Wave Gauges 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.

Physical Modeling of Tsunamis Generated by Submarine Volcanic Eruptions

AbstractSubmarine volcanic eruptions can induce major local and regional tsunami hazards through varied source mechanisms. Large‐scale experiments of tsunamis generated by submarine volcanic eruptions are conducted to study the cylindrical wave generation and propagation in a three‐dimensional wave basin. A unique volcanic tsunami generator (VTG) was deployed at the bottom of the wave basin to generate volcanic tsunamis with repeatable and controlled source parameters. The physical modeling is based on the generalized Froude number defined with the VTG velocity and the near source water depth. The pneumatically driven vertical stroke motion generates leading elevation waves in the wave basin. The tsunami waves generated by the VTG are measured with a wave gauge array. The wave maker performance is characterized by the dimensionless leading wave amplitudes and periods. The experimental data show the variations of the leading wave amplitude, period, and celerity along the radial propagation distance. The generated cylindrical waves belong to the weakly nonlinear wave regime in the near field with decaying wave amplitude along radial propagation. The attenuation rate of the leading wave exceeds the range from the linear wave theory in runs with higher Froude numbers. The dimensionless leading wave period increases with the dimensionless propagation distance due to the dispersion relation. Empirical equations for the characteristic wave parameters such as amplitudes and periods are derived. The experimental results contribute to the understanding of volcanic tsunami generation processes and may serve rapid volcanic tsunami hazard assessments as well as the advancement and validation of numerical models.

Laboratory Study on Wave Attenuation by Elastic Mangrove Model with Canopy

This study evaluates the effectiveness of artificial Kandelia obovata forests in wave attenuation through physical model experiments conducted in a wave flume. The experiments meticulously replicated real-world hydrodynamic conditions and mangrove movement responses using the principles of gravitational and motion similarity, with a scaled 1:10 model of Kandelia obovata. Our approach included comparative experiments against a 1:100 gradient concrete slope to isolate the effects of seabed friction and flume wall reflections. The wave height was measured using strategically placed wave gauges. The findings indicated that the artificial Kandelia obovata forests significantly attenuated waves, with a decrease in the total attenuation capacity as the water depth increased from 2.75 m to 3.28 m under both regular and irregular waves. The elastic mangrove model with a canopy effect led to a 15% increase in wave attenuation over cylindrical models. Predictive models using multivariate nonlinear regression and back propagation neural networks showed that the latter provided a superior accuracy in estimating wave transmission coefficients

Compounding impacts of the earthquake and submarine landslide on the Toyama Bay tsunami during the January 2024 Noto Peninsula event

The January 2024 Noto Peninsula earthquake (Mw 7.6) generated a destructive tsunami in the Sea of Japan region. Locally, inside Toyama Bay, the tsunami arrived at the Toyama wave and tide gauges within 2–3 min of the earthquake. Such an early tsunami arrival is inconsistent with the epicentral distance of ∼60 km. The travel time of the earthquake-induced tsunami is anticipated to be around 20 min, which is confirmed through tsunami simulations. Based on spectral and wavelet analyses of the Toyama tide and wave gauge records, we found 5 min, 14 min, and 32 min dominant wave periods. The shorter wave periods of 5 and 14 min are likely associated with a submarine landslide due to their early arrivals, as evidenced in our wavelet analysis. We then identified a potential submarine landslide location using the tsunami back-propagated travel time technique and visual inspection of the bathymetric profile. Conducting several simulations and comparing simulated and observed waveforms, we identified a seafloor landslide length of approximately 3000 m located ∼4 km offshore Toyama City. Our combined earthquake-landslide source model better reproduces the tsunami observations, indicating the contribution of the submarine landslide to the January 2024 Noto Peninsula tsunami.

