Long-crested Seas Research Articles

The DeRisk database: Extreme design waves for offshore wind turbines

The estimation of extreme loads from waves is an essential part of the design of offshore wind turbines. Standard design codes suggest either to use simplified methodologies based on regular waves, or to perform fully-nonlinear computations. The former may not provide an accurate representation of the real extreme waves, while the latter is too computationally intensive for fast design iterations. Here, we address these limitations by using the fully-nonlinear solver OceanWave3D to establish the DeRisk database, a large dataset of extreme wave kinematics in a two-dimensional domain. From the database, which is open and freely available, a designer can easily extract fully-nonlinear wave kinematics for a wave condition and water depth of interest by identifying a suitable computation in the database and, if needed, by Froude-scaling the kinematics. This will ultimately enable quicker estimations of nonlinear wave loads, speeding up design evaluations. The database sea states cover a range of nondimensional depth of about h∗∈[3.0⋅10−3,6.5⋅10−2] and of nondimensional significant wave height of HS∗∈[1.0⋅10−3,8.0⋅10−3], where h∗=h/(gTP2)[−] and HS∗=HS/(gTP2)[−].The fully-nonlinear solver is validated against the DeRisk model-scale experiments, where a number of long-crested sea state realizations are generated at two different water depths, 33.0[m] and 20.0[m], and the induced force on a stiff monopile with a diameter of D=7.0[m] is measured.Comparison with the experiments shows that the database predicts maximum crest elevations at both depths very accurately. Predictions of the in-line force, obtained by application of the Rainey slender body force model with the database wave kinematics, are accurate for milder storms. However, for stronger storms, where slamming loads from breaking waves dominate, the force computations from the database kinematics provide slightly nonconservative force estimates compared with the standard methodologies such as the embedded stream function and the WiFi JIP model. This discrepancy is mainly due to the lack of a slamming load model in the applied force model. A procedure to add slamming loads to OceanWave3D and to the DeRisk database is currently being developed.

Toward nearshore, bathymetry induced wave amplification in False Bay, South Africa

A seamount called Rocky Bank (RB) has been suspected to spatially focus wave energy toward the eastern periphery of False Bay, South Africa, where it is not uncommon for fishermen to get washed off by waves. Situated at the bay’s mouth, the submerged seamount acts like a refracting lens for incoming long-crested swell. The present study aims at understanding the wave transformation effects of RB and the nearshore bathymetry using the phase-averaging spectral wave model simulating waves in the nearshore. Open ocean conditions around the Cape Peninsula, derived from National Center for Environmental Prediction reanalysis products, were used as model boundary conditions. To establish RB’s influence, a bathymetry without RB was created. The model output indicated that coastal significant wave heights were 9% greater when RB was removed. This difference was largest for smaller incident significant wave height and increasing incident peak period. RB also causes wave convergence via refraction and presents evidence for spatial focusing, a coincidental interference, extreme wave generating mechanism. This result, together with recorded incidents and anecdotal evidence, suggests that the wave transformation effects of RB may be leading to extreme waves along the eastern periphery. Evidence for spatial focusing toward the eastern periphery occurred for peak wave directions between 210° and 245° true north and for peak periods greater than 13 s. The likelihood of a wave leading to an incident is greater in smaller, long-crested seas based on the recent literature for the region. To extend this study to predict rogue wave events within False Bay, a phase-resolving model would be required.

