Showing papers on "Rogue wave published in 2005"

Modulation instability of Stokes wave → freak wave

Abstract: Formation of waves of large amplitude (freak waves, killer waves) at the surface of the ocean is studied numerically. We have observed that freak waves have the same ratio of the wave height to the wave length as limiting Stokes waves. When a freak wave reaches this limiting state, it breaks. The physical mechanism of freak wave formation is discussed.

Predicting rogue waves in random oceanic sea states

Abstract: Using the inverse spectral theory of the nonlinear Schrodinger (NLS) equation we correlate the development of rogue waves in oceanic sea states characterized by the Joint North Sea Wave Project (JONSWAP) spectrum with the proximity to homoclinic solutions of the NLS equation. We find in numerical simulations of the NLS equation that rogue waves develop for JONSWAP initial data that are “near” NLS homoclinic data, while rogue waves do not occur for JONSWAP data that are “far” from NLS homoclinic data. We show the nonlinear spectral decomposition provides a simple criterium for predicting the occurrence and strength of rogue waves.

Numerical Wave Tank: Simulation of Extreme Waves for the Investigation of Structural Responses

Abstract: For the deterministic analysis of extreme structure behavior, the hydrodynamics of the exciting wave field, i. e. pressure and velocity fields, must be known. Whereas responses of structures, e. g. motions, can easily be obtained by model tests, the detailed characteristics of the exciting waves are often difficult to determine by measurements. Therefore, numerical wave tanks (NWT) promise to be a handy tool for providing detailed insight into wave hydrodynamics. In this paper different approaches for numerical wave tanks are introduced and used for the simulation of rogue wave sequences. The numerical wave tanks presented are characterized by the following key features: a) Potential theory with Finite Element discretization (Pot/FE); b) Reynolds-Averaged Navier-Stokes Equations (RANSE) using the Volume of Fluid (VOF) method for describing the free surface. For the NWT using the VOF method three different commercial RANSE codes (CFX, FLUENT, COMET) are applied to calculate wave propagation, whereas simulations based on potential theory are carried out with a wave simulation code developed at T echnical U niversity B erlin (WAVETUB). It is shown that the potential theory method allows a fast and accurate simulation of the propagation of nonbreaking waves. In contrast, the RANSE/VOF method allows the calculation of breaking waves but is much more time-consuming, and effects of numerical diffusion can not be neglected. To benefit from the advantages of both solvers, i. e. the calculation speed (Pot/FE-solver WAVETUB) and the capability of simulating breaking waves (RANSE/VOF-solver), the coupling of both simulation methods is introduced. Two different methods of coupling are presented: a) at a given position in the wave tank; b) at a given time step. WAVETUB is used to simulate the propagation of the wave train from the start towards the coupling position (case A) or until wave breaking is encountered (case B). Subsequently, the velocity field and the contour of the free surface is handed over as boundary (case A) or initial values (case B) to the RANSE/VOF-solver and the simulation process is continued. To validate these approaches, different types of model seas for investigating wave/structure interactions are generated in a physical wave tank and compared to the numerical simulations.Copyright © 2005 by ASME

Experimental Optimization of Extreme Wave Sequences for the Deterministic Analysis of Wave/Structure Interaction

Abstract: For the deterministic analysis of wave/structure interaction in the sense of cause-reaction chains, and for analyzing structure responses due to special wave sequences (e.g. three sisters phenomenon or other rogue wave groups) methods for the precise generation of tailored wave sequences are required. Applying conventional wave generation methods, the creation of wave trains satisfying given local wave parameters and the generation of wave groups with predefined characteristics is often difficult or impossible, if sufficient accuracy is required. In this paper we present an optimization approach for the experimental generation of wave sequences with defined characteristics. The method is applied to generate scenarios with a single high wave superimposed to irregular seas. The optimization process is carried out in a small wave tank. The resulting control signal is then transferred to a large wave tank considering the electrical, hydraulic and hydrodynamical RAOs of the respective wave generator in order to investigate wave/structure interaction at a large scale.Copyright © 2005 by ASME

A wavelet-based algorithm to estimate ocean wave group parameters from radar images

