Head-on Waves Research Articles

EXPERIMENTAL AND NUMERICAL STUDY ON OBLIQUE WAVE-IN-DECK LOADS

Most studies on wave-in-deck loads focus on head-on wave impingement whereas wave-in-deck loads due to waves incident from oblique directions are rarely reported. Numerical simulations for oblique wave-in-deck loads were presented in Iwanowski et al. (2002), Brodtkorb (2008) and Chen et al. (2018). However, in these studies, only numerical validations were performed against either two-dimensional experiments or empirical formulations due to a lack of experimental results. In light of this, we present the experimental results for wave impacts on a solid deck model due to a transient focused wave group incident from oblique direction in this study. The oblique experimental data is compared with the head-on counterpart by Santo et al, (2020) to investigate the incident wave angle effect on wave-in-deck loads. Numerical simulations are carried out to reproduce both the head-on and oblique wave-in-deck experiments using a three-dimensional (3D) numerical wave tank (NWT), and flow field information is interrogated to derive physical insights into complex wave-deck interactions. The solid deck model is a representative of a typical 2nd generation North Sea topside structures commonly exposed to severe winter weather. The configuration is also applicable to coastal structures such as bridges, piers, jetties or docks.

Experimental and numerical study of wave-in-deck loads due to oblique transient wave groups

Wave-in-deck loads due to 45° oblique transient focus wave groups are investigated using model-scale experiments and computational fluid dynamics simulations with emphasis on comparing with head-on wave impacts for a solid cuboid deck model without and with an I-beam grillage beneath. After validation with experiments, numerical results are extended to consider wave-in-deck loads with 22.5° and 67.5° oblique wave directions. Generally, the head-on wave impacts cause larger longitudinal forces on the deck whereas the oblique cases result in larger downward vertical forces. For the deck with grillage case, Santo et al. (2020) and Wang et al. (2022) show that successive large spikes are observed in the force time series of head-on wave impact due to entrapped air-pocket effects in the grillage. However, here it is found that the large spikes are absent in the force time series for the oblique wave impacts and the patterns of forces are similar to the deck without grillage with rather small or no spikes in the force time series. Interrogation of the numerical flowfield reveals evidence that the asynchronous and less effective air entrapment in the grillage for the oblique cases are responsible for the difference. The maximum positive pressure on the underside of the deck is found to be much larger for the deck with grillage than without due to local slamming of jets formed in the grillage.

Study of Two Ships Approaching Process and Towing Motion under Wave Action

The rescue of ships in distress at sea relies mainly on rescue vessels, which includes the approaching process and the towing motion of the two ships. Ship rescue can be reduced to a two-ship problem, primarily involving the relative motion between ships during rescue. We established a mathematical model of ship motion based on the viscous fluid N-S equation, and the approaching process of two Wigley ships under waves was simulated in a two-dimensional plane. Then, according to three-dimensional potential flow theory, the coupled motion response model of the ships under six degrees of freedom was constructed, and calculation models of wind, waves, currents and other environmental disturbance factors were established to numerically calculate the towing motion. The results show that the upstream vessel has a lower heave motion amplitude and higher roll motion amplitude during the approaching process; A ratio of 1.5 times the width of the ship is the critical area where the motion of the two ships interacts with each other; For the berthing process, the faster the motion of the active vessel is, the lower the motion amplitude will be for both upstream and downstream vessels. When towing under rough sea conditions, changes in wave height and towing velocity have a large influence on the coupling effect of the towing system. When towing, head-on waves and low sea conditions are preferred, and the velocity should be sufficiently high to reduce the influence of cable self-weight on the towed ship. According to the simulations, the recommended velocity range is 3–5 m/s. Finally, a ship model scaling model was developed based on the similar quasi-Froude number of the ship model test, and the simulation results were verified by conducting parallel and towing tests of the model in a basin with a spherical wave-maker device.