Effect of wave spreading including multi-directional wave interaction on the responses of a spar platform

This paper deals with the effect of directionality of waves on the responses of a spar-type floating offshore platform. Here, a spar-type offshore platform restrained by four catenary mooring cables is modelled as per the work done by Chen et al. (Ocean Eng 28:863–887, 2001). The numerical model and numerical simulation have been validated by comparing the results (natural periods, RAOs and statistics of response) available in the literature (Steen et al. in Offshore Technology Conference 2004; Wangz et al. in J Mar Sci Appl 8:168–174, 2010). The multi-directional sea spectrum is represented by the product of a cosine power spreading function and a uni-directional JONSWAP wave spectrum. The Quadratic Transfer Functions have been generated for the calculation of drift loads, taking into account the multi-directional wave interaction. The responses of the platform have been obtained under long-crested (uni-directional) and short-crested (multi-directional) sea states and the results thus obtained are compared. Further, the variations in responses due to change in power of spreading function and total spreading angle are also investigated. It is found that due to the multi-directional wave interaction, the second order drift loads assume higher values in all degrees of freedom. Subsequently, in short-crested seas, the structure exhibits higher responses in all degrees of freedom when multi-directional wave interaction is considered. This highlights the need for incorporation of the multi-directional wave interaction while modelling short-crested seas for a realistic assessment of response behaviour of the system.

Individual wave height and wave crest distributions based on field measurements from the northern North Sea

This paper concerns full-scale wave measurements of individual wave heights and crest heights at one location with water depth 190 m in the northern North Sea from 2004 up to date. The surface elevation was recorded by a Saab WaveRadar REX from one location in the northern North Sea. The measured individual wave heights and crest heights have been compared to well-known theoretical distributions. For wave heights, the Rayleigh distribution is found to form a conservative upper bound, whilst the Forristall distribution is considered to show a good accuracy, though somewhat conservative in the most severe sea states. For crest heights, the Rayleigh distribution is found to be nonconservative, whilst the Forristall distributions for long- and short-crested sea both provide reasonable descriptions. Based on the present study, the Forristall distributions for individual wave height and crest heights in long-crested seas are considered to provide the most appropriate descriptions of these measured wave data.

Extreme wave statistics of counter-propagating, irregular, long-crested sea states

Extreme wave statistics of unidirectional and counter-propagating seas are investigated, for the special case of long-crested irregular waves, with laboratory experiments and with numerical simulations using the higher order spectral method. Both the kurtosis of the surface elevation and the exceedance probability of the crest height are larger in unidirectional seas than in counter-propagating seas. Numerical simulations show that even a small amount of wave energy travelling against an essentially unidirectional wave system can significantly reduce the kurtosis of the surface elevation.

Validation of the Boccotti's generalized model for large nonlinear wave heights from laboratory mixed sea states

The presented work aims at validating the generalization of the asymptotic distribution model of Boccotti for large wave heights recently proposed by Tayfun [1] to laboratory generated mixed sea states with two-peak spectra. The input wave spectra are modelled as the sum of two JONSWAP spectra describing unidirectional wave systems with different or identical directions of propagation (crossing or following mixed seas). In order to account for the effect of the energetically dominant wave system on the largest observed waves, the Boccotti's parameters were calculated at the absolute minimum of the autocorrelation function which can differ from the first minimum for some cases of mixed seas, such as those dominated by the swell or seas with comparable contribution of the two spectral components. So far the proposed model has been validated elsewhere against samples of large wave heights exceeding the significant wave height in wind seas and in mechanically generated long-crested seas, both characterized by unimodal spectra and strong third-order nonlinearities. The present study demonstrates that it can predict equally well the tail of the distributions for mixed seas, irrespective of the type of the mixed sea, particularly when the third-order statistics is relatively large. Typically, the mixed seas from the considered offshore basin experiment display such conditions as the propagation distance from the wavemaker increases, though this effect is less pronounced for mixed following than for mixed crossing wave conditions. Moreover, the generalized model remains valid irrespective of the sign of the fourth-order sum Λ which is a key parameter of the distribution. Its good predictive ability is quantified here by the root-mean-square errors between observations and theory.

