbulence modeling and interface tracking, respectively. The results confirm that the efficiency of the HWEC is higher than the efficiency of an OWC and the efficiency of an HFC in both regular and irregular waves. Besides, the efficiency of the HWEC in irregular waves is lower than its efficiency in regular waves. A comparison of the TMA and JONSWAP spectrum on HWEC performance shows that HWEC performance is lower on the JOANSWAP spectrum. This study shows that the use of irregular waves is essential to obtain more realistic results from analyses of the onshore HWEC performance, despite their need for high computational cost.