Second Order Model for Wave Crests Used in Prediction of Green Water Load and Volume on Ships in Random Waves

2005 ◽  
Vol 128 (4) ◽  
pp. 271-275 ◽  
Author(s):  
Hanne Therese Wist ◽  
Dag Myrhaug ◽  
Håvard Rue
Keyword(s):  
Prediction Method ◽  
Second Order ◽  
Green Water ◽  
Wave Crest ◽  
Water Load ◽  
Load Line ◽  
Long Term Prediction ◽  
Height Model ◽  
Crest Height

The probability that a wave crest in a random sea will exceed a specified height has long been recognized as important statistics in practical work, e.g., in predicting green water load and volume on a ship. Nonlinear probability density functions for predicting green water load and volume are presented. The models are based on the parametric model of Ogawa (2003, “Long-Term Prediction Method for the Green Water Load and Volume for an Assessment of the Load Line,” J. Marine Sci. Technol., 7, pp. 137–144) combined with transformation of a second order wave crest height model. The wave crest height model is obtained from second order wave theory for a narrow-banded sea state in combination with transformation of the Rayleigh distribution. Results from the second order models are compared with model tests of a cargo ship presented in Ogawa (2003, “Long-Term Prediction Method for the Green Water Load and Volume for an Assessment of the Load Line,” J. Marine Sci. Technol., 7, pp. 137–144) and the Ogawa models.

Second Order Model for Wave Crests Used in Prediction of Green Water Load and Volume on Ships in Random Waves

2004 ◽  
Author(s):  
Hanne Therese Wist ◽  
Dag Myrhaug ◽  
Ha˚vard Rue
Keyword(s):  
Wave Theory ◽  
Rayleigh Distribution ◽  
Second Order ◽  
Green Water ◽  
Wave Crest ◽  
Random Waves ◽  
Sea State ◽  
Water Load ◽  
Height Model ◽  
Crest Height

The probability that a wave crest in a random sea will exceed a specified height has long been recognized as important statistics in practical work, e.g., in predicting green water load and volume on a ship. Nonlinear probability density functions for predicting green water load and volume are presented. The models are based on the linear model of [1] in combination with transformation of a second order wave crest height model. The wave crest height model is obtained from second order wave theory for a narrow-banded sea state in combination with transformation of the Rayleigh distribution. Results from the models are compared with model tests of a cargo ship presented in [1].

A Super-Long-Term Prediction Method of Earth Polar Motion Based on Spectrum Analysis

2021 ◽  
pp. 619-628
Author(s):  
Weitao Lu ◽  
Lue Chen ◽  
Zhijin Zhou ◽  
Songtao Han ◽  
Tianpeng Ren
Keyword(s):  
Spectrum Analysis ◽  
Polar Motion ◽  
Prediction Method ◽  
Term Prediction ◽  
Long Term Prediction

Prediction of Green Water Events on FPSO Vessels

2003 ◽  
Author(s):  
Alexander Fyfe ◽  
Edward Ballard
Keyword(s):  
Probability Distributions ◽  
Green Water ◽  
Design Stage ◽  
Wave Crest ◽  
Peak Period ◽  
Wave Conditions ◽  
Motion Characteristics ◽  
Central North Sea

Most floating vessels experience some sea states, not necessarily extreme storms, which cause large volumes of green water to flow across the deck. Due to the location of safety critical equipment on the deck of FPSOs, the determination of the likely occurrences and the magnitudes of such events are critical to safe design and operation. A method for the determination of green water heights on the deck of an FPSO has been presented in references 1–5. This paper examines the long-term distributions of heights implied by these references and the identification of sea states in which extreme events are likely to occur. The method is based upon the long term distribution of sea states at the intended location, combined with the motion characteristics of the vessel. Freeboard exceedance at the bow and at a point along the side is considered for two typical FPSO configurations. The methodology presented is widely applicable to many locations but wave conditions typical of the Central North Sea are used by way of illustration. The results presented include long term probability distributions of green water height on deck at locations of interest. Relative contributions of each combination of significant wave height and peak period to the probability of the largest single event in a defined return period are determined and discussed. It is shown that the wave conditions most likely to give rise to the most severe green water events are seldom those characterized by the largest wave crest heights. Instead, there exists a complex dependence on characteristic periods associated with vessel motions and on the long-term occurrences of particular sea states. The ability to predict conditions in which the largest green water events are most likely to occur offers the possibility of providing improved operational guidelines for FPSOs, allowing action to be taken to avoid unfavourable loading conditions and/or vessel headings in certain sea conditions. However, it is also shown that it may be difficult to identify some severe green water sea states from normally available forecast data and hence it is important that appropriate provision is made at the design stage.