The effects of oblique waves and currents on the loadings and performance of tidal turbines

Tidal energy exploitation is at an early deployment stage and costs need to be reduced to improve the long term economic viability of the sector. High costs of tidal turbines are, in part, the result of load uncertainties, which lead to the use of high factors of safety in the design to ensure survival. One of the most important causes of uncertainty is hydrodynamic loadings. To date, most of the scaled model experiments with horizontal axis turbines investigating this issue have been carried out with collinear wave and current directions. To the authors' knowledge, the work presented herein is the first experimental investigation of a horizontal axis turbine model subjected to combined oblique waves and current. Turbine performance and loading are measured for a 1:15 scale model tested in the FloWave circular, combined wave and current basin at the University of Edinburgh (UK). Three different flow directions were tested and each of them were also combined with regular waves in three different directions non-collinear with the flow. Fifteen physical quantities were measured including flow velocity, rotor and foundation loads and turbine speed. Characterisation of loads and turbine performance in those oblique current and wave conditions are presented. Waves affect means and standard deviation of rotor power and thrust, but off-axis waves are associated with lower thrust loads than head-on waves. Compared to current only, rotor torque and thrust standard deviations are higher in the presence of waves and almost twice as high when the wave crest is parallel to the rotor plan. The experimental data associated with this article can be downloaded from http://dx.doi.org/10.7488/ds/2360.

The power-capture of a nearshore, modular, flap-type wave energy converter in regular waves

Bottom-hinged, nearshore flap-type wave energy converters (WECs), have several advantages, such as high power conversion efficiency and survivability. They typically comprise a single flap spanning their full width. However, a potentially beneficial design change would be to split the flap into multiple modules, to make a ‘Modular Flap’. This could provide improvements, such as increased power-capture, reduced foundation loads and lower manufacturing and installation costs. Assessed in this work is the hydrodynamic power-capture of this device, based on physical modelling. Comparisons are made to an equivalent ‘Rigid Flap’. Tests are conducted in regular, head-on and off-angle waves. The simplest control strategy, of damping each module equally, is employed.The results show that, for head-on waves, the power increases towards the centre of the device, with the central modules generating 68% of the total power. Phase differences are also present. Consequently, the total power produced by the Modular Flap is, on average, 23% more smooth than that generated by the Rigid Flap.The Modular Flap has 3% and 1% lower average power-capture than the Rigid Flap in head-on and off-angle waves, respectively. The advantages of the modular concept may therefore be exploited without significantly compromising the power-capture of the flap-type WEC.

Development of a Combined Compact Difference Scheme to Simulate Soliton Collision in a Shallow Water Equation

AbstractIn this paper a three-step scheme is applied to solve the Camassa-Holm (CH) shallow water equation. The differential order of the CH equation has been reduced in order to facilitate development of numerical scheme in a comparatively smaller grid stencil. Here a three-point seventh-order spatially accurate upwinding combined compact difference (CCD) scheme is proposed to approximate the firstorder derivative term. We conduct modified equation analysis on the CCD scheme and eliminate the leading discretization error terms for accurately predicting unidirectional wave propagation. The Fourier analysis is carried out as well on the proposed numerical scheme to minimize the dispersive error. For preserving Hamiltonians in Camassa- Holm equation, a symplecticity conserving time integrator has been employed. The other main emphasis of the present study is the use of u–P–α formulation to get nondissipative CH solution for peakon-antipeakon and soliton-anticuspon head-on wave collision problems.

Wave pressure acting on a seawave slot-cone generator

Any kind of Wave Energy Converter (WEC) requires information on how optimize the device in terms of hydraulic performances and structural responses. This paper presents results on wave loading acting on an innovative caisson breakwater for electricity production. The Seawave Slot-Cone Generator (SSG) concept is based on the known principle of overtopping and storing the wave energy in several reservoirs placed one above the other. Using this method practically all waves, regardless of size and speed are captured for energy production. In the present SSG setup three reservoirs have been used. Comprehensive 2D and 3D hydraulic model tests were carried out at the Department of Civil Engineering, Aalborg University (Denmark) in the 3D deep water wave tank. The model scale used was 1:60 of the SSG prototype at the planned location of a pilot plant at the west coast of the Kvitsøy island (Stavanger, Norway). The analyses of hydraulic model tests have identified the main shapes assumed by wave surfaces at the breakwater and respective spatial and temporal pressure distributions. The influence of wave obliquity and multidirectionality is also described by loading reduction factors referred to the case of long-crested head-on wave attack. Pressure measurements were compared with the prediction method made for caisson breakwaters with sloping top. These results suggest to use the experimental data as design pressures since the design criteria of traditional maritime structures may be not satisfactory for designing innovative breakwater as SSG.

