Short-crested Waves Research Articles

Interactions between swell and colinear wind short crested waves, following and opposing

When wind blows over a water surface during a swell, it generates short-crested, three-dimensional waves that interact with the underlying flow field through a mechanism that ultimately increases the average energy. In the present work, two test cases in which wind is flowing following and opposing a swell are analysed with experiments and are compared with wind–waves-only and swell-only cases. The analysis of the free surface fluctuation and of the flow field, with the three components of fluid velocity measured at the same time through a stereo particle image velocimetry system, leads to an accurate quantification of the energy distribution, of the structure of the oscillating, fluctuating (due to wind–waves) and turbulent kinetic energy, without assumptions on the structure of the flow. The findings demonstrate that the transverse dynamics is a pivotal factor in the transfer of energy in the near-free surface domain, and elucidate the energy transfer between wind–waves and swell. The results also confirm the reduction of oscillating kinetic energy of the swell in the presence of short wind–waves, a process interpreted with different possible mechanisms. There is evidence of the enhancement of wind action in the presence of swell compared to that in the case of wind–waves-only, confirming that energy transfer from the wind to the sea is enhanced when wind flows over a swell. Consequently, when the fetch is influenced by swells generated or propagated from different regions, and during multi-peak sea storms, wave generation models should account for this amplification.

Numerical analysis of coupling effect between sloshing and motion responses of a KCS in uni- and bi-directional waves

The seakeeping behaviour can be severely affected by the coupling between sloshing and ship motions in waves. The sloshing behaviour of liquid-loaded ships in bi-directional waves differs significantly from that in uni-directional waves. Given that ships operate in short-crested or multi-directional waves during their whole service period, it is significant to gain a deeper understanding of the effect of wave directionality on the coupling between sloshing and ship motions. In this study, a KRISO container ship (KCS) model with type-B liquefied natural gas (LNG) cargo tanks is adopted for coupling analysis. The 2D long-crested regular wave is adopted as an uni-directional wave, and three dimensional (3-D) cross wave is adopted as a bi-directional wave. The computational fluid dynamics (CFD) method is applied for the sloshing and seakeeping simulation of the ship model in different wave fields. The differences in wave elevation, sloshing forces, and coupling effects between ship motions and sloshing are studied in these two wave fields by adjusting control parameters such as ship heading angle and filling ratio. The comparative results indicate that sloshing behaviour and coupled motion responses in cross waves should be paid enough attention during ship design and evaluation.

Numerical investigation of the effects of short-crested irregular waves on the performance of a floating power capture platform

This paper presents a novel power capture platform concept consisting of a semi-submersible platform and multiple point-absorber wave energy converters (WECs). The primary objective of the current study is to investigate the dynamic behavior of the power capture platform under short-crested irregular wave conditions. A spreading function is used to modify the JONSWAP spectrum into a wave spectrum that accounts for both frequency and direction. To ensure the reliability of the numerical analysis, three-dimensional potential flow theory and boundary element method (BEM) are utilized to perform mesh convergence analysis and hydrodynamic validation of the platform and WEC models. Time-domain simulations are conducted to evaluate the effects of wave directionality on the platform motion, mooring line tension, and power absorption of the WEC array. In addition, three models, “single WEC”, “WEC array” and “fixed power capture platform” are defined. The influence of hydrodynamic interactions and platform motion are predicted by comparing the power absorption of individual WEC, WEC row, and WEC array among these models. The results show that the effects of wave directionality on the performance of the floating power capture platform cannot be ignored. The findings of this study may provide some insights into the design of power capture platforms. Meanwhile, it is recommended to determine the wave characteristics of the target operational area in advance, in order to find out the optimal design for system stability and power absorption.

Interaction of short-crested waves with cylinder and concentric segmented arc breakwaters

Using the outer breakwater of Palm Jumeirah in Dubai as a physical geometric model, the diffraction problem of short-crested waves interacting with concentric segmented arc structures was theoretically investigated using linear water wave theory. In this study, the watershed was partitioned into two regions, and a unique coordinate system was established to describe the velocity potential function within each region. The interface between the two regions connects the velocity potentials across them using the matching eigenfunction expansion technique. By accounting for the boundary conditions, the integral equation was streamlined into a series of algebraic equations, which were subsequently resolved to determine an unidentified function. The precision of the model was validated through a comparison with findings from the literature. Numerical investigations have elucidated the correlation between changes in wave force, cylinder run-up, and parameters such as the spacing between adjacent arcs, opening angle, and porous coefficient. The numerical results indicated that the impermeable segmented arcs structure provides better protection against short-crested and plane waves, whereas the permeable segmented arc structure provides better protection against standing waves. Interestingly, for a segmented three-arc structure, when the segments are moderately spaced, the protection of the interior region is superior to that of an unsegmented arc structure.

