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

2011 ◽  
Vol 133 (3) ◽  
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.

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

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.

Statistical Analysis of a Set of Basin Waves

2011 ◽  
Author(s):  
Jule Scharnke ◽  
Janou Hennig
Keyword(s):  
Statistical Analysis ◽  
Wave Height ◽  
Water Depth ◽  
Water Waves ◽  
Rayleigh Distribution ◽  
Second Order ◽  
Distribution Functions ◽  
Wave Crest ◽  
Intermediate Water ◽  
Wave Measurements

In a recent paper the effect of variations in calibrated wave parameters on wave crest and height distributions was analyzed (OMAE2010-20304, [1]). Theoretical distribution functions were compared to wave measurements with a variation in water depth, wave seed (group spectrum) and location of measurement for the same initial power spectrum. The wave crest distribution of the shallow water waves exceeded both second-order and Rayleigh distribution. Whereas, in intermediate water depth the measured crests followed the second order distribution. The distributions of the measured waves showed that different wave seeds result in the same wave height and crest distributions. Measured wave heights were lower closer to the wave maker. In this paper the results of the continued statistical analysis of basin waves are presented with focus on wave steepness and their influence on wave height and wave crest distributions. Furthermore, the sampling variability of the presented cases is assessed.

scholarly journals Evolution of a Random Directional Wave and Freak Wave Occurrence

2009 ◽  
Vol 39 (3) ◽  
pp. 621-639 ◽  
Author(s):  
Takuji Waseda ◽  
Takeshi Kinoshita ◽  
Hitoshi Tamura
Keyword(s):  
Wave Height ◽  
Wave Interaction ◽  
Northwest Pacific ◽  
Frequency Bandwidth ◽  
Extreme Wave ◽  
Spectral Parameters ◽  
Freak Wave ◽  
Resonant Wave ◽  
Directional Wave ◽  
Wind Sea

Abstract The evolution of a random directional wave in deep water was studied in a laboratory wave tank (50 m long, 10 m wide, 5 m deep) utilizing a directional wave generator. A number of experiments were conducted, changing the various spectral parameters (wave steepness 0.05 < ɛ < 0.11, with directional spreading up to 36° and frequency bandwidth 0.2 < δk/k < 0.6). The wave evolution was studied by an array of wave wires distributed down the tank. As the spectral parameters were altered, the wave height statistics change. Without any wave directionality, the occurrence of waves exceeding twice the significant wave height (the freak wave) increases as the frequency bandwidth narrows and steepness increases, due to quasi-resonant wave–wave interaction. However, the probability of an extreme wave rapidly reduces as the directional bandwidth broadens. The effective Benjamin–Feir index (BFIeff) is introduced, extending the BFI (the relative magnitude of nonlinearity and dispersion) to incorporate the effect of directionality, and successfully parameterizes the observed occurrence of freak waves in the tank. Analysis of the high-resolution hindcast wave field of the northwest Pacific reveals that such a directionally confined wind sea with high extreme wave probability is rare and corresponds mostly to a swell–wind sea mixed condition. Therefore, extreme wave occurrence in the sea as a result of quasi-resonant wave–wave interaction is a rare event that occurs only when the wind sea directionality is extremely narrow.

Wave Statistics in Nonlinear Sea States

2011 ◽  
Author(s):  
Mohamed Latheef ◽  
Chris Swan
Keyword(s):  
Empirical Distribution ◽  
Nonlinear Effects ◽  
Rayleigh Distribution ◽  
Second Order ◽  
Wave Crest ◽  
Statistical Distributions ◽  
Sea State ◽  
Wave Statistics ◽  
Wave Basin ◽  
Wave Heights

This paper concerns the statistical distribution of both wave crest elevations and wave heights in deep water. A new set of laboratory observations undertaken in a directional wave basin located in the Hydrodynamics laboratory in the Department of Civil and Environmental Engineering at Imperial College London is presented. The resulting data were analysed and compared to a number of commonly applied statistical distributions. In respect of the wave crest elevations the measured data is compared to both linear and second-order order distributions, whilst the wave heights were compared to the Rayleigh distribution, the Forristall (1978) [1] empirical distribution and the modified Glukhovskiy distribution ([2] and [3]). Taken as a whole, the data confirms that the directionality of the sea state is critically important in determining the statistical distributions. For example, in terms of the wave crest statistics effects beyond second-order are most pronounced in uni-directional seas. However, if the sea state is sufficiently steep, nonlinear effects arising at third order and above can also be significant in directionally spread seas. Important departures from Forristall’s empirical distribution for the wave heights are also identified. In particular, the data highlights the limiting effect of wave breaking in the most severe seas suggesting that many of the commonly applied design solutions may be conservative in terms of crest height and wave height predictions corresponding to a small (10−4) probability of exceedance.