Structural stability of detached low crested breakwaters

The aim of the paper is to describe hydraulic stability of rock-armoured low-crested structures on the basis of new experimental tests and prototype observations. Rock armour stability results from earlier model tests under non-depth-limited long-crested head-on waves are reviewed. Results from new 2-D and 3-D model tests, carried out at Aalborg University, are presented. The tests were performed on detached low-crested breakwaters exposed to short-crested head-on and oblique waves, including depth-limited conditions. A formula that corresponds to initiation of hydraulic damage and allows determining armour stone size in shallow water conditions is given together with a rule of thumb for the required stone size in depth-limited design waves. Rock toe stability is discussed on the basis of prototype experience, hard bottom 2-D tests in depth-limited waves and an existing hydraulic stability formula. Toe damage predicted by the formula is in agreement with experimental results. In field sites, damage at the toe induced by scour or by sinking is observed and the volume of the berm is often insufficient to avoid regressive erosion of the armour layer. Stone sinking and settlement in selected sites, for which detailed information is available, are presented and discussed.

複雑な海底地形に設置された長大防波堤の波力平滑化特性

As the length of a caisson becomes long, the wave force per unit length becomes smaller because of the wave phase difference. In this study, we performed hydraulic model test on a long caisson placed on the complicated submarine topography model under various wave conditions in order to investigate the characteristics of wave reduction.It is found that the wave force on a long caisson placed on the complicated submarine topography is reduced significantly in the case of oblique waves. The reduction ratio for multi-directional random waves is smaller than that for uni-directional random waves due to directional spreading. In the case of head-on waves, wave force per unit length on the long caisson becomes smaller because of the dispersion of the wave height and the phase due to wave refraction.

Absorbing boundary condition on elliptic boundary for finite element analysis of water wave diffraction by large elongated bodies

AbstractIn a domain method of solution of exterior scalar wave equation, the radiation condition needs to be imposed on a truncation boundary of the modelling domain. The Bayliss, Gunzberger and Turkel (BGT) boundary dampers of first‐ and second‐orders, which require a circular cylindrical truncation boundary in the diffraction‐radiation problem of water waves, have been particularly successful in this task. However, for an elongated body, an elliptic cylindrical truncation boundary has the potential to reduce the modelling domain and hence the computational effort. Grote and Keller [On non‐reflecting boundary conditions. Journal of Computational Physics 1995; 122: 231–243] proposed extension of the first‐ and second‐order BGT dampers for the elliptic radiation boundary and used these conditions to the acoustic scattering by an elliptic scatterer using the finite difference method. In this paper, these conditions are implemented for the problem of diffraction of water waves using the finite element method. Also, it is shown that the proposed extension works well only for head‐on wave incidence. To remedy this, two new elliptic dampers are proposed, one for beam‐on incidence and the other for general wave incidence. The performance of all the three dampers is studied using a numerical example of diffraction by an elliptic cylinder. Copyright © 2001 John Wiley & Sons, Ltd.

Overtopping Formulas for Caisson Breakwaters with Nonbreaking 3D Waves

From the analysis of an extensive series of two-dimensional and three-dimensional hydraulic model tests on the overtopping response of various types of caisson breakwaters, general design formulas and graphs have been derived. Exponential relationships relate the mean discharge and the percentage of overtopping waves with the relative freeboard. The parametric influence of geometrical changes and of wave obliquity and multidirectionality is described by reduction factors referred to the case of simple vertical structure under long-crested head-on wave attack. Comparisons are made with the three-dimensional overtopping response of sloping structures. Overtopping volumes per wave have also been measured and their distribution fitted with a universal probability function. Even the effects of overtopping waves on pedestrians behind the crownwall were statistically evaluated to allow an upgrading of the existing criteria for the admissible rates over breakwaters.