Soliton groups and extreme wave occurrence in simulated directional sea waves

The evolution of nonlinear wave groups that can be associated with long-lived soliton-type structures is analyzed, based on the data of numerical simulation of irregular deep-water gravity waves with spectra typical to the ocean and different directional spreading. A procedure of the windowed Inverse Scattering Transform, which reveals wave sequences related to envelope solitons of the nonlinear Schrödinger equation, is proposed and applied to the simulated two-dimensional surfaces. The soliton content of waves with different directional spreading is studied in order to estimate its dynamical role, including characteristic lifetimes. Statistical features of the solitonic part of the water surface are analyzed and compared with the wave field on average. It is shown that intense wave patterns that persist for tens of wave periods can emerge in stochastic fields of relatively long-crested waves. They correspond to regions of locally enhanced on average waves with reduced kurtosis. This eventually leads to realization of locally extreme wave conditions compared to the general background. Although intense soliton-like groups may be detected in short-crested irregular waves as well, they possess much shorter lateral sizes, quickly disperse, and do not influence the local statistical wave properties.

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.

Experimental reproduction of inhomogeneous fjord waves

Waves in coastal areas and fjords can present inhomogeneities that affect the responses of very large floating structures. However, spatial inhomogeneities of waves are usually not included in model testing. In this paper, the feasibility of generating inhomogeneous wave conditions in an Ocean basin is investigated. For that purpose, a fast linear numerical model of a basin of constant depth is applied, and an optimization method is presented, that allows to find the control signal for the multiflap wavemaker. Comparisons with experiments in SINTEF’s Ocean basin demonstrate the validity of the method for generating simple monochromatic synthetic waves, as well as short-crested irregular waves representing realistic conditions in Sulafjorden.

On the steady-state interfacial waves with two-dimensional type-A double exact resonance

Steady-state interfacial waves under two-dimensional (2D) type-A exact triad resonance and other related resonances are researched in a two-layer liquid model with a free surface in contact with air. Five groups (groups 1–5) of convergent series solutions are achieved via the homotopy analysis method. It is found that the phenomenon of double exact resonance could exist in periodic interfacial waves if physical parameters correspond to the intersection of two exact resonance curves. The double exact resonance considered here contains a 2D type-A triad resonance and an other resonance. Under the 2D type-A exact triad resonance, the other resonant triad could obviously enlarge or reduce the wave amplitudes and energy proportions of primary and resonant components. Nevertheless, other resonant quartet, quintet, sextet, and septet all produce no influence on interfacial waves when the 2D type-A exact triad resonance occurs. The above-mentioned results indicate that in the neighborhood of the double exact triad resonance, small perturbations of wave vector of a primary component can cause huge changes on wave profiles of free surface and interface, wave amplitude spectrum, and energy distribution of internal waves in real ocean. In addition, the closer the interfacial waves are to the double exact triad resonance, the more possible energy combinations exist in the wave system, and the greater the number of steady-state interfacial wave solutions. All of this should deepen our understanding of nonlinear resonance interactions in short-crested internal waves.

A numerical study of added resistance performance and hydrodynamics of KCS hull in oblique regular waves and estimation of resistance in short-crested irregular waves through spectral method

Research on multidirectional waves is increasing as studies on added resistance advance. In this study, the added resistance of the multidirectional regular waves of the KCS hull was estimated by numerical analysis. The direction of the grid was changed according to the heading angle to consider waves in multiple directions. In addition, the method in which the entire domain moved along the movement of the hull was used without using the overset method to minimize the numerical errors. The added resistance and motion RAOs for each angle and the flow characteristics were compared to support the results. For fluid dynamics, time-averaged stern dynamics pressure, boundary layer, and nominal wake for each heading angle were compared, and differences compared to calm water were also reviewed. Based on the bow quartering sea condition analysis results, the added resistance in long-crested and short-crested irregular wave conditions was estimated using the spectral method. The JONSWAP spectrum was used as the target wave spectrum, and the cos-power type was considered the directional spreading function.

Short crested wave–current interaction with a cylinder and two concentric asymmetric arc-shaped walls

The diffraction problem of the interaction of short-crested incident waves and currents with a combined structure is studied. The combined structure consists of two concentric asymmetric exterior porous arc-shaped cylinders and an impermeable interior cylinder. A variable separation and an eigenfunction expansion method are used to derive the velocity potential for the entire fluid domain. The accuracy of the current model is verified by comparing the results of this study with published calculations. Numerical results reveal the variation of wave force and run-up on the combined structure with current speed, opening angle, and the locations of the two arc exterior cylinders. Moreover, the specific parameter conditions under which the resonance of the wave and structure may occur are analyzed, and the resonance phenomenon may be enhanced owing to the presence of a uniform current. Furthermore, the hydrodynamic performance of segmented arcs in the limiting case is examined. The results show that the segmented arc is not effective in protecting the interior structure when the wavelength is short. The findings of this study are anticipated to provide theoretical direction for the design of nearshore architecture.

