Effects of Second-Order Extreme Waves on the Dynamics of a Non-Linear Floating Body

2012 ◽  
Author(s):  
Vincenzo Nava ◽  
Felice Arena
Keyword(s):  
Wave Model ◽  
Second Order ◽  
Floating Body ◽  
Linear Wave ◽  
Mooring Lines ◽  
Large Wave ◽  
Non Linear ◽  
Rigid Body Model ◽  
Time Domains ◽  
Structural Nonlinearities

Nowadays technical and scientific communities are increasingly interested in the development of technologies for floating devices which can serve different purposes both in coastal and offshore environment. Thus, strong effort is required in the development of correct and efficient algorithms for studying the behavior of such structures under the action of sea wave loadings. At this purpose, in the past few years several approaches were investigated, both in frequency and in time domains, using linear and non-linear structural models and linear and non-linear wave theories. In this note, the effects of nonlinearities in the wave model on the dynamics of a non-linear floating rigid body model are calculated using the second-order Quasi-Determinism (QD) theory (see [1], [2]; [3]) under the action of extremely high waves. Structural nonlinearities consist essentially in non linear damping and nonlinear stiffness due to mooring lines, following the model shown in Nava & Arena, [4]. Numerical nonlinear simulations were performed by means of an algorithm based on the approach showed in Zheng et al. [5], and the results compared to those provided by the nonlinear QD theory. The purpose of this note is to show not only the effects of nonlinearities in the behavior of a floating body and to compare them with those obtained from a linear approach, but also to estimate them through non linear QD theory under the occurrence of a large wave in order to evaluate the reliability of the proposed approach.

scholarly journals Non-linear wave data assimilation with an ANN-type wind-wave model and Ensemble Kalman Filter (EnKF)

2010 ◽  
Vol 34 (8) ◽  
pp. 1984-1999 ◽  
Author(s):  
Ahmadreza Zamani ◽  
Ahmadreza Azimian ◽  
Arnold Heemink ◽  
Dimitri Solomatine
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Wind Wave ◽  
Wave Model ◽  
Linear Wave ◽  
Wave Data ◽  
Non Linear

Flexible Riser Response Induced by Springing of an FPSO Hull

2007 ◽  
Author(s):  
Jelena Vidic-Perunovic ◽  
Niels J. Risho̸j Nielsen ◽  
Haiwen Zhang
Keyword(s):  
High Frequency ◽  
Wave Spectrum ◽  
Analytical Form ◽  
Second Order ◽  
Wave Frequency ◽  
Natural Vibration Frequency ◽  
Linear Wave ◽  
Flexible Riser ◽  
Excitation Wave ◽  
Non Linear

The hydrodynamic analysis of the flexible riser for offshore application is usually limited to the first order wave frequency motions of the floating vessel that holds the riser top end. In this paper effort is made to investigate the influence of non-linear second order springing deflection of the production vessel hull on flexible riser response. The system selected in this study consists of a free-hanging flexible riser configuration attached to an FPSO. Due to resonance between the excitation wave frequency and the natural vibration frequency of the hull, second order flexible vertical motions of the FPSO increase. This may influence the riser loads, presumably the tension force. Vertical motions including the second order high frequency contribution are assigned to the flexible riser at a point of attachment to the vessel. To account for the environmental loading, irregular sea is applied, characterized by modified linear wave spectrum. Second order excitation wave spectrum is truncated by use of WAFO routines for random second order wave simulation and an analytical form of the spectrum that accounts for the non-linear wave effects is proposed. Several environmental conditions are examined in order to consolidate the tendency in riser behaviour. The significance of the high-frequency quadratic terms in the loads along the flexible riser is discussed.

Non-Linear Wave Diffraction Around a Moored Ship

2004 ◽  
Author(s):  
J. Zang ◽  
R. Gibson ◽  
P. H. Taylor ◽  
R. Eatock Taylor ◽  
C. Swan
Keyword(s):  
Wave Diffraction ◽  
Scattering Problem ◽  
Wave Interaction ◽  
Wave Structure ◽  
Second Order ◽  
Linear Wave ◽  
Wave Impact ◽  
Non Linear ◽  
Focused Wave ◽  
Run Up

The objective of this research, part of the FP5 REBASDO Programme, is to examine the effects of directional wave spreading on the nonlinear hydrodynamic loads and the wave run-up around the bow of a floating vessel (FPSO) in random seas. In this work, the non-linear wave scattering problem is solved by employing a quadratic boundary element method. An existing scheme (DIFFRACT developed in Oxford) has been extended to deal with uni-directional and directional bi-chromatic input wave systems, calculating second-order wave diffraction under regular waves and focused wave groups. The second order wave interaction with a floating vessel in a unidirectional focused wave group is presented in this paper. Comparison of numerical results and the experimental measurements conducted at Imperial College shows excellent agreement. The second-order free surface components at the bow of the ship are very significant, and cannot be neglected if one requires accurate prediction of the wave-structure interaction; otherwise a major underestimation of the wave impact on the structure could occur.