Abstract: In recent years, new remote sensing techniques have been developed to measure two-dimensional (2-D) sea surface elevation fields. The availability of these data has led to the necessity to extend the classical analysis methods for one-dimensional (1-D) buoy time series to two dimensions. This paper is concerned with the derivation of group parameters from 2-D sea surface elevation fields using a wavelet-based technique. Wave grouping is known to be an important factor in ship and offshore safety, as it plays a role in dangerous resonance phenomenons and the generation of extreme waves. Synthetic aperture radar (SAR) data are used for the analysis. The wavelet technique is introduced using synthetic ocean surfaces and simulated SAR data. It is shown that the group structure of the ocean wave field can be recovered from the SAR image if the nonlinear imaging effects are moderate. The method is applied to a global dataset of European Remote Sensing satellite (ERS-2) wave mode data. Different group parameters including the area covered by the largest group and the number of groups in a given area are calculated for over 33 000 SAR images. Global maps of the parameters are presented. For comparison, classical 1-D grouping parameters are calculated from colocated wave model data showing good overall agreement with the wavelet-derived parameters. ERS-2 image mode data are used to study wave fields in coastal areas. Waves approaching the island of Sylt in the North Sea are investigated, showing the potential of the wavelet technique to analyze the spatial wave dynamics associated with the bottom topography. Observations concerning changes of wavelength and group parameters are compared to linear wave theory.

On the Profile of Large Ocean Waves

Abstract: Wave data obtained from simulations in an offshore basin and from field measurements were used to provide an assessment of the adequacy of describing the most likely time trace profile around large ocean wave crests based on the information provided by the autocorrelation function. It was concluded that the model is adequate in linear cases, but in high sea states, where nonlinear behaviour is apparent it starts becoming less appropriate.Copyright © 2003 by ASME

Rogue Wave Impact on Marine Structures

Abstract: In this work, the mystery of Rogue Waves is revealed and the impact of these waves on marine structures is investigated. The aim of this thesis is the development and application of methods for the analysis of Rogue Wave impacts. Examples of recorded Rogue Waves are given and the frequency of occurrence is examined by analyzing a five day storm measured in the North Sea. For the realization of deterministic Rogue Waves scenarios in the model basin a linear optimization approach is proposed, synthesizing extreme wave sequences based on predefined parameters. In order to improve the accuracy of the generated wave sequences an experimental optimization method is introduced fitting the wave sequences measured in the wave basin precisely to the target parameter. Resultant wave environments of the optimizations are applied for the analysis of Rogue Wave impacts on different marine structures. In particular, the motions and bending moments of an FPSO and of a crane vessel as well as the motions and splitting forces of a semisubmersible due to Rogue Waves are investigated. The New Year Wave, a Rogue Wave that was recorded at the Draupner platform located in the North Sea, is realized at model scale and varied in experiment with respect to the local wave height and period. The responses of the structures are assessed by numerical simulations applying state of the art ship motion codes and model test. Resultant motions and structural responses are compared to frequency-domain methods for design and to rules from classification societies and discussed with regard to their applicability to Rogue Wave impacts. For the precise numerical simulation of nonlinear wave propagation, numerical wave tanks based on potential theory and on the Navier-Stokes equations are presented. A new coupling approach for the fast and accurate simulation of nonlinear wave evolution is proposed, combining the advantages of two different numerical strategies.

The shallow water limit of the Zakharov Equation and consequences for (freak) wave prediction

Abstract: Finite amplitude deep-water waves are subject to nonlinear focussing, which when the phases are right, may give rise to giant waves or freak waves. The same process is responsible for the Benjamin-Feir instability. In shallow water, finite amplitude surface-gravity waves generate a current and deviations from the mean surface elevation. This stabilizes the Benjamin-Feir instability and the process of nonlinear focussing ceases to exist when kh < 1.363. This is a well-known property of surface gravity waves (Benjamin, 1967; Whitham, 1974) and, here it is shown for the first time, that the usual starting point for wave evolution studies, namely the Zakharov equation, shares this property as well. Consequences for (freak) wave prediction are pointed out.

