Distribution of energy in propagation for ocean extreme wave generation in hydrodynamics laboratory

An accurate description of extreme waves is necessary in order to estimate maximum wave forces on offshore structures. On several occasions freak waves have been observed in the past, some causing severe damage. In order to model such extreme wave conditions with a computational fluid dynamics (CFD) model, emphasize needs to be put on the wave generation. One possibility is to use focused waves of first or second order based on irregular sea state wave spectra. For focused waves, the wave phase is chosen, so that the waves focus in a predetermined location at a specified time. Numerical tests have shown, that generating extreme waves based on this method is somewhat limited. The individual wave components are steep enough, that they start to break before the focus location. In the current paper, transient wave packets are used for extreme wave generation. This way, extreme waves can be generated that are higher, but only break at the concentration point. The transient wave packets method is implemented in the open-source CFD software REEF3D. This model uses the level set method for interface capturing. For the hydrodynamics, the Navier-Stokes equations are solved in three dimensions. The code employs a staggered Cartesian mesh, ensuring tight pressure-velocity coupling. Complex geometries are handled with a ghost cell immersed boundary method. High-performance computing is enabled through domain decomposition based parallelization. Convection discretization of the different flow variables is performed with the fifth-order WENO (weighted essentially non-oscillatory) scheme. For the explicit time treatment a third-order Runge-Kutta scheme is selected. In order to validate the extreme wave generation, numerical tests in an empty wave tank are performed and compared with experimental data. Then, the extreme wave breaking on a vertical circular cylinder is investigated.

The aim of this study is to try to establish new criteria for the design of offshore structures against extreme forces caused by breaking waves. The objective is to study shock forces and drag and inertia wave forces by means of several series of laboratory experiments and extensive field measurements. Ina series of laboratory experiments dispersion properties of water waves are used to generate a non-steady situation where one wave train overtakes another resulting in-the generation of an extreme wave. Collisions between wave solutions are studied in detail qualitatively and quantitatively, and results are obtained for characteristic wave properties: form, attenuation, dispersion, initiation and type of breaking, total pressure head and shock pressures. Results are also included for cases where currents are superimposed upon the mechanism for the generation of extreme waves. This deterministic approach in the laboratory will later be followed by extensive field measurements on a concrete gravity platform in the North Sea. Shock pressures near mean water level together with spectral and directional wave properties will be recorded in the field. The laboratory experiments showed that three distinct types of breaking waves could be generated by wave-wave interaction in deep water, namely plunging breakers, deep water bores and spilling breakers. Field data on extreme waves obtained from wave rider buoys was analysed with the zero downcross method which provided a wave height parameter relevant to the evaluation both of shock pressures and of the operation and stability of smaller vessels. Crest front steepness of the waves was used in the analysis as the total wave steepness s = H/L is not sufficient for asymmetric waves. The magnitude of shock pressures depends on the type and the wave form of the breaking waves. INTRODUCTION One of the main subjects of importance in marine technology is wave action. Wave action does not only consist of a very regular symmetric and steady design wave passing a fixed or floating structure. For an offshore engineer wave action should also include impacts against structures from very asymmetric non-steady extreme waves and breaking waves. The generation of extreme waves and breaking waves in deep water is therefore of practical importance and research efforts should be directed into this field for three reasons.The breaking of waves is the principal loss mechanism regulating the growth of the sea state toward spectral equilibrium under steady winds. (PHILLIPS 1966)Breaking waves are the most efficient mechanism for transfer of momentum from wind to mean surface flow in the form of ocean currents. (LONGUET-HIGGINS 1969)In advanced sea states breaking waves exert by far the largest individual loads on floating and fixed structures with all, the following implications both for design and operation.