Stone mobility and longshore transport at reshaping breakwaters

Physical model tests have been performed in two different wave flumes to analyse the threshold of stone movement and quantify the frequency and length of displacements due to head-on wave attacks at a reshaping breakwater. Data on stone movements were obtained from the observation of cumulative displacements at the end of each wave attack and from video records during the attack. Threshold conditions, frequency of movement and displacement length are expressed as function of a suitably modified stability number. A simple model is defined relating longshore transport due to oblique wave attack to stone mobility. The transport model is based on the assumption that movement statistics is affected by obliquity only through the appropriate mobility index and that stones move during up- and down-rush in the direction of incident and reflected waves. Without any calibration, results compare favourably with experimental data available in literature in the range of low mobility conditions where movement statistics was observed. A calibration is provided in order to obtain an accurate transport formula valid in a wide mobility range i.e. for reshaping breakwaters and up to gravel beaches.

Méthodes d'investigation sur modèles réduits des différents problèmes d'hydraulique côtière

This article gives a brief review of the possibilities and the range of applicability of the scale model as a means of hydraulic research into changes undergone by a sea coast. Considering only the action of waves on a sea shore, some of the conditions for its representation in correct similitude on the model are as follows:__ 1) Reproduction of the main aspects of wave propagation__i.e. refraction, diffraction, reflection__which requires an undistorted model; 2) Reproduction of the mode of wave generation, for waves from the open sea generally do not produce the same beach profiles as local wind waves; 3) Reproduction of the effect of waves on the beach material. It is very difficult to choose a suitable model material as Froude similitude is seldom achieved; not only the grain size of the material, but especially its density must be carefully determined if it is to show the same "potential transportability" as the prototype material. The model and prototype materials should, in theory, be in similitude with regard to the following properties:__ (i) Grain acceleration from rest and sinking velocity; (ii) Sediment discharge for a given wave size; (iii) Respective proportions of bed and suspended sediment loads. These conditions cannot generally be reconciled, except in very special cases where a very local effect is investigated to a comparatively large scale. The choice of a bed material and the corresponding model scale distortion and wave reproduction scales thus finally depends on the type of problem to be solved. This may also apply to the mode of wave generation. In view of this difficulty, an attempt has been made to classify such problems, as follows:__ Investigation of problems associated with sediment drift along a coast and changes in the shore line. The all-important requirement here is to reproduce the sediment drift as affected by wave obliquity, most of which takes place within the area between the breaking waves and the top edge of their wash. In this case, even though wind waves may sometimes be involved, paddle generating equipment may be adequate if rapidly adjustable for direction so as to enable the energy spectrum resulting from the various wave directions during the year to be reproduced. This type of representation provides a perfectly acceptable means of studying the development of a coastal spit, the silting-up of a harbour, methods of keeping a lagoon in open communication with the sea, etc. Though these models are usually slightly distorted and involve a certain amount of compromising, they can nevertheless be made to supply some very interesting indications. It is difficult, however, to use them for really accurate quantitative interpretation of the effects of the requisite structures and the determination of their dimensions. Investigation of the development of a beach cross-section and erosion due to head-on wave attack. This type of problem necessitates a more precise reproduction of wave action throughout the developing cross-section and, especially, of sediment drift out to sea. It is difficult to reproduce these effects with a paddle type generator, for the outward current along the sea bed associated with real-life wind waves is not reproduced On the model. Wind generating facilities may prove necessary in such cases; a 600 square meter tank featuring a set of thirty-four 2 H.P. fans has been built at SO.-GR. E.A.H. to investigate a protection scheme for a beach subjected to wind waves at various sea level conditions. The adjustment of such a model is obviously a very delicate matter; an essential prerequisite is the reproduction of developments observed in real life, with the waves and water levels which are likely to have caused them. The authors have found by experience that such effects can be very satisfactorily reproduced with such wind wave generating equipment, which also enables very fiat beaches to be obtained on the model with very little scale distortion. Conclusion. An experimental hydraulic model study can contribute some very interesting indications for problems associated with the effect of wind waves on coasts and beaches; such information provides very useful guide lines for coastal development and protection work, despite the difficulty of reproducing to a correct scale the effects of the various factors associated with wave type and propagation upon the shore. Though a model with slight scale distortion and conventional wave generating equipment is generally adequate to study the effects of oblique wave attack upon a sea shore, a study of shore erosion under practically head-on wave attack may, to be really accurate, also require means of simulating wind wave formation in order to reliably reproduce the action of such waves, or to produce the requisite "seaward" drift of the model shore material.