Multidirectional Random Waves Research Articles

Real-time inverse estimation of multi-directional random waves from vessel-motion sensors using Kalman filter

The real-time inverse estimation of the ocean wave spectra and elevation from a vessel-motion sensor is highly valuable, although it is still in the early stages of development. The Kalman filter method using motion measurements has advantages over other methods in terms of real-time capability, cost savings, and easy installation. In this paper, the Kalman filter method is developed for the inverse estimation of multi-directional waves in real time. The problematic divergence in the high-frequency region encountered by previous papers using similar approaches is resolved by employing the Wiener filter method. The developed method is also shown to be robust against potential sensor noises. The real-time multidirectional-wave spectrum and elevations can be recovered, including the high-frequency region, using the developed methodology with the numerically generated motion-sensor signals with noise. The developed Kalman filter algorithm is tested and validated for various sea states of uni- and multi-directional waves. The inverse estimation of multi-directional waves is generally less accurate compared to that of unidirectional waves, mainly due to the significant increase of unknowns (component waves) in the Kalman filter processes. Nevertheless, the overall wave spectra, elevation time series, significant wave heights, peak period, main direction, and directional spreading were well recovered.

Prediction of near-field uni-directional and multi-directional random waves from far-field measurements with artificial neural networks

Predictions of several minutes of phase-resolved waves ahead of time from the measurements of wave-time-series at upstream locations are important for many marine operations. Making use of the knowledge of wave propagation, we design the input-output data and fine-tune the architecture of an artificial neural network (ANN) to push its capacity for the wave predictions. The study cases include uni-directional and multi-directional waves with mild to large wave steepness. The ANN models are trained on simulated random waves of JONSWAP spectrum with significant wave height and peak spectral wave period taken from a North Sea wave statistical data. Results demonstrate that the ANN models with single or multi-inputs from a 1 km upstream far-field locations can predict near-field waves with errors ranging from 2.6% to 12% for both uni- and multi-directional waves. The model accuracy is dependent on the wave steepness. Sensitivity studies show that the network model's hyper-parameters might need to be changed for different wave conditions. There are also possible optimal locations for far-field wave probes that will give the optimal prediction at the near-field.

Random wave action on pile group foundations with complex geometry for sea-crossing bridges

To explore the mechanical properties of pile group foundations (PGFs) with complex geometry in sea-crossing bridges under ocean wave action, this study develops a numerical model for predicting wave loads on PGFs under multidirectional random wave action. Furthermore, an experimental model of the PGF composed of a quasi-elliptical pile cap and 13 tilted piles is designed and made based on the gravity similarity criterion. By performing model experiments and numerical analysis, the mechanical characteristics of the PGF model under random wave action, the effect of principal wave direction angle and random wave directionality, and the influence of the pile cap on wave loads of tilted piles are systematically investigated. The results show that the calculated results of the presented numerical model match well with the experimental data. The frequency characteristics of wave loads on the PGF model are mainly determined by the wave spectrum. The increase of the significant period improves the contribution of the pile group to the horizontal wave loads on the PGF. The effect of the principal wave direction on the vertical wave loads on the PGF is not obvious under the experimental wave conditions. Neglecting the wave directionality will overestimate the wave loads in the principal wave direction and vertical direction on the PGF. Under the influence of diffraction waves from the pile cap, the wave loads on the pile group and the piles where the wave finally acts are easily amplified when the wave number is small, but in the large wave number case, the wave loads on the pile group and the piles below the middle of the pile cap may be weakened.

Numerical research on the interaction of multi-directional random waves with an offshore wind turbine foundation

Real sea waves are multi-directional, but most studies on wave–structure interaction have focused on unidirectional waves. In this study, a coupled model between a potential flow solver and OpenFOAM wave basin is adopted to investigate multi-directional wave loads on an offshore wind turbine foundation. The coupled model is extended to multi-directional wave states based on the single summation method combined with the JONSWAP spectra. The numerical results are validated against the experimentally obtained values. Multi-directional waves are short-crested, the elevations are random in the wave field, and the wave pressures induced on the two sides of the cylinder are not symmetric about the principal wave direction, leading to a non-zero transverse force. In addition, the effects of wave directionality and relative ratio of foundation diameter and wavelength on wave loads are analysed. For multi-directional waves, the effects of wave directionality on transverse wave force are more sensitive than those on normal force. Wave run-up on the up-wave side increases as the directional spreading parameter decreases. In addition, wave directionality plays a complex role in the wave run-up load induced on the back side, which is found to be controlled by the relative ratio of the cylinder diameter and wavelength.

