Second-order statistics and ‘designer’ waves for violent free-surface motion around multi-column structures

Extreme wave–structure interactions are investigated using second-order diffraction theory. The statistics of surface elevation around a multi-column structure are collected using Monte Carlo-type simulations for severe sea states. Within the footprint of a realistic four-column structure, we find that the presence of the structure can give rise to extreme crest elevations greater than twice those at the same return period in the incident wave field. Much of this extra elevation is associated with the excitation of second-order near-trapped modes. A ‘designer’ incident wave can be defined at each point around the structure for a given sea state as the average input wave to produce extreme crest elevations at a given return period, and we show that this wave can be simply vertically scaled to estimate the response at other return periods.

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Characterization of Extreme Wave Conditions for Wave Energy Converter Design and Project Risk Assessment

Journal of Marine Science and Engineering ◽

10.3390/jmse8040289 ◽

2020 ◽

Vol 8 (4) ◽

pp. 289 ◽

Cited By ~ 4

Author(s):

Vincent S. Neary ◽

Seongho Ahn ◽

Bibiana E. Seng ◽

Mohammad Nabi Allahdadi ◽

Taiping Wang ◽

...

Keyword(s):

Return Period ◽

Wave Energy ◽

Wave Energy Converter ◽

Extreme Value Analysis ◽

Extreme Wave ◽

Energy Converter ◽

Sea State ◽

Value Analysis ◽

Wave Conditions ◽

Wave Models

Best practices and international standards for determining n-year return period extreme wave (sea states) conditions allow wave energy converter designers and project developers the option to apply simple univariate or more complex bivariate extreme value analysis methods. The present study compares extreme sea state estimates derived from univariate and bivariate methods and investigates the performance of spectral wave models for predicting extreme sea states at buoy locations within several regional wave climates along the US East and West Coasts. Two common third-generation spectral wave models are evaluated, a WAVEWATCH III® model with a grid resolution of 4 arc-minutes (6–7 km), and a Simulating WAves Nearshore model, with a coastal resolution of 200–300 m. Both models are used to generate multi-year hindcasts, from which extreme sea state statistics used for wave conditions characterization can be derived and compared to those based on in-situ observations at National Data Buoy Center stations. Comparison of results using different univariate and bivariate methods from the same data source indicates reasonable agreement on average. Discrepancies are predominantly random. Large discrepancies are common and increase with return period. There is a systematic underbias for extreme significant wave heights derived from model hindcasts compared to those derived from buoy measurements. This underbias is dependent on model spatial resolution. However, simple linear corrections can effectively compensate for this bias. A similar approach is not possible for correcting model-derived environmental contours, but other methods, e.g., machine learning, should be explored.

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The Second Order Statistics of High Waves in Wind Sea and Swell

Volume 2: Structures, Safety and Reliability; Petroleum Technology Symposium ◽

10.1115/omae2007-29676 ◽

2007 ◽

Author(s):

Peter Tromans ◽

Luc Vanderschuren ◽

Kevin Ewans

Keyword(s):

Wave Height ◽

Probabilistic Method ◽

Second Order ◽

Wave Crest ◽

Extreme Wave ◽

Type Method ◽

Second Order Statistics ◽

Linear Effects ◽

Wind Sea ◽

Steep Waves

The statistics of extreme wave crest elevation and wave height have been calculated for realistic, directionally spread sea and swell using a probabilistic method tested and described previously. The non-linearity of steep waves is modelled to second order using Sharma and Dean kinematics and a response surface (reliability type) method is used to deduce the crest elevation or wave height corresponding to a given probability of exceedance. The effects of various combinations of sea and swell are evaluated. As expected, in all cases, non-linearity makes extreme crests higher than the corresponding linear ones. The non-linear effects on wave height are relatively small.