On the kurtosis of deep-water gravity waves

In this paper, we revisit Janssen’s (J. Phys. Oceanogr., vol. 33 (4), 2003, pp. 863–884) formulation for the dynamic excess kurtosis of weakly nonlinear gravity waves in deep water. For narrowband directional spectra, the formulation is given by a sixfold integral that depends upon the Benjamin–Feir index and the parameter $R={\it\sigma}_{{\it\theta}}^{2}/2{\it\nu}^{2}$, a measure of short-crestedness for the dominant waves, with ${\it\nu}$ and ${\it\sigma}_{{\it\theta}}$ denoting spectral bandwidth and angular spreading. Our refinement leads to a new analytical solution for the dynamic kurtosis of narrowband directional waves described with a Gaussian-type spectrum. For multidirectional or short-crested seas initially homogeneous and Gaussian, in a focusing (defocusing) regime dynamic kurtosis grows initially, attaining a positive maximum (negative minimum) at the intrinsic time scale ${\it\tau}_{c}={\it\nu}^{2}{\it\omega}_{0}t_{c}=1/\sqrt{3R}$, or $t_{c}/T_{0}\approx 0.13/{\it\nu}{\it\sigma}_{{\it\theta}}$, where ${\it\omega}_{0}=2{\rm\pi}/T_{0}$ denotes the dominant angular frequency. Eventually the dynamic excess kurtosis tends monotonically to zero as the wave field reaches a quasi-equilibrium state characterized by nonlinearities mainly due to bound harmonics. Quasi-resonant interactions are dominant only in unidirectional or long-crested seas where the longer-time dynamic kurtosis can be larger than that induced by bound harmonics, especially as the Benjamin–Feir index increases. Finally, we discuss the implication of these results for the prediction of rogue waves.

Emergence of coherent wave groups in deep-water random sea

Extreme surface waves in a deep-water long-crested sea are often interpreted as a manifestation in the real world of the so-called breathing solitons of the focusing nonlinear Schrödinger equation. While the spontaneous emergence of such coherent structures from nonlinear wave dynamics was demonstrated to take place in fiber-optics systems, the same point remains far more controversial in the hydrodynamic case. With the aim to shed further light on this matter, the emergence of breatherlike coherent wave groups in a long-crested random sea is investigated here by means of high-resolution spectral simulations of the fully nonlinear two-dimensional Euler equations. The primary focus of our study is to parametrize the structure of random wave fields with respect to the Benjamin-Feir index, which is a nondimensional measure of the energy localization in Fourier space. This choice is motivated by previous results, showing that extreme-wave activity in a long-crested sea is highly sensitive to such a parameter, which is varied here by changing both the characteristic spectral bandwidth and the average wave steepness. It is found that coherent wave groups, closely matching realizations of Kuznetsov-Ma breathers in Euler dynamics, develop within wave fields characterized by sufficiently narrow-banded spectra. The characteristic spatial and temporal scales of wave group dynamics, and the corresponding occurrence of extreme events, are quantified and discussed by means of space-time autocorrelations of the surface elevation envelope and extreme-event statistics.

Experimental validation of non-linear deterministic prediction schemes for long-crested waves

This paper describes the experimental validation of non-linear deterministic prediction tools for unidirectional seas, based on the use of two different non-linear wave models: (i) a so called “second order model enhanced”, which is analytic, and (ii) the numerical HOS wave model, which is run at order 3 in our simulations. Both prediction models use time traces of the surface elevation measured at one or several wave probes as an initial condition. Two effective data assimilation processes are used to optimize the model-reconstructed probes measurements, and thus ensure proper initial conditions for the forecast. The validation of our prediction tools on model-generated wave data has been reported in the previous paper (Blondel et al., 2010). Accurate predictions were reported compared to linear predictions. In the present study, the predictions are compared to different sets of laboratory measurements collected in a towing tank. The good agreement between the model-predicted surface elevations and the related experimental measurements indicates that our models can predict irregular long-crested seas more accurately than basic linear approaches with computational costs compatible with the short-term constraint.