Global Loads on an FPSO Induced by a Set of Freak Waves

Abstract: The paper presents a systematic study of the structural loads induced by abnormal waves on a FPSO. This work is a follow-up of a previous investigation that explored the possibility of using freak, abnormal or episodic waves as additional wave load conditions to be considered in the design of ships and offshore platforms. In the previous work, a procedure was developed and implemented to adopt deterministic time series of wave elevation, which may include abnormal waves, as reference design conditions to calculate the wave induced structural loads on ships. An application example was presented for a FPSO subjected to the well known New Year Wave trace that was measured during a severe storm in Central North Sea. In the present paper, the same procedure is applied to obtain the wave induced structural loads on a FPSO, but a systematic investigation is carried out by using a large set of wave traces. These wave traces have been measured at different occasions in the North Sea, additionally at one location in the Central Gulf of Mexico, and they all include episodic freak waves. In this way it is possible to assess the influence of realistic rogue wave characteristics on the wave induced structural loads. Finally, and based on the platform responses to all wave traces, some statistics are produced, regarding the platform responses and structural loads induced by rogue waves.Copyright © 2005 by ASME

Large-scale model study on cylinder groups subject to breaking and nonbreaking waves

Abstract: To investigate group interaction effects on nonbreaking and breaking wave loads on a vertical cylinder as a function of cylinder group configurations and spacing, extensive and systematic large-scale model tests were performed in the Large Wave Channel (GWK) of the Coastal Research Centre (FZK), Hannover. A total of 345 tests, including 15 group configurations with spacing up to three times the cylinder diameter were investigated using regular and irregular nonbreaking wave trains as well as breaking freak waves. The experimental set-up, the test programme and first results of the experiments are reported, showing unexpected interaction effects with regard to the maximum wave loads associated with both breaking and nonbreaking waves.

Properties of Extreme Waves

Abstract: In the safety assessment of both fixed and floating offshore structures it is necessary to ensure that the structure has sufficient strength to withstand the most extreme combination of environmental loads likely to be experienced during the design life. However significant uncertainties remain concerning the characteristics of real, extreme, three-dimensional waves. The research described in this report focuses upon: � Wave crest heights and the potential loss of air gap for fixed structures by examining the distribution of wave crest elevations in storms. � Directional spreading of wave energy and the effect upon particle kinematic field by examining the wave spreading factor, (also known as wave kinematics factor) for translating between 2-D and 3-D seas. In parallel research has been undertaken on wave front steepness using the same full scale data and this is being published [Stansell et al, (2003)]. This report and the work it describes were funded by the Health and Safety Executive (HSE). Its contents, including any opinions and/or conclusions expressed, are those of the authors alone and do not necessarily reflect HSE policy. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means (electronic, mechanical, photocopying, recording or otherwise) without the prior written permission of the copyright owner. ii ACKNOWLEDGEMENTS The authors are grateful to Total for supporting the operation of the environmental monitoring station and data collection programme at North Alwyn platform and to Health and Safety Executive Offshore Safety Division, United Kingdom, for funding this research. The authors are grateful to Jun Zhang and his research group, Ocean Engineering Program, Texas A&M University, USA for the permission to use the Hybrid wave model program. The authors extend their thanks to Marc Prevosto, IFREMER and George Z. Forristall, Shell International exploration and production, The Netherlands, for helpful discussions on the crest height probability models. iii iv CONTENTS Page No. Executive Summary vii 1. Introduction 1 1.1 General background 1 1.2 Project objectives 2 1.3 The North Alwyn Metocean Station and data collection 2 2. Storm Data Analysis 5 2.1 Storm data selection and methodology 5 2.2 Directional spectra and spreading functions 5 2.3 Variations in wave parameters 6 2.4 Variation in other directional parameters during storms 7 2.5 Spreading index 7 2.6 Wave kinematics factor 9 3. Crest Height Distribution 11 3.1 Wave crest height probability 11 3.2 Comparison of …

Deterministic aspects of nonlinear modulation instability

Abstract: Different from statistical considerations on stochastic wave fields, this paper aims to contribute to the understanding of (some of) the underlying physical phenomena that may give rise to the occurence of extreme, rogue, waves. To that end a specific deterministic wavefield is investigated that develops extreme waves from a uniform background. For this explicitly described nonlinear extension of the Benjamin-Feir in- stability, the soliton on finite background of the NLS equation, the global down-stream evolving distortions, the time signal of the extreme waves, and the local evolution near the extreme position are investigated. As part of the search for conditions to obtain extreme waves, we show that the extreme wave has a specific optimization property for the physical energy, and comment on the possible validity for more realistic situations.

