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The peak to trough distributions of nonlinear high sea waves in bimodal sea states in deep water are investigated. The statistical distribution of wave height is first analyzed by considering the Boccotti's expression, where the parameters of the distribution are calculated for some bimodal spectra of sea states recorded in the Atlantic Ocean. The nonlinear crest and trough distributions are then obtained, particularizing for two peaked spectra the second-order Fedele and Arena expression, which depends on two parameters. The results have been finally validated by means of Monte Carlo simulations of second-order random waves with bimodal spectra. [DOI: 10.1115/1.3160657]

Floating systems, such as ships, barges, or semisubmersibles, show a dynamical behavior, which is determined by their internal structure and the operating conditions caused by external forces e.g., due to waves and wind. Due to the complexity of the system, which commonly includes coupling of multiple components or nonlinear restoring forces, the response can exhibit inherently nonlinear characteristics. In this paper different models of floating systems are considered. For the idealized case of purely harmonic forcing they all show nonlinear behavior such as subharmonic motion or different steady-state responses at constant operating conditions. The introduction of random disturbances leads to deviations from the idealized case, which may change the overall response significantly. Advantages and limitations of the different mathematical models and the applied numerical techniques are discussed. [DOI: 10.1115/1.3160649]

This paper considers the effect of wave age on wind gust spectra over wind waves. Here, two wind gust spectra based on maritime data are used to serve the purpose of demonstrating the effect of wave age; the spectra according to Wills et al. (1986 'Offshore Mean Wind Profile,' Department of Energy, Offshore Technical Report No. OTH86226) and Ochi and Shin (1988, 'Wind Turbulent Spectra for Design Considerations of Offshore Structures,' Proceedings of the 20th Offshore Technology Conference, Houston, TX, Paper No. 5736, pp. 461-467). The effect of wave age is taken into account by using the Volkov (2001, 'The Dependence on Wave Age,' in Wind Stress Over the Ocean, Cambridge University Press, Cambridge, UK, pp. 206-217) sea surface roughness formula. The wave age independent Charnock (1955, 'Wind Stress on a Water Surface,' Q. J. R. Meteorol. Soc., 81, pp. 639-640) sea surface roughness is used as a reference. The results are valid for wind waves in local equilibrium with steady wind in laterally homogeneous flow. An example of results demonstrates a clear effect of wave age on the wind gust spectra; also, distinct differences between the two spectra for a given wave age are demonstrated. Finally, an example of application is provided, demonstrating clear effects of the two spectra and the sea surface roughness on slowly varying surge motion of a marine structure due to wind gust. [DOI: 10.1115/1.3124130] Keywords: dynamic wind, wind gust spectra, sea surface roughness, wave age, wind generated ocean waves, slowly varying surge motion

The Gaussian linear wave model which has been successfully used in ocean engineering for more than half a century, is well understood, and there exist both exact theory and efficient numerical algorithms for calculation of the statistical distribution of wave characteristics. It is well suited for moderate seastates and deep water conditions. One drawback, however, is its lack of realism under extreme or shallow water conditions, in particular, its symmetry. It produces waves, which are stochastically symmetric, both in the vertical and in the horizontal direction. From that point of view, the Lagrangian wave model, which describes the horizontal and vertical movements of individual water particles, is more realistic. Its stochastic properties are much less known and have not been studied until quite recently. This paper presents a version of the first order stochastic Lagrange model that is able to generate irregular waves with both crest-trough and front-back asymmetries. [DOI: 10.1115/1.3124134]

An approach for calculating turbulent flows in a wave-current boundary layer over a slowly varying bed is presented. Waves are periodic in time with several harmonics. In this paper, we adopt a time invariant eddy viscosity model, in which the eddy viscosity is linearly proportional to the distance from the bed. The boundary-layer flow field is solved analytically in terms of Fourier components. The approach allows fast computations and can be easily included in a phase resolving wave propagation model. As a part of the results, bottom shear stress and the spatial variation of the boundary layer thickness are also obtained. Present results compare well with experimental data and can explain the asymmetries in the bottom shear stress under sawtooth shaped waves. DOI: 10.1061/(ASCE)0733-9429(2008)134:2(225) CE Database subject headings: Ocean waves; Turbulence; Boundary layers; Eddy viscosity; Shear stress; Ocean bottom.

The structural loads on a floating production, storage, and offloading platform induced by a large set of realistic (measured) abnormal waves are compared with the loads induced by 'design storms' and also with the minimum values required by Classification Society rules. The design storms have a duration of 3 h and correspond to the 100 yr contour of the scatter diagram of the Northern North Sea. Time domain simulations are performed with a time domain seakeeping program that accounts for the most important nonlinear effects. The results are analyzed to obtain probability distributions of the sagging and hogging peaks of the vertical bending moment. Several theoretical distributions are fitted to the simulated realizations.