Spatial Variation of Wave Force Acting on a Vertical Detached Breakwater Considering Diffraction

In this study, the analytical solution for diffraction near a vertical detached breakwater was suggested by superposing the solutions of diffraction near a semi-infinite breakwater suggested previously using linear wave theory. The solutions of wave forces acting on front, lee and composed wave forces on both side were also derived. Relative wave amplitude changed periodically in space owing to the interactions between diffracting waves and standing waves on front side and the interactions between diffracting waves from both tips of a detached breakwater on lee side. The wave forces on a vertical detached breakwater were investigated with monochromatic, uni-directional random and multi-directional random waves. The maximum composed wave force considering the forces on front and lee side reached maximum 1.6 times of wave forces which doesn’t consider diffraction. This value is larger than the maximum composed wave force of semi-infinite breakwater considering diffraction, 1.34 times, which was suggested by Jung et al. (2021). The maximum composed wave forces were calculated in the order of monochromatic, uni-directional random and multi-directional random waves in terms of intensity. It was also found that the maximum wave force of obliquely incident waves was sometimes larger than that of normally incident waves. It can be known that the considerations of diffraction, the composed wave force on both front and lee side and incident wave angle are important from this study.

A Three-Dimensional Numerical Model with an L-Type Wave-Maker System for Water Wave Simulations by the Moving Boundary Method

A three-dimensional numerical wave tank was developed based on Reynolds averaged Navier–Stokes equations and the volume of fluid method. The moving boundary method is adopted in this model to generate water waves. Piston-type wave-makers are mimicked for the total replication of the physical wave tank conditions. Two-dimensional regular and irregular waves are simulated, with the capability to trigger the active wave absorption algorithm. The two-sided wave-maker system with L-type arrangement is adopted in this model to expand the effective wave areas for three-dimensional waves. Oblique regular waves and multidirectional random waves are simulated, yielding a good agreement with theoretical solutions. The results indicate that this numerical model is an effective tool to provide finer details or complement data unavailable due to the physical setting of a tank experiment.

Spectral boundary element modeling of water waves in Pohang New Harbor and Paradip Port

A novel mathematical model formulation based on spectral boundary element method (SBEM) is presented to examine the wave response in the Pohang New Harbor (PNH), South Korea and Paradip port, Odisha, India. In SBEM, the boundary element method (BEM) is coupled with the spectral element method (SEM) to enhance the numerical accuracy of the present numerical scheme. The numerical solution on each boundary element is obtained by using boundary integral associated with Chebyshev point discretization. The boundary Integrals are transformed using Jacobians and evaluated with Clenshaw Curtis Quadrature rule. Convergence analysis is performed on rectangular domain for present scheme, BEM and hybrid finite element method (HFEM), which shows that the present numerical scheme is better as compared to other traditional numerical schemes. Further, the simulation results are validated with BEM, analytical method and experimental data from Lee (1971) and Ippen and Goda (1963). The wave amplification is obtained at six record stations inside the PNH, South Korea and Paradip port, Odisha, India. In addition, the spectral density is also determined for multidirectional random waves propagating towards the PNH and Paradip port at the same record station. The resonant frequencies are estimated in PNH and Paradip port for the safe navigation of moored ship.

Effects of random winds and waves on a long-span cross-sea bridge using Bayesian regularized back propagation neural network

Uncertainties from random multiple factors bring great challenges for assessing response of long-span bridges. This study proposes a dynamic analysis framework by integrating the wind–wave–bridge system with Bayesian regularized back propagation neural network, and then investigates stochastic response of a cross-sea cable-stayed bridge under extreme wind and wave parameters. The wind–wave–bridge system involving wind–bridge and wave–bridge interactions is constructed to calculate dynamic response of the bridge by Newmark-β method, considering stationary fluctuating wind fields and multidirectional random wave fields. To reduce the calculation cost, a Bayesian regularized back propagation neural network model is introduced, and the model evaluation is carried out to illustrate its accuracy and efficiency. After performing small-scale finite element analyses, the response statistics are obtained and later used as the known samples for training the neural network. The power spectrum analyses of the deterministic results are performed to investigate the contribution mechanism of the wind and wave. Finally, the correlation between the bridge response and the single wind–wave parameter is given by uncertainty analysis of the Bayesian regularized back propagation neural network model. The results show that the proposed framework is capable of capturing the nonlinear bridge response resulting from nonlinear wind and wave loads, which, however, is significant different from that under wind alone. The bridge response receives significant contribution from wind and waves relative to the vibration characteristic of the bridge at smaller wind and wave loads. The contribution from vibration characteristic of the bridge becomes significant at larger wind and wave loads. The uncertainty analyses illustrate the significant effects of four wind and wave parameters on girder, tower, and submerged structure.