Research on extreme wave generation is one intensive research on water wave study because the fact that the occurrence of this wave in the ocean can cause serious damage to the ships and offshore structures. One method to be used to generate the wave is self-correcting. This method controls the signal on the wavemakers in a wave tank. Some studies also consider the nonlinear wave generation in a wave tank by using numerical approach. Study on wave generation is essential in the effectiveness and efficiency of offshore structure model testing before it can be operated in the ocean. Generally, there are two types of wavemakers implemented in the hydrodynamic laboratory, piston-type and flap-type. The flap-type is preferred to conduct a testing to a ship in deep water. Single flap wavemaker has been explained in many studies yet snake-type wavemaker (has more than one flap) is still a case needed to be examined. Hence, the formulation in controlling the wavemaker need to be precisely analyzed such that the given input can generate the desired wave in the space-limited wave tank. By applying the same analogy and methodhology as the previous study, this article represents multi-directional wave generation by implementing snake-type wavemakers.

On several occasions, freak waves have been observed in the past, some causing severe damage. In order to model such extreme wave conditions, one possibility is to use focused waves of first- or second-order based on irregular sea-state wave spectra. The wave phase is chosen such that the waves focus at a predetermined location and time, but the individual wave components become steep and start breaking before the focus location for large amplitudes. In this study, transient wave packets are used for extreme wave generation. Extreme waves are generated that are higher and only break at the concentration point using the transient wave packets method implemented in the open-source CFD model REEF3D. Model validation is performed by comparison to experimental results. The generation of wave packets with an 8.3 times shorter focus distance is investigated and the wave is replicated in a shorter domain with a 9% higher crest. The method is further used to generate a steepness induced-breaking wave and calculation of extreme wave forces on an offshore structure is demonstrated.

Numerical study on wave attenuation of extreme waves by emergent rigid vegetation patch

Extreme wave phenomena in down-stream running modulated waves

Little is known about wave forces caused by extreme breaking waves in deep water. This study presents certain results from simulation of the kinematics of plunging breakers in deep water obtained both from carefully controlled laboratory experiments and from numerical simulation. In the experiments extreme waves are generated in three ways:The dispersion properties of gravity waves are used to generate a transient situation in which the energy of the individual waves in a wave train concentrates towards a specified point in time and space, resulting in one extreme wave;Very steep Stokes waves of finite amplitude are forced to break at a selected point in deep water due to superposition of a subharmonic disturbance;Very steep Stokes waves are forced to break at a selected point due to superposition of' a superharmonic disturbance. In the numerical model, the development of the (breaking) wave profile, the particle velocities and the accelerations within the wave are simulated. We exact free-surface conditions. are satisfied, and good results are achieved up to the point where the overhanging crest hits the wave front. Comparison of the plunging breakers generated in the wave flume and calculated numerically, shows good agreement with respect to the wave geometry. The measured and calculated velocities also agree well at depths larger than approximately one wave amplitude below the mean water level. In the wave crest near the plunging jet, the measured velocities are, however, 1.5 times as large as the calculated velocities. This may be due to the difference in the method of generating the plunging breakers in the two cases. Experiments so far have now confirmed that transient, near breaking and breaking waves attain velocities up to 2.8 times the first order phase velocity. The results may be applied to the operation and evaluation of stability of ships under severe sea conditions. Further, they provide the basis for the estimation of wave drag and inertia forces from extreme breaking waves in deep water with many applications for the design and safety of offshore structures. INTRODUCTION In order to evaluate safety at sea, a basic need is a prediction of the characteristics of extreme sea states. There is an extensive literature on the subject of the' mysterious disappearances of ships, both large and small. A high percentage of these mysteries can be solved by even a cursory study of so-called "freak waves" (a freak being "capricious change"), which are more correctly termed episodic waves. By definition an episode is a recurring event, and so it is with huge waves on the continental shelves. Episodic waves occur in virtually all such areas during certain predictable times of the year. The origin of episodic waves is not fully understood. It is believed that a shoaling mechanism, unique to a certain geographic location as well as a particular random phase relationship between waves, can account for the phenomenon.

