Quasi-determinism Theory Research Articles

DESIGN OF A FLOATING PLATFORM FOR AN INNOVATIVE DUCTED WIND TURBINE

This paper analyses the dynamics loads exerted by waves on a floating offshore platform in the Straits of Messina, (South of Italy), hosting an innovative ducted wind turbine. The force exerted by largest sea waves occurring during lifetime on the floating platform are predicted by the quasi-determinism theory, which foresees what happens if a group of waves of exceptionally large height occurs at a given point in the sea.

Extrapolation of ship capsize probability over significant wave height: Foundation on wave groups theory

The paper lays formal foundation for the “extrapolation over significant wave height” technique which has recently been incorporated into the Second Generation Intact Stability Criteria of the International Maritime Organization (IMO) for assessing the dynamic stability of ships in waves. The technique aims at estimating efficiently a ship's tendency to capsize in relatively mild sea conditions through parsimonious simulations of ship motion. To address the rarity of capsizes in such conditions, extrapolation is employed for the probability value obtained from severer sea states differing only in their significant wave heights. In its current version, the approach extrapolates as if capsize was caused solely by exceptionally large wave encounters, thus ignoring phenomena such as resonance or wave grouping. Herein, the concept is revisited from the perspective of the “critical wave groups” method which is demonstrated as a general framework enabling rigorous “extrapolation over significant wave height” formulations. In this setting, two new extrapolation models are developed from basic principles as improvements to the one suggested by the IMO. The first model accounts for the joint effect of wave heights and periods, while the second additionally integrates the temporal dependence between consecutive wave heights into the extrapolation scheme. The accuracy of the theoretical predictions as well as their sensitivity to the amount of available data are evaluated for the case of beam-sea rolling assuming two different spectrum types as possible characterizations of the prevailing wave conditions. Justification about the extrapolation capabilities of the derived models is provided in view of the advances in extreme wave stochastics accommodated by the theory of Quasi-Determinism.

MNLS simulations of surface wave groups with directional spreading in deep and finite depth waters

We simulate focusing surface gravity wave groups with directional spreading using the modified nonlinear Schrödinger (MNLS) equation and compare the results with a fully-nonlinear potential flow code, OceanWave3D. We alter the direction and characteristic wavenumber of the MNLS carrier wave, to assess the impact on the simulation results. Both a truncated (fifth-order) and exact version of the linear dispersion operator are used for the MNLS equation. The wave groups are based on the theory of quasi-determinism and a narrow-banded Gaussian spectrum. We find that the truncated and exact dispersion operators both perform well if: (1) the direction of the carrier wave aligns with the direction of wave group propagation; (2) the characteristic wavenumber of the carrier wave coincides with the initial spectral peak. However, the MNLS simulations based on the exact linear dispersion operator perform significantly better if the direction of the carrier wave does not align with the wave group direction or if the characteristic wavenumber does not coincide with the initial spectral peak. We also perform finite-depth simulations with the MNLS equation for dimensionless depths (k_{text {p}}d) between 1.36 and 5.59, incorporating depth into the boundary conditions as well as the dispersion operator, and compare the results with those of fully-nonlinear potential flow code to assess the finite-depth limitations of the MNLS.

On the Average Shape of the Largest Waves in Finite Water Depths

AbstractThis paper investigates the average shape of the largest waves arising in finite water depths. Specifically, the largest waves recorded in time histories of the water surface elevation at a single point have been examined. These are compared to commonly applied theories in engineering and oceanographic practice. To achieve this both field observations and a new set of laboratory measurements are considered. The latter concern long random simulations of directionally spread sea states generated using realistic Joint North Sea Wave Project (JONSWAP) frequency spectra. It is shown that approximations related to the linear theory of quasi-determinism (QD) cannot describe some key characteristics of the largest waves. While second-order corrections to the QD predictions provide an improvement, key effects arising in very steep or shallow water sea states are not captured. While studies involving idealized wave groups have demonstrated significant changes arising as a result of higher-order nonlinear wave–wave interactions, these have not been observed in random sea states. The present paper addresses this discrepancy by decomposing random wave measurements into separate populations of breaking and nonbreaking waves. The characteristics of average wave shapes in the two populations are examined and their key differences discussed. These explain the mismatch between findings in earlier random and deterministic wave studies.