2D Model For Addu City Project - Wave Transformation Over Reef Flat

Van Oord DMC was awarded the Contract for the Reclamation by Dredging and Shore Protection works for land in Addu City by The Ministry of National Planning, Housing and Infrastructure of the Maldives. The Scope of Works consists of the Design and Construction of (among others) Reclamation and Shore Protection Works on various locations in the Addu City atoll. The project execution started in 2022 and has been finalized at the end of 2023. The design of the Shore Protection Works has been verified in 2022 by means of 2D physical model testing in the wave flume of DHI in Denmark. Cross-sections of shore protection works for three different reclamation areas have been tested, where this abstract will focus on 2 locations at the outside of the atoll: Maradhoo and Four Lane Link Road (4LLR). All dimensions given in this abstract are prototype values, unless otherwise specified. The length scale of the both models was selected at 1:30. The foreshore of the 2 tested cross-sections is very typical for atolls, consisting of a relatively shallow reef flat followed by a very steep slope to deep water. The modelled foreshores are presented in Figure 1. This figure also shows the locations of the wave gauges, which were placed both offshore (near the wave generator) and on top of the reef flat (in front of the structure). The tested seabed levels directly at the toe of the 4LLR and Maradhoo structures were MSL-0.70m and MSL-0.40m respectively. The target wave conditions were defined in deep water (in front of the wave generator), with design wave heights (Hm0) between 3.8m and 4.4m and 120% overload conditions. The tested peak wave periods (Tp) varied between 11.9s and 19.7s.

Measurement Of Spatial-Temporal Waves In The Laboratory Using Computer Vision Technolog

Given the complexity of ocean wave phenomena, physical modeling continues to be essential in various engineering and research applications. Wave height, a characteristic measured in nearly all projects, is commonly assessed using resistance/capacitance wave gauges. However, a significant limitation of these traditional wave gauges is their point-based nature, which restricts their ability to describe detailed spatial wave characteristics, especially during wave nonlinearity or when waveforms change. Furthermore, to reconstruct the 3D wave field, an array of wave gauges is often employed alongside an appropriate interpolation algorithm. Additionally, wave gauges may alter flow/wave conditions in specific scenarios. To address these limitations, various non-intrusive measurement techniques have been proposed. Gomit et al. (2022) classified these into stereoscopic, projection, and light-based methods, including LiDAR (Blenkinsopp et al., 2012), RGB-D cameras (Martínez-Aranda et al., 2018), and binocular stereo vision (Li et al., 2022). However, their applicability is constrained by factors such as optical setup complexity and device cost. With the rapid advancement of computer vision technology, it is possible to improve these issues and better describe temporal and spatial wave field variations using such techniques. This conference contribution details the reconstruction of the temporal and spatial 3D free water surface using photogrammetry techniques applied to images from consumer webcams. It also compares these results with measurements obtained from a wave gauge.

Validation Of A Nonlinear Wave Decompistion Method Including Shoaling

It is important to decompose the incident and the reflected waves when performing physical or numerical experiments in a wave flume. Especially when large reflection is expected, from for example a breakwater, the total measured signal can significantly deviate from the incident signal. Different techniques exist to decompose a signal into incident and reflected signals. For 1D wave flumes a method based on co-located wave gauges (Nwogu, 1989) or multiple wave gauges (Røge Eldrup and Lykke Andersen, 2019, Zelt and Skjelbreia, 1993) is commonly applied. The latter is the focus of this abstract since recently, the decomposition method based on multiple wave gauges was extended to be applicable to nonlinear irregular waves by including bound waves and amplitude dispersion (Eldrup and Lykke Andersen, 2019). Moreover, the practical requirements for the nonlinear wave decomposition methods were described in De Ridder et al. (2023). Most of the nonlinear wave decomposition methods are only applicable to a flat bed and will introduce an error when it is applied on a sloping foreshore which is typically the case in physical model experiments. Padilla and Alsina (2020) derived a general framework including shoaling of bound waves and Lykke Andersen and Eldrup (2021) presented a method for nonlinear regular waves over a sloping bed. However, a nonlinear decomposition method for irregular waves over a sloping bed has never been verified with physical model experiments. In this abstract the nonlinear decomposition method for irregular waves as presented in De Ridder et al. (2023) is extended with the effects of shoaling and its effects are verified with a physical model experiment.