On the breaking parameters of signalling problem

Abstract: This research is motivated by the requirement of hydrodynamic laboratories to generate extreme waves for testing ships in steep, large amplitude wave fields It is also desired that such a wave will not break in its spatial evolution before reaching the tested ship position For this purpose, finding criteria that determine if wave breaking will occur is important In the study of wave breaking, Banner etal [1] proposed a non-dimensional quantity that can be interpreted as the dynamic of the maximal square of wave steepness over the spatial domain The investigation uses a simulation model to calculate the evolution of ocean waves for a given initial profile that depends on certain parameters A threshold value for the quantity that marks the breaking of waves was found Different from Banner's initial value problems, in this contribution we will consider the signalling problem: a time signal is prescribed to a wave maker in a wave tank that produces propagating waves running in initially still water The aim is to observe the resulting nonlinear effects on the waves and to study in which cases the waves will or will not break This also leads to a threshold value for the steepness of signal at wavemaker and for adjusted Banner's quantity as the breaking parameter of signalling problem In this observation we consider similar classes of waves as in [1], namely Bichromatic waves and Benjamin Feir-waves, and investigate the evolution by using a numerical simulation code HUBRIS developed by Westhuis [2] The validity of this code has been tested against laboratory experiments The result of our investigations is that for both classes the parameters of wave breaking are more extreme in the signaling case than in the case of Banner's initial value problem

Wave EnergyFocusing in aThree-dimensional Numerical WaveTank

Abstract: Directional wave energy focusing in space is one of the mechanisms that may contribute to the generation of a rogue wave in the ocean. To this effect, in this paper, we study the generation of extreme waves in a three-dimensional numerical wave tank from the motion of a snake wavemaker. The numerical model solves incompressible fully nonlinear free-surface Euler equations for potential flow, using a higher-order Boundary Element Method and a mixed Eulerian-Lagrangian time updating. Recent improvements of this numerical model have consisted in the implementation of the Fast Multipole Algorithm, in order to improve the computational efficiency of the spatial solver. A typical case of a near breaking rogue wave is presented as an application. A description of the particular geometry of such a wave is given, as well as preliminary results for the particle velocities at the surface and under the wave crest.

Extreme Wave Events in a Hydrodynamic Laboratory

Abstract: We adopt the spatial ‘nonlinear Schrodinger’ (NLS) equation as a simple mathematical model for nonlinear surface wave evolution in a wave tank of a hydrodynamic laboratory. This equation has many exact solutions, of which we only study a family of solutions which describes extreme wave events in the laboratory. This solution is known as the ‘Soliton on Finite Background’ (SFB) and it describes the ‘modulation instability’ (Akhmediev and Ankiewicz, 1997). In the context of water waves, this instability is known as the ‘Benjamin-Feir instability’ since Benjamin and Feir (1967) investigated the stability of a modulated wave train both theoretically and experimentally. In this presentation, we focus on the physical properties of the SFB and the comparison with experiments in a wave tank of the Maritime Research Institute Netherlands (MARIN). The SFB in the far field is a ‘continuous wave’ with a constant amplitude 2r0 and a wave frequency ω0, modulated with a modulation frequency ν. While running downstream, this signal becomes an extreme wave event; reaches a large amplitude at a certain position while preserving the modulation period. After passing the extreme position, it continues to evolve downstream to a situation similar to the initial signal. At the position where the SFB is an extreme wave event, there are times at which the real-valued amplitude vanishes and the phase becomes undefined, resulting in a ‘phase singularity’ phenomenon. In one modulation period, there is a pair of these singularities. Due to this phenomenon, the physical wave field shows a ’wavefront dislocation’, when merging waves or splitting waves are observed. The experimental setup is a wave tank of 200 m long, with 3.55 m water depth, a wavemaker on one side, and an absorbing beach on the other side. Wave gauges are installed at several positions to capture signals of the generated wave. Applying the inverse problem and using the ‘maximum temporal amplitude’ (Andonowati and van Groesen, 2003), we designed the initial signal of the SFB such that extreme wave events should occur at a specified position, namely at 150 m from the wavemaker. Due to the discrete positions of the wave gauges, the precise position of the extreme wave cannot be determined very well. However, the experiments showed nonbreaking waves with a large amplitude. These waves have an asymmetric structure compared to the ones from the theoretical SFB. Furthermore, the experimental results also show a phase singularity phenomenon. Yet, instead of a pair of singularities as in the SFB, the experiments show only one singularity in one modulation period (van Groesen et al, 2005; Huijsmans et al, 2005). Keywords: freak wave event, Soliton on Finite Background, phase singularity and wavefront dislocation.