An Approach to Calculate the Probability of Wave Impact on an FPSO Bow

2004 ◽  
Author(s):  
C. Guedes Soares ◽  
R. Pascoal ◽  
E. M. Anta˜o ◽  
A. J. Voogt ◽  
B. Buchner
Keyword(s):  
Impact Load ◽  
Second Order ◽  
Experimental Program ◽  
Ship Motions ◽  
Linear Wave ◽  
Wave Steepness ◽  
Wave Impact ◽  
Non Linear ◽  
Local Wave ◽  
The Impact

This work aims at characterizing the probability of wave impact and expected impact load on the bow geometry of an FPSO. In order to determine the instants when impact occurs, an experimental program was performed on a specific bow shape. The bow was instrumented with pressure transducers and the test program, also making use of video recordings, was designed such that it was possible to determine the correlation between undisturbed wave shape and the impact pressure time traces. It has been found that wave impact at the bow is highly correlated with the local wave steepness, which for very high waves has at least second order effects. A comparison between the probability distributions of local wave steepness of the experimental undisturbed wave time trace and numerical simulations of second order wave theory is provided and it confirmed that the latter is very adequate for calculations. The experimental results were further used to determine how the probability of impact varies with free surface vertical velocity. It was found that the significant wave height of the sea state itself does not have significant influence on the result and a regression model is derived for that type of bow. The proposed model for determining the probability of impact load is based on combining both models. The analytical nature makes it fast and easy to expand to other cases of interest and some example calculations are shown to demonstrate the relative ease of the procedure proposed. The position of the impact is determined by the non-linear wave crests and the ship motions. The ship motions can be determined based on a linear response to the non-linear waves considered.

scholarly journals COUPLING STOKES AND CNOIDAL WAVE THEORIES IN A NONLINEAR REFRACTION MODEL

1988 ◽  
Vol 1 (21) ◽  
pp. 42
Author(s):  
Thomas A. Hardy ◽  
Nicholas C. Kraus
Keyword(s):  
Nonlinear Refraction ◽  
Wave Model ◽  
Wave Theory ◽  
Quantitative Agreement ◽  
Wave Mode ◽  
Finite Amplitude ◽  
Second Order ◽  
Stokes Wave ◽  
Linear Wave ◽  
Cnoidal Wave

An efficient numerical model is presented for calculating the refraction and shoaling of finite-amplitude waves over an irregular sea bottom. The model uses third-order Stokes wave theory in relatively deep water and second-order cnoidal wave theory in relatively shallow water. It can also be run using combinations of lower-order wave theories, including a pure linear wave mode. The problem of the connection of Stokes and cnoidal theories is investigated, and it is found that the use of second-order rather than first-order cnoidal theory greatly reduces the connection discontinuity. Calculations are compared with physical model measurements of the height and direction of waves passing over an elliptical shoal. The finite-amplitude wave model gives better qualitative and quantitative agreement with the measurements than the linear model.

The evolution of large ocean waves: the role of local and rapid spectral changes

2006 ◽  
Vol 463 (2077) ◽  
pp. 21-48 ◽  
Author(s):  
R.S Gibson ◽  
C Swan
Keyword(s):  
Wave Spectrum ◽  
Wave Model ◽  
Ocean Waves ◽  
Order Theory ◽  
Second Order ◽  
Large Wave ◽  
Wave Event ◽  
Focused Wave ◽  
Wave Models ◽  
Directional Sea States