Directional Spectrum Estimation For Sea States Generated By The Single Summation Method

The influence of directional spreading of waves is significant for wave-induced loads, wave breaking and nonlinearity of the waves. For physical model testing performed at test facilities such as the Ocean and Coastal Engineering Laboratory at Aalborg University, it is crucial to validate if the test conditions match the target sea states by measurement and analysis of the generated directional wave field. Most of the existing methods assumes a double summation sea state to be present which is valid in the prototype. However, waves in the laboratory are usually generated by single summation. The current paper presents a method to analyse short-crested waves generated by the single summation method. Compared to similar methods oblique reflections are considered instead of only in-line reflections. The results show that the method successfully decomposes the incident and reflected wave fields in the time domain. Thus, for example the incident wave height distribution may be obtained. The sensitivity of the new method to additional reflective directions, noise, calibration errors and positional errors of the wave gauges was found small.

Wave front perturbation effect on the variability of monopile wave impact loads

The slamming wave force and pressure variabilities for monopile wave impacts are studied as functions of wave breaking shape and transverse perturbations on the breaking wave front. The impacting wave topology is characterized as slosh, flip-through, $\varOmega$ , overturning and fully broken. Fifty test repetitions are conducted for each type of wave impact to assess the variability of force impulse, force and pressure. The results for the unperturbed cases show that the slamming force is highest among the nominal slosh, flip-through and $\varOmega$ tests, and that the slamming force variability is highest for the first two. We demonstrate that the slamming force and pressure variabilities decrease notably after selecting and regrouping the tests by similar crest heights and temporal slopes measured at an upstream wave gauge. The group representing $\varOmega$ wave impacts shows the largest mean slamming force and peak pressure, and their variability is the highest among all groups. Further, the effect of lateral perturbations on the pressure, force and impulse variabilities is investigated. Due to the perturbations, the slamming pressure variability for the wave impacts in which the wave front hits the monopile surface increases significantly. The variability of the slamming force is also increased for the perturbed impacts; however, it is smaller than the slamming pressure variability. The force impulse variability shows a low sensitivity to perturbations, and its magnitude is smaller than that of the force variability. Finally, the slamming pressure using fifteen pressure sensors for five selected events is studied. For these tests, oscillations at frequencies associated with structural or bubble oscillations are seen. Further, the air entertainment is documented through video recordings.

Slip distribution of the 2024 Noto Peninsula earthquake (MJMA 7.6) estimated from tsunami waveforms and GNSS data

AbstractThe 1 January 2024 Noto-Hanto (Noto Peninsula) earthquake (MJMA 7.6) generated strong ground motion, large crustal deformation and tsunamis that caused significant damage in the region. Around Noto Peninsula, both offshore submarine and partially inland active faults have been identified by previous projects: Ministry of Land, Infrastructure, Transport and Tourism (MLIT) and Japan Sea Earthquake and Tsunami Research Project (JSPJ). We inverted the tsunami waveforms recorded on 6 wave gauges and 12 tide gauges around Sea of Japan and the GNSS data recorded at 53 stations in Noto Peninsula to estimate the slip amount and seismic moment on each of active faults. The results show that the 2024 coseismic slips were 3.5 m, 3.2 m, and 3.2 m on subfaults NT4, NT5 and NT6 of the JSPJ model, located on the northern coast of Noto Peninsula and dipping toward southeast. A smaller slip, 1.0 m, estimated on NT8 on the southwestern end of the 2024 rupture, may be attributed to its previous rupture during the 2007 Noto earthquake. The total length of these four faults is ~ 100 km, and the seismic moment is 1.90 × 1020 Nm (Mw = 7.5). Almost no slip was estimated on the northeastern subfaults NT2 and NT3, which dip northwestward, opposite to NT4–NT5–NT6, and western subfault NT8. Aftershocks including the MJMA 6.1 event occurred in the NT2–NT3 region, but they are smaller than the potential magnitude (Mw 7.1) those faults can release in a tsunamigenic earthquake. Similar features are also found for the MLIT model; the 2024 slip was only on F43 along the northern coast of Noto Peninsula, and northeastern F42 did not rupture, leaving potential for future event. Graphical Abstract