On the extreme value statistics of spatio-temporal maximum sea waves under cyclone winds

Safety of shipping is an ever growing concern. In a summary, Faulkner investigated the causes of shipping casualties (2002, “Shipping Safety: A Matter of Concern,” Ingenia, The Royal Academy of Engineering, Marine Matters, pp. 13–20) and concluded that the numbers of unexplained accidents are far too high in comparison to other means of transport. From various sources, including insurers data over 30% of the casualties are due to bad weather (a fact that ships should be able to cope with) and a further 25% remain completely unexplained. The European project MaxWave aimed at investigating ship and platform accidents due to severe weather conditions using different radars and in situ sensors and at suggesting improved design and new safety measures. Heavy sea states and severe weather conditions have caused the loss of more than 200 large cargo vessels within the 20years between 1981 and 2000 (Table 1 in Faulkner). In many cases, single “rogue waves” of abnormal height as well as groups of extreme waves have been reported by crew members of such ships. The European Project MaxWave deals with both theoretical aspects of extreme waves and new techniques to observe these waves using different remote sensing techniques. The final goal is to improve the understanding of the physical processes responsible for the generation of extreme waves and to identify geophysical conditions in which such waves are most likely to occur. Two-dimensional sea surface elevation fields are derived from marine radar and space borne synthetic aperture radar data. Individual wave parameters such as maximum to significant wave height ratios and wave steepness, are derived from the sea surface topography. Several ship and offshore platform accidents are analyzed and the impact on ship and offshore design is discussed. Tank experiments are performed to test the impact of designed extreme waves on ships and offshore structures. This article gives an overview of the different work packages on observation of rogue waves, explanations, and consequences for design.

Wave crest height and steepness are crucial parameters for the design of ships and offshore structures. For irregular sea states, they are commonly predicted by using linear wave theory and a Eulerian description of the fluid motion. This theory only applies when the wave steepness is small and it fails to capture extreme wave events. Such linear solutions can also be extended by including second-order terms in order to provide more realistic wave properties. The paper describes a model for irregular long-crested waves that is based on a modified linear solution derived from a Lagrangian description of the fluid, i.e. by considering the motion of individual fluid particles. Lagrangian solutions have the advantage of showing realistic wave profiles with sharp crests and broad troughs already at the first order, whereas these features only appear at the second order when using the Eulerian approach. Still, a severe drawback with the former is that the mass conservation is not fulfilled exactly. The aim of the modification in the present Lagrangian model is to ensure that the mass conservation is always fulfilled in the solution. This is done by using the second-order residual in the continuity equation to lift up the fluid particles vertically. Comparative investigations of wave properties such as the crest height and the wave steepness are further carried out by making use of both numerical case studies and wave tank recordings. The wave models used in the comparisons include linear and second-order Eulerian solutions as well as the modified linear Lagrangian one.

The dynamics of surface wave propagation based on the Benjamin Bona Mahony equation

Rogue waves are extreme waves in the ocean that appear from nowhere and disappear without a trace. They are usually modelled by the nonlinear Schrödinger equation (NLS), which describes nonlinear phenomena such as modulational instability and solitons on finite backgrounds. In this study, the periodic nonlinear Fourier transform (NFT) for the NLS equation is applied to simulate ocean surface waves in deep water. The temporal and spatial structures of surface waves are obtained by evolving JONSWAP time series using the NLS equation. Several parameters extracted from the NFT spectra of the initial time series are investigated as predictors for the maximum wave height during evolution. We investigate several parameters from the literature, and find that with suitably optimized coefficients, a NFT-based parameter based on the largest unstable mode has a good correlation with the overall maximum wave amplitude. This new spectral criterion can contribute to rogue wave forecasting under extreme sea states.