On the probability of down-crossing and up-crossing rogue waves

By means of the direct numerical simulation of directional waves on the surface of deep water, it is shown that extreme waves can exhibit such asymmetry that the occurrence of deeper troughs is several times more likely on the wave rear slopes. This effect becomes most pronounced in the case of steep short-crested waves. It is not related to the Benjamin–Feir instability but is a result of complex contribution from nonlinear combination harmonics, mainly cubic in nonlinearity. The discovered asymmetry can lead to remarkably different estimates of the rogue wave probability based on either down- or up-zero-crossing methods for individual wave selection, commonly used in the oceanography.

Prediction of wave-induced ship motions based on integrated neural network system and spatiotemporal wave-field data

This study introduces an artificial neural network system for ship motion prediction in seaways. To consider the physical characteristics of wave-induced ship motions, neural networks based on a Long Short-Term Memory (LSTM) encoder and decoder, and a convolutional neural network (CNN) are integrated. The LSTM encoder computes the state vector representing the memory effects of motion-induced radiated waves based on past motion records, that is, a sequence-to-one model. In the LSTM decoder, the motion time series is predicted using the encoded initial state vector and foreseen information on the ocean wave field around a vessel, that is, a sequence-to-sequence model. In addition, a CNN is adopted to compress the wave data into a vector sequence. Particularly, the present CNN uses spatiotemporal wave-field data, not a wave signal at single location. To validate the proposed system, a database for training the integrated system was constructed using a physics-based seakeeping program for various sea states. By applying the trained model, deterministic predictions were performed for a new ocean environment, and the accuracy and reliability of the testing results are investigated according to the input data and neural network structures. From the simulation results, it was confirmed that the present encoder–decoder system can conduct ship motion forecasting by effectively considering the motion memory effects and wave excitations as in the ship hydrodynamic model. In addition, excitations and resulting motion responses by short-crested waves can be considered through CNN-based wave-field data processing. Finally, the present machine-learning model also showed the capability of extracting ship operation information (maneuvering quantities) from the given wave-field data.

STABILITY OF RUBBLE MOUND STRUCTURES UNDER OBLIQUE WAVE ATTACK

Stability formulae for armour layers of rubble mound breakwaters are generally developed for perpendicular wave attack and do not include effects of oblique waves. Waves usually attack breakwater obliquely as the sea wave is three dimensional. Several studies have been performed to investigate the effect of wave angle (beta) on the armor stability. Galland (1994), Yu et al. (2002), Wolters and Van Gent (2010) and van Gent (2014) performed laboratory experiments to consider effects of oblique waves on the stability of armour layers. They performed tests with long-crested and/or short-crested waves on rock and concrete armours. The aim of this study is to find an appropriate and compatible reduction factor for EBV stability formulae.

Interfacial capillary–gravity short-crested waves

Interfacial capillary–gravity short-crested waves

Nonlinear statistical characteristics of the multi-directional waves with equivalent energy

Directional distribution is believed to have a significant impact on the statistical characteristics in multi-directional sea states. In real sea states, short-crested waves are discrete not only in frequency but also in direction. For the former one, they are well explained in unidirectional mode, but for the latter one, they are not. In this paper, the kurtosis of short-crested waves with equivalent energy is first discussed. Unimodal-spectrum-multi-direction sea states and bimodal-spectrum-multi-direction sea states are simulated for a long time in a numerical wave basin based on the high-order spectral method. In the equivalent sea-swell sea state, the spatial evolution of kurtosis becomes more inhomogeneous, along with the maximum value of kurtosis being larger and the area where the maximum value occurs wider in the configuration with a crossing angle β = 40° than that with β = 0°, while little variations in swell-dominated and wind-sea-dominated states. A positive linear correlation between wavelet group steepness and kurtosis is obtained in a unimodal sea state, but not applied to a crossing sea state characterized by a bimodal spectrum. The exceedance probability of wave height and wave crest distribution at maximum kurtosis is also given. These findings can help predict the probability of extreme waves occurring, guiding the selection of ocean engineering sites to avoid extreme configurations.