Experimental and numerical study of the gated and ungated ogee spillway

This study was carried out by combining numerical modeling and experimental measurements to investigate the hydraulic characteristics of ungated and gated ogee spillways with high head ratios. The primary objective was to validate the use of a numerical model as a complementary approach to the experimental model for simulating the hydraulic behavior of these spillways, providing a more comprehensive understanding of their hydraulic properties under varying conditions of head ratios and relative gate openings. An Acoustic Doppler Velocimeter (ADV) was used to measure the vertical flow velocity distributions, and ultrasonic sensor wave gauges were used to obtain the time history of the water level. The results of the measurements were compared with the simulation results using a model fitted with three different turbulence models (realizable k-ε, RNG k-ε, k-ω SST). The numerical model was developed using OpenFOAM. With respect to the ungated spillway, three different head ratios ranging from 1.4 to 4.6, which correspond to high head ratios, were investigated. Similarly, three different relative gate openings ranging from 0.5 to 2 were investigated for the gated spillway. The results of water surface profiles and velocity profiles suggest that the numerical and experimental models achieve a good agreement for sections located further away from the spillway. For the ungated spillway, the simulation results for the near-spillway sections are enhanced when the head ratio increases. Considering the velocity profiles and error analysis, the realizable k–ε model was found to best predict the results of the experimental model. A discussion about the discharge equation, velocity fields, pressure fields, and the corner separation zone is also included in this study.

On the wave attenuation properties of seagrass meadows

The wave attenuation properties of seagrass meadows were investigated in a flume facility using dynamically-scaled models of seagrass exposed to regular long crested waves. Experiments were conducted for 66 wave conditions and with four plant densities; waves were measured with eight resistance wave gauges. The data collected represent the most-comprehensive dataset of its kind. They reveal that the wave attenuation coefficient KD of a seagrass meadow reaches a uniform value after a distance of approximately 1.5–3 times the water depth from the meadow start and that both KD and the drag coefficient Cd depend significantly on the plant density. An improved model of KD based on the work of Lei and Nepf (2019) is proposed that takes into account the effects of the solid volume fraction of the plant model through a correction on Cd and that of plant density via an effective vegetation frontal area av−e. The effective vegetation frontal area is described as a power law of the roughness density λf. The model, which was validated with the data of KD obtained from the laboratory experiments described herein, displays an excellent agreement with data from the literature. It can predict KD accurately also for cases whereby the maximum wave orbital excursion is comparable with the blade length, despite this condition violates the model’s assumptions. This work provides a comprehensive dataset and a new model that can be used to improve the prediction of wave attenuation of seagrass meadows.

Preliminary Performance Assessment of the Wave Parameter Retrieval Algorithm from the Average Reflected Pulse

To obtain new information about surface waves, it is proposed to use an underwater acoustic wave gauge, and an assessment of its effectiveness can be performed using a numerical simulation and field experiment. A new device, an underwater acoustic wave gauge named “Kalmar”, was developed by the Institute of Applied Physics of the Russian Academy of Sciences for long-term, all-weather monitoring of wind waves. The instrument uses ultrasound to probe the water surface from underwater and can be used to verify remote sensing data. In this work, the capabilities of the device are tested and compared with ADCP data. Two independent methods for processing underwater acoustic wave gauge data are discussed and compared. One of them is completely new for acoustic measurements and is based on the analysis of the shape of the reflected acoustic pulse averaged over space and time. The other allows processing individual reflected pulses and calculating the time implementation of the distance to the water surface. It is shown that two independent methods of significant wave height retrieval from the acoustic wave gauge measurements are highly correlated. The “Kalmar” acoustic wave gauge and the RDI WH-600 acoustic Doppler current profiler operated simultaneously at the test site in Gelendzhik from 1 February to 10 February 2020. The significant wave heights measured by the two instruments are in good agreement.