Dynamic Analysis of Spar Hull Transportation

The transportation of a truss-spar hull from a transport barge of 6000 ton topside module on the spar hull is investigated in the present study. Two possible routes from a fabrication yard in Teeside, England to the Gulf of Mexico are considered in the paper. The results of motion responses of the transport barge obtained from a spectral analysis and the limiting criteria of sea fastening, deck wetness and lateral acceleration are compared and the route selection is discussed. Long-crested waves and short-crested seas as well as the joint probabilities of significant wave heights and wave periods in different sea areas are considered. Generally speaking, the results for long-crested seas are higher than those for short-crested waves.

Influence of crest and group length on the occurrence of freak waves

A large number of simulations have been performed to reveal how the occurrence of freak waves on deep water depends on the group and crest lengths for fixed steepness. It is found that there is a sharp qualitative transition between short- and long-crested sea, for a crest length of approximately ten wavelengths. For short crest lengths the statistics of freak waves deviates little from Gaussian and their occurrence is independent of group length (or Benjamin–Feir index, BFI). For long crest lengths the statistics of freak waves is strongly non-Gaussian and the group length (or BFI) is a good indicator of increased freak wave activity.

Wave feedforward control of floating production systems

Wave basin tests have been conducted on a 129,600t turret-moored floating production system with wave feedforward control in long-crested and directional seas between 7m and 13.5m significant wave height. Strategies for generating real-time signals of wave drift processes either from vessel motions or directly from wave probes, and the integration of these signals into self-tuning and modified LQG control system, are described. The results indicate that adaptive control algorithms incorporating signals either from direct wave measurement or derived from the vessel's wave-frequency motions, can reduce the low-frequency motions of the system in both short- and long-crested seas.

Statistics of Combined Linear and Quadratic Springing Response of a TLP in Random Waves

Abstract The paper presents the results of statistical analyses of combined first-order and second-order, sum-frequency response in heave, pitch, and roll of a TLP structure subjected to random, long-crested seas. The results are based on available numerically calculated data for the linear and quadratic transfer functions from the waves to the hydrodynamic loads on the TLP. It has also been assumed that the equations of motion in heave, pitch, and roll can be reasonably well approximated by a set of uncoupled, linear, and time-invariant equations.

Time-Domain Structural Response Simulation in a Short-Crested Sea

The responses of an offshore tower due to short-crested and long-crested ocean waves are investigated. A time-domain analysis is performed utilizing the recently developed method of generating sample functions of random processes. Numerical results include time histories of the water particle velocity and acceleration for ocean waves generated by mean wind velocity of 33 ft/sec (10 m/s) and 66 ft/sec (20 m/s) and also time histories of the tower response due to long-crested and short-crested seas. A direct comparison has been made between the responses obtained for long-crested and short-crested sea waves.

Estimating ocean wind wave spectra by means of underwater sound

Measurements of the spectrum of ocean surface reradiated acoustic signals generated by an omnidirectional, sinusoidal source are used to estimate the ocean surface wave-height spectrum, and the results are compared with wave-staff measurements made simultaneously in the scattering area. Plane-wave physical optics theory is applied to a long-crested sea surface model to verify Marsh's hypothesis that for low sea states the spectrum of acoustic waves reradiated by the rough, moving sea surface consists of a specular component at the transmitted frequency and a scattered component, which is the weighted surface wave-height spectrum. The approach employs theories by Parkins, Clay and Medwin, and Pierson. The weighting function applied to the surface spectrum depends on signal frequency, experimental geometry, and mean-square wave height. Continuous-wave signals at 127 and 1702 Hz were transmitted from fixed, omnidirectional sources to receivers 4.5 and 31 km downrange. Additionally, wave height was monitored continuously by resistance wave staff. The time series records of sound-pressure level and ocean wave height were analyzed for spectral content. Agreement between theory and experiment is good when the acoustic sideband levels are not more than 25 dB below the level of the specular component. The experimental results are also interpreted in light of Parkins' spherical wave theory, and the differences between the plane and spherical wave theories are discussed.