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The Second Order Statistics of High Waves in Wind Sea and Swell

Journal of Offshore Mechanics and Arctic Engineering ◽

10.1115/1.2979799 ◽

2011 ◽

Vol 133 (3) ◽

Cited By ~ 1

Author(s):

Peter Tromans ◽

Luc Vanderschuren ◽

Kevin Ewans

Keyword(s):

Wave Height ◽

Probabilistic Method ◽

Nonlinear Effects ◽

Second Order ◽

Wave Crest ◽

Extreme Wave ◽

Type Method ◽

Second Order Statistics ◽

Wind Sea ◽

Steep Waves

The statistics of extreme wave crest elevation and wave height have been calculated for realistic, directionally spread sea and swell using a probabilistic method tested and described previously. The nonlinearity of steep waves is modeled to the second order using Sharma and Dean kinematics, and a response surface (reliability type) method is used to deduce the crest elevation or wave height corresponding to a given probability of exceedance. The effects of various combinations of sea and swell are evaluated. As expected, in all cases, nonlinearity makes extreme crests higher than the corresponding linear ones. The nonlinear effects on the wave height are relatively small.

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Second-Order Vertical Diffraction Forces on Truncated Cylinders

Journal of Offshore Mechanics and Arctic Engineering ◽

10.1115/1.2833914 ◽

1996 ◽

Vol 118 (4) ◽

pp. 259-266 ◽

Cited By ~ 3

Author(s):

D. C. Weggel ◽

J. M. Roesset ◽

M.-H. Kim

Keyword(s):

Aspect Ratio ◽

Incident Wave ◽

Diffraction Theory ◽

Second Order ◽

Wave Frequency ◽

Double Frequency ◽

Order Diffraction ◽

Parametric Studies ◽

Truncated Cylinders ◽

Force Components

A number of parametric studies were performed on a series of single, truncated cylinders in deep water using second-order potential theory. The cylinders were subjected to a monochromatic incident wave field. Second-order vertical diffraction force components were computed and plotted to illustrate their variation with cylinder aspect ratio and incident wave frequency. These plots make it possible to obtain rough estimates of vertical second-order diffraction force quantities on cylindrical components without having to perform second-order diffraction theory computations. The double-frequency heave response amplitude operator RAO(2) for a freely floating truncated cylinder is presented as a function of cylinder aspect ratio and incident wave frequency. Calculations of the RAO(2) were made using the total double-frequency diffraction force and the first-order radiation coefficients evaluated at the double-frequency.

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Springing Analysis of Elastic Vessels in Head and Oblique Seas Including Nonlinear Effects Due to Second Order Diffraction Pressures

23rd International Conference on Offshore Mechanics and Arctic Engineering, Volume 1, Parts A and B ◽

10.1115/omae2004-51518 ◽

2004 ◽

Author(s):

Haiping He ◽

Armin W. Troesch ◽

Yung Sup Shin ◽

Boo-Ki Kim

Keyword(s):

Theoretical Calculations ◽

Bending Moment ◽

Nonlinear Effects ◽

Diffraction Theory ◽

Ocean Waves ◽

Second Order ◽

Sea State ◽

Zero Crossing ◽

Sum Frequency ◽

State Dependent

The wave-induced vibration of the ship hull, commonly called springing, may not produce extreme stresses, but it is likely to have a direct effect on fatigue-life estimates due to its high frequency content. This research investigates the second order contribution to the springing bending moment from the sum frequency of incident ocean waves in both head and oblique seas. The computer program developed here extends the ABS SSRS (Ship Spring Response System) program to oblique seas using Troesch’s oblique sea linear diffraction theory [1]. The theoretical calculations for forward speed are modified by an empirical factor to correlate more closely with experimental results. An example calculation on a Bulk Carrier was performed for different heading angles. For one such representative sea state, the overall increase to the total bending moment from the nonlinear, sum-frequency excitation is found to be less than 12%. However, the nonlinear springing (RMS) increases the total RMS springing over the linear springing by more than 5 times in some stations, which has significant implications for fatigue studies. A sea state sweep study (using ITTC spectrum) also shows the springing effects are highly sea state dependent. Overall, springing effects decrease as zero crossing periods increase, which indicates springing is important in sea states with short waves and becomes less significant in sea states with long waves.

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