Experimental Study on Wave Transmission Coefficient of Double Cylindrical Floating Breakwater in a Wave Basin

Floating breakwater is a better alternative than the conventional method. It is an effective coastal engineering unit used to protect coastal regions such as harbours and marinas from erosive waves. It has many other applications such as offshore renewable energy generation, infrastructure preservation, temporary structure, and provides a controlled environment for aquaculture activities. The floating breakwater such as the double cylindrical floating breakwater (DCFB) is claimed to have effective wave attenuation characteristics. A lab scale investigation was done by placing the DCFB in a controlled wave basin in with wave generator to generate wave and wave gauge to quantify the wave transmission coefficient. The wave transmission coefficient represents the effectiveness of the breakwater system in attenuating incoming waves, where an effective breakwater system will result in a low transmission coefficient value. In this study, the DCFB’s effectiveness in terms of wave transmission coefficient was investigated with two different configurations where the spacing between the cylinders of the DCFB units are 0.2 m and 0.6 m respectively. Results show that the configuration of DCFB units with 0.5 m cylinder spacing are more effective in absorbing incoming wave height resulting in lower transmission coefficient. Furthermore, some prospective areas had been identified for future enhancement.

The Effect of Different Swell and Wind-Sea Proportions on the Transformation of Bimodal Spectral Waves over Slopes

In the laboratory experiment, 1:25 scaled models are constructed to investigate the effect of different swell and wind-sea proportions on the wave transformation. The source of the wave spectrum is related to the wave conditions in the Gulf of Guinea. Swell from the westerlies and local wind-sea forms the bimodal spectral waves in the region. To better understand the transformation of bimodal spectral waves, a series of wave conditions are measured by the wave gauges in a wave flume. Based on the wave spectrum at the Bight of Benin, the wave transformation along the slopes and variations of different swell proportions are analyzed. The result of the wave height variations shows that the slope and swell proportion play a significant role in the maximum wave height, and the wave height has an upward trend with a large swell proportion. The analysis of wave nonlinearity is conducted, showing that the large swell proportion in the wave spectrum leads to a more significant nonlinearity before wave breaking. Combining the variations of wave height and wave nonlinearity, the influence of bimodal spectral waves on nearshore wave prediction, shoreline change, marine operations, and structure design is discussed.

Hydrodynamic and energy-harvesting performance of an isolated oscillating water column device: An experimental study

Most previous experimental studies on the hydrodynamic and aerodynamic performances of an oscillating water column (OWC) wave energy converter were conducted in a wave flume. In this study, an experimental study on an isolated OWC plant is carried out in a wave tank. The interactions between the OWC system and incident regular and irregular waves are analyzed by measuring the surrounding wave fields using a wave gauge array. The wave distribution patterns and reflection ratios of the OWC model are presented. In addition, the free-surface elevation, air pressure varying amplitude, turbine torque output, and relative capture width ratios and efficiencies in regular and irregular wave scenarios are measured and analyzed. The operating performances of the OWC model are analyzed and compared to the results derived from the flume tests. An overall performance reduction of over 20% can be observed in the wave tank tests. In addition, the representative results of the overall capture width ratio of the OWC model derived from irregular wave tests are corrected from the scaling effects caused by the similarity contradiction.

Real time water surface elevation using video camera

In recent years, image processing has become a popular tool in wave flume experiments. In Indonesia, the use of image processing methods for measuring instruments in wave flume experiments has not been widely used. Therefore, in this study, an image processing method using image data from a digital camera was used in real time to measure the water surface elevation in the wave flume. Regular and irregular waves were measured with this image processing technique. The measurement results using this video camera were calibrated with wave gauges. The results showed that the measurement method using video images has a small difference less than 7% in wave height and wave period error. Therefore, this method can be a solution as a low cost measuring tool in wave flume or in field observations.