A numerical study on the dynamic response of a floating spar platform in extreme waves

The investigation of the interaction of floating structures with very high waves, also known as freak or rogue waves, is of crucial importance for the analysis of their ultimate design conditions. The representation of such waves is usually achieved through computationally intensive numerical simulations. In this paper, a deterministic approach is proposed, to represent extreme wave groups in the space–time domain. The free surface profile for a Gaussian sea is obtained by means of the Quasi-Determinism theory, and the corresponding dynamic response of a spar-type support for floating offshore wind turbines in parked rotor conditions is analyzed. The Quasi-Determinism theory and the nonlinear equation of motion of the structure are coupled through an in-house time-domain numerical code. Wave forces and structure motions in surge, heave and pitch are obtained. A parametric analysis is carried out to investigate the effects of the criteria used for the definition of the extreme wave, its position of occurrence and the initial conditions in terms of body motions. The results obtained give a clear insight into the physics of the wave–structure interaction phenomenon for extremely high waves in Gaussian seas and allow to identify a few load combinations, corresponding to the severest wave conditions for the floating structure.

Verification of Quasi-Determinism theory against Baltic Sea Data

Verification of Quasi-Determinism theory against Baltic Sea Data

An exact Hamiltonian coupled-mode system with application to extreme design waves over variable bathymetry

A novel, exact, Hamiltonian system of two nonlinear evolution equations, coupled with a time-independent system of horizontal differential equations providing the Dirichlet-to-Neumann operator for any bathymetry, is applied to the study of the evolution of wave trains in finite depth, aiming at the identification of nonlinear high waves in finite depth, and over a sloping bottom. The vertical structure of the wave field is exactly represented up to the instantaneous free surface, by means of an appropriately constructed, rapidly convergent, local vertical series expansion of the wave potential. This Hamiltonian system is used for studying the fully nonlinear refocusing of transient wave groups, obtained by linear backpropagation of high-amplitude wave trains constructed by the theory of quasi-determinism. The results presented give a first quantification of the effects of sloping bottom and of spectral bandwidth on rogue-wave dynamics and kinematics, in finite depth.

Space-time extreme wind waves: Analysis and prediction of shape and height

In this study, we present the analysis of the temporal profile and height of space-time (ST) extreme wind waves. Wave data were gathered from an observational ST sample of sea surface elevations collected during an active sea state, and they were examined to detect the highest waves (exceeding the rogue wave threshold) of specific 3D wave groups close to the apex of their development. Two different investigations are conducted. Firstly, local maximum elevations of the groups are examined within the framework of statistical models for ST extreme waves, and compared with observations and predictions of maxima derived by one-point time series of sea surface elevations. Secondly, the temporal profile near the maximum wave crests is analyzed and compared with the expectations of the linear and second-order nonlinear extension of the Quasi-Determinism (QD) theory. Our goal is to verify, with real sea data, to what extent, one can estimate the shape and the crest-to-trough height of near-focusing large 3D wave groups using the QD and ST extreme model results. From this study, it emerges that the elevations close to the crest apex are narrowly distributed around a mean profile, whilst a larger dispersion is observed away from the maximum elevation. Yet the QD model furnishes, on average, a fair prediction of the maximum wave heights, especially when nonlinearities are taken into account. Moreover, we discuss how the combination of ST extreme and QD model predictions allows establishing, for a given sea condition, the portrait of waves with very large crest height. Our results show that these theories have the potential to be implemented in a numerical spectral model for wave extreme prediction.

Numerical modeling of space-time wave extremes using WAVEWATCH III

A novel implementation of parameters estimating the space-time wave extremes within the spectral wave model WAVEWATCH III (WW3) is presented. The new output parameters, available in WW3 version 5.16, rely on the theoretical model of Fedele (J Phys Oceanogr 42(9):1601-1615, 2012) extended by Benetazzo et al. (J Phys Oceanogr 45(9):2261–2275, 2015) to estimate the maximum second-order nonlinear crest height over a given space-time region. In order to assess the wave height associated to the maximum crest height and the maximum wave height (generally different in a broad-band stormy sea state), the linear quasi-determinism theory of Boccotti (2000) is considered. The new WW3 implementation is tested by simulating sea states and space-time extremes over the Mediterranean Sea (forced by the wind fields produced by the COSMO-ME atmospheric model). Model simulations are compared to space-time wave maxima observed on March 10th, 2014, in the northern Adriatic Sea (Italy), by a stereo camera system installed on-board the “Acqua Alta” oceanographic tower. Results show that modeled space-time extremes are in general agreement with observations. Differences are mostly ascribed to the accuracy of the wind forcing and, to a lesser extent, to the approximations introduced in the space-time extremes parameterizations. Model estimates are expected to be even more accurate over areas larger than the mean wavelength (for instance, the model grid size).