The induced wave energy damping effect owing to rearrangement rubble mound breakwater

To maintain the calmness of the harbor, rubble mound breakwaters are one of the practical measures to protect sailing and mooring waters. This paper investigates the effect of relocated rubble mound breakwaters on tranquillity in Busan yacht range and the impact of bridge piers at the entrance of the yacht range based on physical hydraulic modeling using multi-directional random waves. It is obtained that the sufficient tranquillity can be due to securely moored yachts, owing to newly relocated rubble mound breakwaters away from piers. The experimental results also showed the distribution of the energy difference’ dependence on various wave directions. The experimental findings are valuable for the design of Busan yacht marina, and are of reference to other port projects.

Modelling Wave Transmission and Overtopping Based on Energy Balance Equation

Wave transmission and overtopping around nearshore breakwaters can have significant influence on the transmitted wave parameters, which affects wave conditions and sediment transportation and becomes the focus of design in engineering. The objective of this paper is to present a simplified model to estimate these important wave parameters. This paper describes the incorporation of wave transmission and overtopping module into a wave model for multi-directional random wave transformation based on energy balance equation with the consideration of wave shoaling, refraction, diffraction, reflection and breaking. Wen’s frequency spectrum and non-linear dispersion relation are also included in this model. The influence of wave parameters of transmitted waves through a smooth submerged breakwater has been considered in this model with an improved description of the transmitted wave spectrum of van der Meer et al. (2000) by Carevic et al. (2013). This improved wave model has been validated through available laboratory experiments. Then the verified model is applied to investigate the effect of wave transmission and overtopping on wave heights behind low-crested breakwaters in a project for nearshore area. Numerical calculations are carried out with and without consideration of the wave transmission and overtopping, and comparison of them indicates that there is a considerable difference in wave height and thus it is important to include wave transmission and overtopping in modelling nearshore wave field with the presence of low-crested breakwaters. Therefore, this model can provide a general estimate of the desired wave field parameters, which is adequate for engineers at the preliminary design stage of low-crested breakwaters.

Theoretical analysis of extreme wave oscillation in Paradip Port using a 3-D boundary element method

A mathematical model is developed to estimate the amplification of multidirectional random waves in the Paradip port, Odisha, India under the resonance conditions. A 3-D boundary element method with the consideration of variable bathymetry is utilized for solving Laplace equation in an irregular domain including the partial reflection boundary condition. The current numerical scheme is validated through the comparison of simulation results with previous well-defined studies along with measurement data for the rectangular harbor. Six key recorder stations are chosen as port location of moored ship to analyze the wave response in the Paradip port for multidirectional random waves. Further, wave spectrum is also estimated based on Fast Fourier Transformation (FFT) with respect to wave period at six recorder stations. Actual bathymetry of Paradip port is utilized to estimate the wave height ratio at each record station for the incident waves with different directions. Further, the resonance frequencies are determined for each directional incident wave and safe locations in Paradip port is also identified based on the simulation results. Thus, the proposed numerical scheme can be utilized to foster the prediction of wave profile in the realistic ports or harbors with complex geometries for the safe navigation.

Numerical investigation of multidirectional random wave interaction with a large cylinder

To investigate the multidirectional wave run-up and forces on a large cylinder, a numerical model of multidirectional random wave loads on a large-scale cylinder is established based on the linear theory of wave interaction with a large-scale bottom-mounted vertical cylinder. The incident directional wave is specified using a discrete form of the Mitsuyasu-type spreading function. A wave basin experiment was carried out, and the numerical calculation results were verified by the results of the physical experiment. The results indicate that the wave directionality has significant effects on the distribution of the wave run-up around the cylinder. The transverse wave force occurs due to which the multidirectional waves at the two sides of the cylinder are totally different from each other at any time because of the wave directionality. Specially, for the multidirectional random wave with small directional spreading parameter ( s = 5), the transverse force Fy is about 57% of the normal force Fx and cannot be neglected any more. Results can provide reference for the real engineering design.