Measuring near-field wave elevation with monocular vision using self-supervised learning techniques

Ocean waves are among the most influential factors affecting marine mechanical systems. The existing methods for measuring wide-area wave-field data have limitations and require high maintenance costs. Therefore, it is crucial to develop a reliable and efficient field measurement method for wide-area wave fields. This study proposes a monocular vision-based approach for wave field measurement, where the depth of each pixel is equalised to summation of the depth of the mean water surface and the depth variation induced by wave elevation. A deep network was trained using a self-supervised algorithm to approximate the depth variation induced by wave elevation. A loss of representative features was proposed to improve the performance of deep networks. The images of an open-source dataset were used to train and validate the proposed model. By using the proposed method, the images were utilised to reconstruct the three-dimensional wave field of the test set. The time history and wave spectrum of the wave fields were compared with those calculated by existing method and measured by wave gauge. The influence of the training set on the measurement results was also investigated. The results indicate that the proposed method is capable of performing effective near-field wave measurements by monocular images, effectively reducing the device requirements, and increasing update frequency for ocean wave measurement.

Wave environment analysis at Norwegian harbours for land-based aquaculture facilities using a combined phase-averaging and phase-resolving numerical modelling approach

Numerical wave modelling of Norwegian coastal areas is challenging due to the drastically varying bathymetry, irregular coastline, and large domains of interest. The widely used phase-averaging models are limited by such bathymetric and topographic conditions. Phase-resolving models provide higher accuracy regarding strong nonlinear wave transformations with the trade-off of a higher computational cost. This study provides a combined phase-averaging and phase-resolving modelling approach to analyse the wave conditions for on-shore aquaculture facilities at the site candidates Fiskenes and Breivik, Andøya, Norway. The phase-averaging spectral model SWAN is used for the offshore sea state analysis based on the offshore hind-cast data. The analysis is performed on cascade nested grids, with increasing accuracy closer to the proposed harbour locations. A novel interpolation algorithm is proposed to provide comprehensive sea state information with every offshore wave directions without requiring additional simulations. The critical wave conditions are identified from SWAN and used as input to the open-source phase-resolving fully nonlinear potential flow model REEF3D::FNPF. Four scenarios are investigated and densely spaced wave gauges in the entire computational domain provide the distribution of significant wave height. The combined and cascade simulation approach helps to achieve a balance between computational efficiency and accuracy for large-scale marine environment assessment. The results show detailed wave statistics in the entire area of relevance near both harbours and provide a quantitative reference for both the site choice and the harbour design.

Enhancing efficiency and measuring sloshing in oscillating water column (OWC) systems: An experimental investigation of novel inlet geometry optimization and innovative measurement method

Sea wave characteristics could be the most crucial sloshing occurrence caused by OWCs. In this paper, an OWC with different inlet geometries has been investigated experimentally to optimize the performance and reduce sloshing. Eight wave gauges (WG) are applied to measure water free surface to determine the sloshing. The results showed that the converter performance decrease when sloshing occurs. To reduce sloshing, four inlet openings were installed at the inlet of OWC, and to achieve optimal efficiency in sloshing conditions, the geometry optimization done by genetic algorithm; then, the converter's performance with optimum inlet was experimentally investigated, sloshing phenomenon was observed in 4 frequencies in converter without opening; However, after installing the optimal opening, sloshing occurred in only one frequency, and also in this case, sloshing was 42 % reduced. The data correlation results showed a positive correlation between the frequency and the Top Free Surface of water inside the OWC (shown by a line called TFS) angle. At the same time, there is a negative correlation between the frequency and the flow rate, pressure difference, and power generated. The comparison of the converter results with opening and without opening shows that the correlation between frequency and other variables is always lower in the case with opening. Also, geometry optimization improved the sloshing frequency's 42.89 % performance.