This paper concerns the formation of large-focused or near-focused waves in both unidirectional and directional sea-states. When the crests of wave components of varying frequency superimpose at one point in space and time, a large, transient, focused wave can occur. These events are believed to be representative of the largest waves arising in a random sea and, as such, are of importance to the design of marine structures. The details of how such waves form also offer an explanation for the formation of the so-called freak or rogue waves in deep water. The physical mechanisms that govern the evolution of focused waves have been investigated by applying both the fully nonlinear wave model of Bateman et al . (Bateman et al . 2001 J. Comput. Phys . 174 , 277–305) and the Zakharov's evolution equation (Zakharov 1968 J. Appl. Mech. Tech. Phys . 9 , 190–194). Aspects of these two wave models are complementary, and their combined use allows the full nonlinearity to be considered and, at the same time, provides insights into the dominant physical processes. In unidirectional seas, it has been shown that the local evolution of the wave spectrum leads to larger maximum crest elevations. In contrast, in directional seas, the maximum crest elevation is well predicted by a second-order theory based on the underlying spectrum, but the shape of the largest wave is not. The differences between the evolution of large waves in unidirectional and directional sea-states have been investigated by analysing the results of Bateman et al . (2001) using a number of spectral analysis techniques. It has been shown that during the formation of a focused wave event, there are significant and rapid changes to the underlying wave spectrum. These changes alter both the amplitude of the wave components and their dispersive properties. Importantly, in unidirectional sea-states, the bandwidth of the spectrum typically increases; whereas, in directional sea-states it decreases. The changes to the wave spectra have been investigated using Zakharov's equation (1968). This has shown that the third-order resonant effects dominate changes to both the amplitude of the wave components and the dispersive properties of the wave group. While this is the case in both unidirectional and directional sea-states, the consequences are very different. By examining these consequences, directional sea-states in which large wave events that are higher and steeper than second-order theory would predict have been identified. This has implications for the types of sea-states in which rogue waves are most likely to occur.

Wave Statistics for Intermediate Depth Water: New Waves and Symmetry

2002 ◽  
Author(s):  
P. H. Taylor ◽  
B. A. Williams
Keyword(s):  
Linear Part ◽  
Wave Theory ◽  
Order Theory ◽  
Small Degree ◽  
Second Order ◽  
Linear Wave ◽  
Intermediate Water ◽  
Wave Statistics ◽  
Non Linear ◽  
The Hilbert Transform

A study has been made into the average shape of large crests and troughs during several storms using wave elevation data from the WACSIS measurement programme. The analysis techniques adopted were data-driven at all times, in order to test whether 2nd order wave theory could reproduce important features in the field data. The sea surface displayed obvious non-linear behaviour, reflected in the fact that the shapes of crests were always sharper and larger than their trough equivalents. Assuming that the dominant non-linear correction is second order in the wave steepness (but without a knowledge of the detailed form of 2nd order theory), the average shapes of maxima in the underlying linear wave components were shown to match NewWave. This NewWave is the scaled auto-correlation function for a linear random process with the same power spectrum as the measured waves. Thus, NewWave was shown to be an acceptable model for the linear part of large waves on intermediate water depth (here ∼17m). Assuming that NewWave is a good model for the linear part of large crests and troughs, a value for the second order coefficient required to estimate crest elevation statistics was derived from the measured data for several storms. This coefficient was in good agreement with the results of the 2nd order random simulations of Forristall and Prevosto. As well as studying vertical asymmetry, required for crest and trough statistics, horizontal asymmetry was examined using the Hilbert transform. Compared to a large amount of vertical asymmetry, the analysis showed that there was virtually no horizontal asymmetry for the bulk of the waves in the records. However, there is a very small degree of horizontal asymmetry exhibited in the largest waves in the records. Thus, given a surface elevation record, it is difficult to distinguish the direction of the time axis, again consistent with most of the non-linearity being due to simple 2nd order bound waves.

scholarly journals Directional Coherent Wave Group From an Assimilated Non-linear Wavefield

2021 ◽  
Vol 9 ◽  
Author(s):  
Takuji Waseda ◽  
Shogo Watanabe ◽  
Wataru Fujimoto ◽  
Takehiko Nose ◽  
Tsubasa Kodaira ◽  
...  
Keyword(s):  
Wave Field ◽  
Wave Model ◽  
Linear Wave ◽  
Wave Group ◽  
Wave Groups ◽  
Radar Images ◽  
Coherent Wave ◽  
Non Linear ◽  
Directional Wave ◽  
Reconstructed Wave

The presence of coherent wave groups in the ocean has been so far postulated but still lacks evidence other than the indication from the radar images. Here, we attempt to reconstruct a wave field to monitor the evolution of a directional wave group based on a phase resolving two-dimensional non-linear wave model constrained by the stereo images of the ocean surface. The reconstructed wave field of around 20 wavelength squared revealed a coherent wave group compact in both propagating and transverse directions. The envelope of the wave group seems to be oriented obliquely to the propagation direction, somewhat resembling the directional soliton that was theoretically predicted and experimentally and numerically reproduced recently. A comparison with a constrained linear wave model demonstrated the coherence of the non-linear wave group that propagates for tens of wavelengths. The study elaborates a possibility of a spatially coherent short crested wave group in the directional sea.

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