New Insights in Extreme Crest Height Distributions: A Summary of the ‘CresT’ JIP

2011 ◽  
Author(s):  
Bas Buchner ◽  
George Forristall ◽  
Kevin Ewans ◽  
Marios Christou ◽  
Janou Hennig
Keyword(s):  
Single Point ◽  
Field Measurements ◽  
Order Theory ◽  
Second Order ◽  
Wave Crest ◽  
Height Distribution ◽  
Extreme Waves ◽  
Wave Height Distribution ◽  
Floating Platforms ◽  
Crest Height

The objective of the CresT JIP was ‘to develop models for realistic extreme waves and a design methodology for the loading and response of floating platforms’. Within this objective the central question was: ‘What is the highest (most critical) wave crest that will be encountered by my platform in its lifetime?’ Based on the presented results for long and short-crested numerical, field and basin results in the paper, it can be concluded that the statistics of long-crested waves are different than those of short-crested waves. But also short-crested waves show a trend to reach crest heights above second order. This is in line with visual observations of the physics involved: crests are sharper than predicted by second order, waves are asymmetric (fronts are steeper) and waves are breaking. Although the development of extreme waves within short-crested sea states still needs further investigation (including the counteracting effect of breaking), at the end of the CresT project the following procedure for taking into account extreme waves in platform design is recommended: 1. For the wave height distribution, use the Forristall distribution (Forristall, 1978). 2. For the crest height distribution, use 2nd order distribution as basis. 3. Both the basin and field measurements show crest heights higher than predicted by second order theory for steeper sea states. It is therefore recommended to apply a correction to the second order distribution based on the basin results. 4. Account for the sampling variability at the tail of the distribution (and resulting remaining possibility of higher crests than given by the corrected second order distribution) in the reliability analysis. 5. Consider the fact that the maximum crest height under a complete platform deck can be considerably higher than the maximum crest at a single point.

Long-Term Area Statistics for Maximum Crest Height Under a Fixed Platform Deck

2018 ◽  
Author(s):  
Øistein Hagen ◽  
Jørn Birknes-Berg ◽  
Ida Håøy Grue ◽  
Gunnar Lian ◽  
Kjersti Bruserud ◽  
...  
Keyword(s):  
Time Series ◽  
North Sea ◽  
Extreme Values ◽  
Second Order ◽  
Irregular Waves ◽  
Scatter Diagram ◽  
Short Term ◽  
Wave Impact ◽  
Crest Height

As offshore reservoirs are depleted, the seabed may subside. Furthermore, the extreme crests estimates are now commonly higher than obtained previously due to improved understanding of statistics of non-linear irregular waves. Consequently, bottom fixed installations which have previously had sufficient clearance between the deck and the sea surface may be in a situation where wave impact with the deck must be considered at relevant probability levels. In the present paper, we investigate the long-term area statistics for maximum crest height under a fixed platform deck for 2nd order short crested and long crested sea based on numerical simulations as a function of platform deck dimension for jackets. The results are for one location in the northern North Sea, but some key results are also reported and verified for a more benign southern North Sea location. Time domain simulations for long crested and short crested waves over a spatial domain with dimension of a platform deck are performed, and relevant statistics for airgap assessment determined. Second order waves are simulated for the different cells in the (Hs, Tp) scatter diagram for Torsethaugen two-peak wave spectrum for long-crested and short-crested sea. A total of 1000 3-hour sea states are generated per cell, and time series generated for 160 spatial points under a platform deck. Short-term and long-term statistics are established for the maximum crest height as function of platform dimension; inline and transverse to the wave direction, and over the area. Results are given for the linear sea and for the second order time series. The annual q-probability estimates for the maximum crest height over area as a function of platform dimension is determined for a location at the Norwegian Continental Shelf by weighting the short-term statistics for the individual cells in the scatter diagram with the long-term probability of occurrence of the sea state. To reduce the number of numerical second order simulations, the effect of excluding cells that have a negligible effect on the long term extreme crest estimate is discussed. The percentiles in the distribution of maximum crest (over area) in design sea states that corresponds to the extreme values obtained from the long-term analysis are determined for long crested and short crested sea. The increase in the extreme crest over an area compared to the point in space estimate is estimated for both linear and second order surface elevation.