Extreme waves can lead to damage to floating offshore structures as a result of airgap problems, greenwater on the deck or slamming to the hull. As the physics of these problems are different, there is no single way of identifying and characterizing extreme waves. As part of the investigations into the effect of extreme waves on deepwater floating structures, this paper focuses on the challenges of the numerical prediction of platform response due to extreme waves. This will be done by using an improved Volume Of Fluid (iVOF) method. Two case studies are presented, which both required specific extensions of the methodology. First green water simulations on a FPSO are discussed, requiring the coupling of a linear diffraction code to the iVOF method as part of a domain decomposition. Second the dynamic response of a TLP to an extreme wave is studied, requiring the integrated analysis of the wave loading and platform response. Introduction Hurricanes Ivan, Katrina and Rita in the Gulf of Mexico showed the importance of extreme waves for all types of offshore structures [1-5]. Extreme waves can lead to damage to floating offshore structures as a result of airgap problems, greenwater on the deck or slamming to the hull. As the physics of these problems are different, there is no single way of identifying and characterizing extreme waves: - For airgap problems, the crest ampltidue of the waves is the most important aspect. Therefore, it is important to know the ratio Ac/Hs between Crest Amplitude (Ac) and Significant wave height (Hs). In [6] the detailed analysis of an observed extreme wave in a model basin is described. It was shown that even in a wave with moderate steepness (Hs=11.9 m, Tp=15.3 s), generated with a random phase model, extreme wave crests can be observed. The measured wave had a Ac/Hs ratio of 1.59. As a pilot study into the understanding of the occurrence of this type of extreme waves, [6] describes the spatial development of this wave in the basin, see Figure 1. Figure 1: Spatial development of a wave in a model basin (from [6]) (Available in full paper) It should be noted ofcourse that even for fixed platforms the crest amplitude is not the only factor, the structure itself can clearly enhance the local wave elevation [7]. - For floating structures such as TLPs, Semis and Spars the wave loading and response is even more complex, as was shown in recent tests on the Snorre TLP [8]. The dynamic response of the platform to the wave impact can be the main factor in the survivability of the platform. Figure 2: Airgap tests on the Snorre TLP (from [8]) (available in full paper) In [8] the important observation was made that extreme wave and airgap problems belong to the group of (what was called) ‘badly behaved’ problems. A ‘badly behaved’ problem is a problem with a step or discontinuity in the response. For a fixed platform or TLP it can for instance occur that the deck is not hit in the 100 year wave as the maximum wave crest just passes below the deck.

Extreme waves are an important factor in coastal structures both offshore structures and onshore structure design. However, due to the difficulty of measuring ocean waves, many areas still do not have measured wave height data. Data processing is required to transform the measured wind data into wind-wave value in order to solve this issue. This study aims to analyze extreme waves based on wind data from BMKG Panjang and BMKG Radin Inten II stations. For analysis of determination of extreme waves can be done by using Fisher Tippet Type I (Gumbel) and Weibull methods. The result show that Weibull method gives the higher value than Gumbel method, with the maximum percentage of 43.04% at the 2-year return period.

An important question in the context of rogue waves is whether the statistical properties of individual waves, and in particular the probability of extreme and rogue waves, can be linked to the properties of the underlying wave spectrum of the relevant sea state. It has been suggested that a narrow wave spectrum (in frequency or direction) combined with a large wave steepness may lead to increased occurrence of extreme waves. Parameters based on the ratio of the wave steepness to the spectral band-widths have therefore been suggested as indicators of increased probability of extreme waves. However, for realistic ocean conditions the success of such parameters seems to be questionable. In this paper, we investigate relations between short-time wave statistics and wave spectral properties by using machine learning methods that can take a much wider range of spectral properties, or even the entire directional wave spectrum, into account. Numerical simulations with a nonlinear wave model that provides phase-resolved wave information are combined with wave spectra from a spectral wave model. Machine learning methods are then employed to investigate how well the wave statistics can be predicted from knowledge about the wave spectrum. The results are discussed in the context of existing parameters suggested as indicators of rogue waves, as well as with respect to potential warning against sea states in which extreme waves are expected to occur, based on wave-forecast from spectral wave models.