Remotely sensed short-crested breaking waves in a laboratory directional wave basin

Remotely sensed short-crested breaking waves in a laboratory directional wave basin

Wave-by-wave prediction for spread seas using a machine learning model with physical understanding

Accurate surface wave predictions have the potential to greatly enhance the safety and efficiency of many offshore applications, such as active control of wave energy converters and floating wind turbines. However, real-time wave prediction becomes increasingly challenging when large directional spreading is considered. To address this challenge, the present study introduces a machine learning model that utilizes an Artificial Neural Network (ANN) for predicting moderate directional spreading waves. Linear, short-crested wave time histories are synthesized numerically to assess the capability of our machine learning model. The ANN model demonstrates better prediction capability than a recently developed theoretical scheme (Hlophe et al., 2022), extending the prediction horizon by approximately one peak period into the future. Further, a quantile loss function is introduced to quantify the uncertainty, enhancing the practical value of the developed model in decision-making processes and engineering applications, such as the active control of offshore renewable energy systems.

Nearshore Observations and Modeling: Synergy for Coastal Flooding Prediction

Coastal inundation has recently started to require significant attention worldwide. The increasing frequency and intensity of extreme events (sea storms, tsunami waves) are highly stressing coastal environments by endangering a large number of residential areas, ecosystems, and tourist facilities, and also leading to potential environmental risks. Predicting such events and the generated coastal flooding is thus of paramount importance and can be accomplished by exploiting the potential of different tools. An example is the combination of remote sensors, like marine radars, with numerical models. Specifically, while instruments like X-band radars are able to precisely reconstruct both wave field and bathymetry up to some kilometers off the coast, wave-resolving Boussinesq-type models can reproduce the wave propagation in the nearshore area and the consequent coastal flooding. Hence, starting from baseline simulations of wave propagation and the conversion of water elevation results into radar images, the present work illustrates the reconstruction of coastal data (wave field and seabed depth) using a specifically suited data processing method, named the “Local Method”, and the use of such coastal data to run numerical simulations of coastal inundation in different scenarios. Such scenarios were built using two different European beaches, i.e., Senigallia (Italy) and Oostende (Belgium), and three different directional spreading values to evaluate the performances in cases of either long- or short-crested waves. Both baseline and inundation simulations were run using the FUNWAVE-TVD solver. The overall validation of the methodology, in terms of maximum inundation, shows its good performance, especially in cases of short-crested wind waves. Furthermore, the application on Oostende Beach demonstrates that the present methodology might work using only open-access tools, providing an easy investigation of coastal inundation and potential low-cost integration into early warning systems.

Analysis of FPSO Motion Response under Different Wave Spectra

A variety of floating structures at sea play a vital role in the exploitation and utilization of marine resources. The study about interactions between waves and structures is necessary for the impact of the harsh marine environment on the motion and service life of structures. Currently, most studies about the seakeeping of structures are based on simplified regular waves. Because the regular waves do not truly restore the actual wave conditions at sea, the simulation of irregular waves has great practical importance to the study of interactions between waves and structures. Based on the potential flow theory and high-order boundary element method (HOBEM), a Fortran code is developed in this paper and named as SWBI (Solver for Wave–Body Interactions). This program consists of the following two parts: a time–domain numerical model about interactions between waves and 3D structures is based on weakly nonlinear method, and a numerical model about simulation of the nonlinear regular waves, the long-crested irregular waves, and the short-crested irregular waves. This Fortran code is used to simulate the motion of Floating Production Storage and Offloading (FPSO) under three different ocean wave spectra (including ITTC two-parameters spectrum, JONSWAP spectrum and the most likely spectral form of Ochi-Hubble) and found that: To a certain extent, the difference in the motion of FPSO under different wave spectra have a connection with different type of wave, sea conditions and incident angle. The difference in roll of FPSO is quite significant in short-crested irregular waves. The range of FPOS’s roll under the JONSWAP spectrum is the largest when the incident angle is 30°, and range of FPOS’s roll under the most likely spectral form of Ochi-Hubble is the largest when the incident angle is 90°.

Long-term analysis of wave-induced loads using High Order Spectral Method and direct sampling of extreme wave events

An approach for running long-term analysis of the wave environment and associated wave-induced structural loads, which includes effects of nonlinearity, irregularity and short crestedness of ocean waves is presented. The suggested approach combines a novel event-sampling technique with the efficient nonlinear wave solver High Order Spectral Method (HOSM) to represent the long-term wave environment by a large, yet computationally feasible, number of short-crested wave events which are simulated in HOSM. For the present study, HOSM is enhanced with a wave-breaking model, which improves the description of steep sea states in which wave breaking plays a role.Extensive validation of HOSM and the implemented wave-breaking model is carried out through comparison with model-test results for wave-crest statistics in long- and short-crested sea states and through direct comparison with CFD simulations.The proposed methodology is demonstrated on a case study considering a 106 years long-term analysis of wave crests and wave-in-deck loads, using a simplified load model to estimate drag loads on a deck structure.