Prediction of Wave Force on a Long Structure of Semi-infinite Breakwater Type Considering Diffraction

In this study, the wave force distribution acting on a semi-infinite and vertical-type long structure is investigated considering diffraction. An analytical solution of the wave force acting on long structures is also suggested in this study. The wave forces on long structures are evaluated for monochromatic, uni-directional random, and multi-directional random waves. Diffraction effects in front of the breakwater and on the lee side of the breakwater are considered. The wave force on a long structure becomes zero when the relative length of the breakwater (1/L) is zero. The diffraction effects are relatively strong when the relative length of the breakwater is less than 1.0, and the wave forces decrease greatly for long structure when the relative length of the breakwater is larger than 0.5. Therefore, it is necessary to consider diffraction effects when the relative length of the breakwater is less than 1.0, and the relative length of the breakwater must be at least 0.5 in order to obtain a reduction of wave force on long structures.

Multi-directional random wave interaction with an array of cylinders

Based on the linear theory of wave interaction with an array of circular bottom-mounted vertical cylinders, systematic calculations are made to investigate the effects of the wave directionality on wave loads in short-crested seas. The multi-directional waves are specified using a discrete form of the Mitsuyasu-type spreading function. The time series of multi-directional wave loads, including both the wave run-up and wave force, can be simulated. The effect of wave directionality on the wave run-up and wave loading on the cylinders is investigated. For multi-directional waves, as the distribution of wave spreading becomes wider, the wave run-up at some points around the cylinders is found to increase. This suggests that multi-directional wave run-up tends to be larger than unidirectional wave run-up. In addition, the wave directionality has a significant influence on the transverse force. The biggest transverse force is found to occur on the rear cylinder rather than the front one. This is quite different from the results in unidirectional waves and should be paid much more attention in the design of offshore structures. At last, the possibility of the near-trapping under the multi-directional random waves is investigated. It is found that the near-trapping also occurs for multi-directional wave conditions.

위상을 포함한 다방향 불규칙파 조건에서의 이안류 수치모의

Recently, Choi et al.(2015) showed that a numerical simulation of the SandyDuck experiment under a directional random wave environment agreed well with the experimental data including the wave height distribution of the random waves, the well-developed longshore current and its energetic fluctuation. Based on the Boussinesq modeling, this study investigates the effect of the alongshore variations, which are induced by not only the field topography but also the phase interaction of multidirectional random waves in the surf zone wave field, on the rip currents. As a result, transient rip currents as well as topographical rip currents cause the complicated surfzone circulation and mixing process due to their interactions in a multi-directional random wave condition while the topographical rip currents are dominant in a monochromatic wave condition. 핵심용어: SandyDuck experiment, rip current, directional random waves, Boussinesq modeling, FUNWAVE, SandyDuck 실험, 이안류, 다방향 불규칙파, ë¹„ì„ í˜• Boussinesq ë°©ì •ì‹

Boussinesq modeling of longshore currents in the SandyDuck experiment under directional random wave conditions

To investigate surf zone hydrodynamics in a directional random wave environment, a numerical simulation of the SandyDuck experiment was performed for 2 October 1997 using the Boussinesq model FUNWAVE. This simulation utilized the field topography and the offshore spectrum constructed from observed datasets. The simulation results agreed well with the experimental data to reveal a wave height distribution of the random waves as well as the well-developed longshore current and its energetic fluctuation. The simulation also revealed that longshore variations were induced by not only the field topography but also the phase interaction of multidirectional random waves in the surf zone wavefield, and subsequently complicated the mixing process with fluctuations of longshore currents and rip currents in the nearshore current field. Based on the Boussinesq modeling, further simulations were performed using incident wave spectra that varied in the frequency and directional spreading. The simulation results confirmed that random waves with broader frequency-directional spectra tended to produce weaker mean longshore currents, which were associated with the early dissipation of relatively short wave components and the small moments of broad wave spectra. In addition, it was found that the energetic nearshore fluctuations, which involved complicated evolutions of vortices, did not vary significantly according to the frequency and directional spreading. However, the results of the monochromatic unidirectional wave revealed relatively weak and organized nearshore fluctuations (i.e., instabilities), even though this simulation also revealed a stronger longshore current with stronger wave breaking than did the random wave simulations.