Space-time evolution of wave groups in crossing seas with the Quasi-determinism theory

The space‐time evolution of wave groups in crossing seas is investigated. Profiles were calculated by applying Quasi‐determinism theory of Boccotti in its first formulation starting first from the laboratory data and then using the theoretical spectrum used for wave generation, given that a very high crest takes place at a fixed point in the basin. The analysis of the predictions shows that the group with the high crest is given by the superposition of two wave groups, associated one to the low‐frequency component of the spectrum and the other to the high‐frequency one. Different locations of high crest occurrence were considered in order to study the effect of the change in spectrum on the deterministic profiles. The comparison between the predictions obtained by the two modalities of application of the theory shows agreement when the spectrum at any point maintains almost the same characteristic of the spectrum measured in correspondence of the high crest occurrence location. Finally the analysis of the second‐order contribution revealed that the nonlinear effect gives higher and steeper crests and lower and flatter troughs than the linear ones whatever is the sea state considered being the greatest in presence of the wind wave dominated spectrum.

Evaluation of the Horizontal Wave Forces on Piles

Reliability of offshore platforms is an important issue in the prevention of environmental disasters. In this paper, the variation of the horizontal force exerted on an offshore gravity platform is analyzed to achieve a deep comprehension of a storm scenario. Considering the wave motion as a potential motion, the quasi-determinism theory is applied to obtain the kinematic characteristics of a storm. The evolution of force against time is analyzed through the Morison's equation, diffraction theory, and a simplified method. Moreover, two case studies are examined, one in the Ortona region of the Italian coast and the other in the Gulf of Alaska, USA.

On the distribution of wave heights in the space domain

Wind-generated waves are measured on a straight line by means of a gauge array. These measurements yield the distribution of the wave heights in the space domain, on deep water, in stationary sea states. This result is compared with the theoretical distribution based on the linear quasi-determinism theory.

Field Verification of Quasi-Determinism Theory for Wind Waves Interacting with Vertical Breakwater

AbstractProfiles of exceptionally large waves before a vertical breakwater were obtained by using a gauge array. These profiles were compared with the profiles obtained using the quasi-determinism (QD) theory. The experiment performed in the field confirmed the QD theory for a wave field that is strongly nonhomogeneous in space.

Space–time measurements of oceanic sea states

Stereo video techniques are effective for estimating the space–time wave dynamics over an area of the ocean. Indeed, a stereo camera view allows retrieval of both spatial and temporal data whose statistical content is richer than that of time series data retrieved from point wave probes. We present an application of the Wave Acquisition Stereo System (WASS) for the analysis of offshore video measurements of gravity waves in the Northern Adriatic Sea and near the southern seashore of the Crimean peninsula, in the Black Sea. We use classical epipolar techniques to reconstruct the sea surface from the stereo pairs sequentially in time, viz. a sequence of spatial snapshots. We also present a variational approach that exploits the entire data image set providing a global space–time imaging of the sea surface, viz. simultaneous reconstruction of several spatial snapshots of the surface in order to guarantee continuity of the sea surface both in space and time. Analysis of the WASS measurements show that the sea surface can be accurately estimated in space and time together, yielding associated directional spectra and wave statistics at a point in time that agrees well with probabilistic models. In particular, WASS stereo imaging is able to capture typical features of the wave surface, especially the crest-to-trough asymmetry due to second order nonlinearities, and the observed shape of large waves are fairly described by theoretical models based on the theory of quasi-determinism (Boccotti, 2000). Further, we investigate space–time extremes of the observed stationary sea states, viz. the largest surface wave heights expected over a given area during the sea state duration. The WASS analysis provides the first experimental proof that a space–time extreme is generally larger than that observed in time via point measurements, in agreement with the predictions based on stochastic theories for global maxima of Gaussian fields.