For an improved design of ships and offshore structures with regard to their behavior under severe weather conditions, wave height and steepness as well as the shape of the wave profile have to be considered. In this paper, the extreme new year wave as documented in numerous publications is varied with respect to wave height and period. These varied wave sequences are realized and measured in a model tank and applied to the investigation of motions and bending moments of a floating production storage and offloading ship. The results are compared to the responses in the original wave train. An investigation of the riskiness of extreme wave sequences in comparison with existing rules concludes this paper

Nonlinear contributions in near-surface particle velocities under extreme crests in random seas can be important in the prediction of wave loads. Four different prediction methods are compared in this paper The purpose is to observe and evaluate differences in predicted particle velocities under high and extreme crests, and how well they agree with measurements. The study includes linear prediction, a second-order random wave model, Wheeler's method [1970, 'Method for Calculating Forces Produced by Irregular Waves,' JPT, J. Pet. Technol., pp. 359-367] and a new method proposed by Grue et al. [2003, 'Kinematics of Extreme Waves in Deep Water, '' Appl. Ocean Res., 25, pp. 355366]. Comparison to laboratory data is also made. The whole wave-zone range from below still water level up to the free surface is considered. Large nonlinear contributions are identified in the near-surface velocities. The results are interpreted to be correlated with the local steepness kA. Some scatter between the different methods is observed in the results. The comparison to experiments shows that among the methods included, the second-order random wave model works best in the whole range under a steep crest in deep or almost deep water, and is therefore recommended. The method of Grue et al. works reasonably well for z > 0, i.e., above the calm water level while it overpredicts the velocities for z < 0. Wheeler's method, when used with a measured or a second-order input elevation record, predicts velocities fairly well at the free surface z = [[eta].sub.max], but it underpredicts around z = 0 and further below. The relative magnitude of this latter error is slightly smaller than the local steepness [kA.sub.0] and can be quite significant in extreme waves. If Wheeler's method is used with a linear input, the same error occurs in the whole range, i.e., also at the free surface. Keywords: marine technology, hydrodynamics, ocean waves, kinematics

A set of wave data generated in an offshore tank is studied. The set of the largest waves in those sea states is studied with respect to steepness, asymmetry, and nonlinearity. It was possible to find some waves that were classified as abnormal or freak according to presently accepted criteria. Their statistics connected to steepness and nonlinearity was determined. Comparison of the nonlinearity as well as statistics of the largest waves in the offshore tank and at sea was performed so as to identify any limitation in reproduction of the properties of large waves in model basins.

This paper is concerned with evaluating the effect of heavy weather avoidance on the long-term wave-induced loads on ships. Two hydrodynamic codes, VERES based on a 2D strip theory and WASIM based on a 3D Rankine panel method, are employed to calculate the wave-induced loads and motions on various vessels. Two models for heavy weather avoidance are envisaged. The first one is based on the assumption that operational criteria relevant to vertical acceleration, green water, and bottom slamming are fulfilled. The second one is based on the assumption that the sea state forecasts are available to the shipmaster and that rerouting is made. Based on the first model, the effect of the heavy weather avoidance on the long-term wave-induced hull girder loads is evaluated. In particular, the effect of hydrodynamic analysis methods and wave scatter diagram are also assessed. The calculated values are compared with those given in ship rules. The results show that several factors should be critically assessed in evaluating the accuracy of the ship rule values.

There is clearly no immediate answer to the question posted by the title of this paper. Inasmuch as that there are not much definitively known about rogue waves and that there is still no universally accepted definition for rogue waves in the ocean, we think there might just be even more than one kind of rogue waves to contend with. While the conventional approach has generally designated waves with [H.sub.max]/[H.sub.s] greater than 2.2 as possible rogue waves, based on Rayleigh distribution considerations, there is conspicuously no provision as to how high the ratio of [H.sub.max]/[H.sub.s] can be and thus not known how high can a rogue wave be. In our analysis of wave measurements made from a gas-drilling platform in South Indian Ocean, offshore from Mossel Bay, South Africa, we found a number of cases that indicated [H.sub.max]/[H.sub.s] could be valued in the range between 4 and 10. If this were to be the case, then these records could be considered to be 'uncommon' rogue waves, whereas a record of [H.sub.max]/[H.sub.s] in the range between 2 and 4 could be considered to comprise 'typical' rogue waves. On the other hand, the spikes in the [H.sub.max] data could have been caused by equipment malfunction or some other phenomenon. Clearly, the question of whether or not there are different kinds of rogue waves cannot be readily answered by theoretical considerations alone and there is a crucial need for long-term wave time-series measurements for studying rogue waves.

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 20 years 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.