Wave spectral modeling of multidirectional random waves in a harbor through combination of boundary integral of Helmholtz equation with Chebyshev point discretization

A mathematical model is presented to predict the wave spectrum in a complex geometry harbor domain due to the diffraction of multidirectional random waves propagating through entrance of the harbor from the open sea. An accurate description of the harbor geometry, bathymetry and an incident wave spectrum are required. The solution of Helmholtz equation in the bounded and unbounded region is obtained by 2-D boundary integral method with the consideration of partial reflection and corner point approximation. Moreover, the Chebyshev point discretization is applied on boundary of the harbor to improve the accuracy of the numerical scheme. The principle of superposition is adopted to simulate the directional random waves based on the solution of monochromatic incident waves. The form of Mitsuyasu’s frequency spectrum was utilized for the random wave simulation. The wave spectra for multidirectional random waves are analyzed at various recorder stations in the Pohang New Harbor (PNH). Comparison of simulation results with in situ measurement data recorded at various recorder observatories in the PNH demonstrates the feasibility and accuracy of our proposed method. After this study, we analyzed the wave height distribution in the whole PNH domain. Based on the simulation results, some tactic has been introduced to reduce the wave amplitude in the PNH. Our primary results confirm that present numerical model is accurate and flexible to implement on various real harbors to predict the multidirectional random wave diffraction.

경사면을 입사하는 불규칙파랑의 방향 비대칭 매개변수 및 최대 방향분포 매개변수

해안선에 비스듬히 입사하는 다방향 불규칙파랑은 굴절에 의해 방향 비대칭성이 발생한다. 방향 비대칭은 최대 방향분포 매개변수(S max )와 연관된 비대칭 매개변수의 항으로 표현된다. 본 연구에서는 심해에서 다양한 주파향각과 최대 방향분포 매개변수 등의 특징을 갖는 다방향 불규칙파랑에 대해 수심 변화에 따른 비대칭 매개변수와 최대 방향분포 매개변수의 변화를 계산하였다. 계산 값들은 파랑의 방항 비대칭성을 무시한 Goda and Suzuki(1975)에 의한 결과와는 다르다. 비대칭 매개변수와 최대 방향분포 매개변수의 계산을 위해 JONSWAP 스펙트럼(Hasselmamn et al., 1973)과 Lee et al.(2010)의 방향 분포 함수를 사용하였다. 계산 과정과 결과들은 일반화를 위해 심해에서의 유의파고, 첨두주기, 첨두주기에 해당하는 파장 등으로 무차원화 하였다.

Numerical simulation of multi-directional random wave transformation in a yacht port

This paper extends a prediction model for multi-directional random wave transformation based on an energy balance equation by Mase with the consideration of wave shoaling, refraction, diffraction, reflection and breaking. This numerical model is improved by 1) introducing Wen’s frequency spectrum and Mitsuyasu’s directional function, which are more suitable to the coastal area of China; 2) considering energy dissipation caused by bottom friction, which ensures more accurate results for large-scale and shallow water areas; 3) taking into account a non-linear dispersion relation. Predictions using the extended wave model are carried out to study the feasibility of constructing the Ai Hua yacht port in Qingdao, China, with a comparison between two port layouts in design. Wave fields inside the port for different incident wave directions, water levels and return periods are simulated, and then two kinds of parameters are calculated to evaluate the wave conditions for the two layouts. Analyses show that Layout I is better than Layout II. Calculation results also show that the harbor will be calm for different wave directions under the design water level. On the contrary, the wave conditions do not wholly meet the requirements of a yacht port for ship berthing under the extreme water level. For safety consideration, the elevation of the breakwater might need to be properly increased to prevent wave overtopping under such water level. The extended numerical simulation model may provide an effective approach to computing wave heights in a harbor.

다방향 불규칙파가 투과성 잠제 주변의 3차원 파동장에 미치는 영향

This study proposes an improved 3-D model that includes a new non-reflected wave generation system for oblique incident and multi-directional random waves, which enables us to estimate the effect of the various wave-types on 3-D wave fields in a coastal area with permeable submerged breakwaters. Then, using the numerical results,the three-dimensional wave field characteristics around permeable submerged breakwaters are examined in cases of oblique incident and multi-directional random waves. Especially, the wave height, mean surface elevation and mean flow around the submerged breakwaters are discussed in relation to the variation of incident wave condition.