Distributions of Wave Heights in Time Domain in Stationary Sea States

AbstractAbout 6,300,000 pressure head waves beneath the sea surface were recorded by an array of 26 transducers aligned orthogonally to the coastline of Reggio Calabria, Italy. The data set covered spectra from very narrow unimodal to very broad multimodal and waves from shallow to deep waters. Herein, the quasi-determinism (QD) theory is proven to be very effective in predicting the probability of large-wave heights as well as the period and particle acceleration of these waves both on deep and shallow waters. In addition, the Tayfun model for predicting the probability of large-wave heights is also proven to be highly effective.

Space-time evolution of random wave groups with high waves based on the quasi-determinism theory

In this paper, the space-time evolution of ocean wave groups when a large wave occurs is studied. The theoretical wave profiles have been firstly investigated by applying Boccotti's quasi-determinism (QD) theory up to second-order. It is shown that the theory can describe the wave groups either in the time domain at any fixed point, or in the space domain at any fixed instant of time. Validation of the theory is then proposed by considering laboratory generated time series representing the evolution of the famous New Year wave at the Draupner platform. It has been concluded that the evolution of the largest wave in a sea state may be predicted well by the theoretical nonlinear profiles of the QD theory.

Field verification of quasi-determinism theory for wind waves in the space–time domain

Profiles of exceptionally large waves in wind seas were obtained using a gauge array that was nearly aligned in the dominant wave direction; the length of these profiles ranged from 1.5 to 3.0 times the dominant wavelength. The profiles were also obtained through calculations using the quasi-determinism theory from the datasets of the sea states. The possibility to observe waves in the space–time domain enables us to obtain a remarkable confirmation of the quasi-determinism theory.

Wave height distributions in bimodal sea states from offshore basins

The paper presents results for the distribution of wave heights from laboratory generated bimodal sea states. Data collected at the DHI offshore basin are analyzed and compared with results based on wave records from the MARINTEK offshore basin. The comparisons are done for three groups of mixed sea states: wind-sea dominated, swell-dominated and energy-equivalent, determined on the basis of the parameter sea-swell energy ratio ( SSER), which have been generated according to the model of Guedes Soares (1984). In some sea states abnormal or freak waves have been observed. The quasi-determinism theory of Boccotti is used to expand some linear narrowband models to second order, thus providing validation of the adequacy of the equations to represent the linear components of the wave heights. Also, the data are compared with the predictions of a third order model using as a nonlinear correction the coefficient of kurtosis. Due to the coexistence of wind-sea and swell, the core of the autocovariance function in some cases demonstrates a global minimum which is the second local minimum in the sequence. This can affect the fitting ability of distributions whose parameters depend on the form of the autocorrelation function or its envelope. The results for MARINTEK and DHI data show similar patterns of fit between predicted and observed exceedance probabilities for the considered classes of bimodal spectra.

A Field Experiment on the Recurrence of Large Waves in Wind Seas

Wind generated sea waves are generally regarded as an example of pure randomness in nature. Here we give a proof that the matter is not exactly so: some identical sequences of relatively large waves were found many hours apart from one another. This finding supports the theory of quasi determinism of sea waves.

Nonlinear Crest Height Distribution in Three-Dimensional Ocean Waves

The interest and studies on nonlinear waves are increased recently for their importance in the interaction with floating and fixed bodies. It is also well-known that nonlinearities influence wave crest and wave trough distributions, both deviating from the Rayleigh law. In this paper, a theoretical crest distribution is obtained, taking into account the extension of Boccotti’s quasideterminism theory (1982, “On Ocean Waves With High Crests,” Meccanica, 17, pp. 16–19), up to the second order for the case of three-dimensional waves in finite water depth. To this purpose, the Fedele and Arena (2005, “Weakly Nonlinear Statistics of High Random Waves,” Phys. Fluids, 17(026601), pp. 1–10) distribution is generalized to three-dimensional waves on an arbitrary water depth. The comparison with Forristall’s second order model (2000, “Wave Crest Distributions: Observations and Second-Order Theory,” J. Phys. Oceanogr., 30(8), pp. 1931–1943) shows the theoretical confirmation of his conclusion: The crest distribution in deep water for long-crested and short-crested waves are very close to each other; in shallow water the crest heights in three-dimensional waves are greater than values given by the long-crested model.