Effects of Avoidance of Heavy Weather on the Wave Induced Load on Ships

2006 ◽  
Author(s):  
Zhi Shu ◽  
Torgeir Moan
Keyword(s):  
Green Water ◽  
Vertical Acceleration ◽  
Sea State ◽  
Hull Girder ◽  
Term Prediction ◽  
Strip Theory ◽  
Operational Criteria ◽  
Wave Induced ◽  
Long Term Prediction

This paper is concerned with evaluating the effect of avoidance of heavy weather 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 proposed. The first is based upon the assumption that operational criteria relevant to vertical acceleration, green water and bottom slamming are fulfilled. The second one is based upon the assumption that the sea state forecasts are available to the ship master, and that rerouting is made. And based on the first model considering avoidance of heavy weather and the hydrodynamics results calculated from two codes, the wave induced hull girder loads are obtained. The results are discussed. In particular, the effect of different hydrodynamic codes and various scatter diagrams are assessed. After all, the long term prediction of wave induced hull girder loads considering the effect of avoidance of heavy weather will give a relatively more realistic evaluation of the extreme hull girder loads. Finally the results from ship rules will also be re-evaluated compared with the long term prediction with and without heavy weather avoidance.

Analysis and Applications of Second Order Models for Maximum Crest Height

2002 ◽  
Author(s):  
Harald E. Krogstad ◽  
Stephen F. Barstow
Keyword(s):  
Time Series ◽  
Wave Height ◽  
Water Depth ◽  
Second Order ◽  
Wave Steepness ◽  
Data Set ◽  
Wave Data ◽  
Definite Improvement ◽  
Crest Height

Expressions for the maximum crest height are reviewed and tested on data from five different sensors in the WACSIS data set. The overall agreement is good and the analysis supports that second order models give accurate expressions for the distribution of the maximum crest height for varying water depth and wave steepness. In the second part of the paper, the expressions are combined with the existing extreme crest and wave height framework and applied to sets of time series and long term wave data. It is concluded that the 2nd order models represent a definite improvement over earlier empirical parametrizations.

A Modified Linear Lagrangian Model for Irregular Long-Crested Waves

2009 ◽  
Author(s):  
Se´bastien Fouques ◽  
Carl Trygve Stansberg
Keyword(s):  
Mass Conservation ◽  
Second Order ◽  
Lagrangian Model ◽  
Wave Crest ◽  
Lagrangian Description ◽  
Wave Steepness ◽  
Linear Solution ◽  
Fluid Particles ◽  
Wave Properties ◽  
Crest Height

Wave crest height and steepness are crucial parameters for the design of ships and offshore structures. For irregular sea states, they are commonly predicted by using linear wave theory and a Eulerian description of the fluid motion. This theory only applies when the wave steepness is small and it fails to capture extreme wave events. Such linear solutions can also be extended by including second-order terms in order to provide more realistic wave properties. The paper describes a model for irregular long-crested waves that is based on a modified linear solution derived from a Lagrangian description of the fluid, i.e. by considering the motion of individual fluid particles. Lagrangian solutions have the advantage of showing realistic wave profiles with sharp crests and broad troughs already at the first order, whereas these features only appear at the second order when using the Eulerian approach. Still, a severe drawback with the former is that the mass conservation is not fulfilled exactly. The aim of the modification in the present Lagrangian model is to ensure that the mass conservation is always fulfilled in the solution. This is done by using the second-order residual in the continuity equation to lift up the fluid particles vertically. Comparative investigations of wave properties such as the crest height and the wave steepness are further carried out by making use of both numerical case studies and wave tank recordings. The wave models used in the comparisons include linear and second-order Eulerian solutions as well as the modified linear Lagrangian one.

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