Observations of Surface Wave–Current Interaction

2017 ◽  
Vol 47 (3) ◽  
pp. 615-632 ◽  
Author(s):  
Leonel Romero ◽  
Luc Lenain ◽  
W. Kendall Melville
Keyword(s):  
Surface Wave ◽  
Gulf Of Mexico ◽  
Wave Height ◽  
Significant Wave Height ◽  
Second Order ◽  
Wave Crest ◽  
Significant Wave ◽  
Wave Statistics ◽  
Whitecap Coverage ◽  
Current Interaction

AbstractWave–current interaction can result in significant inhomogeneities of the ocean surface wave field, including modulation of the spectrum, wave breaking rates, and wave statistics. This study presents novel airborne observations from two experiments: 1) the High-Resolution Air–Sea Interaction (HiRes) experiment, with measurements across an upwelling jet off the coast of Northern California, and 2) an experiment in the Gulf of Mexico with measurements of waves interacting with the Loop Current and associated eddies. The significant wave height and slope varies by up to 30% because of these interactions at both sites, whereas whitecap coverage varies by more than an order of magnitude. Whitecap coverage is well correlated with spectral moments, negatively correlated with the directional spreading, and positively correlated with the saturation. Surface wave statistics measured in the Gulf of Mexico, including wave crest heights and lengths of crests per unit surface area, show good agreement with second-order nonlinear approximations, except over a focal area. Similarly, distributions of wave heights are generally bounded by the generalized Boccotti distribution, except at focal regions where the wave height distribution reaches the Rayleigh distribution with a maximum wave height of 2.55 times the significant wave height, which is much larger than the standard classification for extreme waves. However, theoretical distributions of spatial statistics that account for second-order nonlinearities approximately bound the observed statistics of extreme wave elevations. The results are discussed in the context of improved models of breaking and related air–sea fluxes.

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

2015 ◽  
Vol 373 (2033) ◽  
pp. 20140113 ◽  
Author(s):  
J. R. Grice ◽  
P. H. Taylor ◽  
R. Eatock Taylor
Keyword(s):  
Return Period ◽  
Incident Wave ◽  
Wave Structure ◽  
Diffraction Theory ◽  
Second Order ◽  
Trapped Modes ◽  
Extreme Wave ◽  
Sea State ◽  
Second Order Statistics ◽  
Column Structure

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.

Effects of Two-Peak Spectra on Wave Crest Statistics

2003 ◽  
Author(s):  
Elzbieta M. Bitner-Gregersen ◽  
O̸istein Hagen
Keyword(s):  
Frequency Spectrum ◽  
Time Domain ◽  
Second Order ◽  
Wave Crest ◽  
Wave Statistics ◽  
Wind Sea ◽  
2D And 3D ◽  
Jonswap Spectrum

Effects of two-peak spectra on the second order wave statistics is investigated by second order time domain simulations. Particular attention is given to the wave crest statistics. The two-peak Torsethaugen frequency spectrum (1996) currently used by the Norwegian industry is adopted. Both 2D and 3D seas are considered, and for 3D different directional spreading functions for wind sea and swell are applied. The results for the Torsethaugen frequency spectrum are compared with prediction given by the JONSWAP spectrum and the 2nd order Forristall (2000) crest model.

The Spatial Analysis of an Extreme Wave in a Model Basin

2007 ◽  
Author(s):  
Bas Buchner ◽  
Radboud van Dijk ◽  
Arjan Voogt
Keyword(s):  
Wave Propagation ◽  
Wave Spectrum ◽  
Normal Wave ◽  
Rayleigh Distribution ◽  
Order Theory ◽  
Second Order ◽  
Wave Crest ◽  
Extreme Waves ◽  
Extreme Wave ◽  
Linear Dispersion

As a pilot study into the understanding of the occurrence of extreme waves, the spatial development of an extreme wave (Ac/Hs = 1.59) in a model basin was investigated. This wave occurred in a wave spectrum that was not extremely steep and non-linear. It is observed that the extreme wave develops in less than half the wavelength from a relatively normal wave into an extreme crest. The wave crest stays high and constant over a large distance (almost 75m). Linear dispersion is not able to predict the wave propagation towards the observed extreme wave crest. Second order theory improves the prediction of the crest amplitude, but not enough. The crest amplitude is still underestimated. This is confirmed by the plots of the probability of extremes. The linear Rayleigh distribution underestimates the crest amplitudes. The second order distribution follows the measurements much better, but also in this case typically the highest 10 crests in a 3 hours storm are underestimated.

Wavelet Analysis of an Extreme Wave in a Model Basin

2008 ◽  
Author(s):  
Kevin Ewans ◽  
Bas Buchner
Keyword(s):  
Phase Locking ◽  
Spectral Characteristics ◽  
Nonlinear Effects ◽  
Wave Crest ◽  
Order Effects ◽  
Extreme Wave ◽  
Average Spectrum ◽  
Propagating Waves ◽  
Wave Event ◽  
High Frequency Waves

Analyses of laboratory wave records including extreme crests, based on the continuous wavelet transform, are reported. The analyses have provided further insight into the spectral characteristics of these extreme events. During the period of the extreme wave crest, spectral levels over all frequencies are substantially elevated by comparison with average spectrum for the complete wave record. This was also observed in a similar analysis of the famous New Year wave event that occurred at the Draupner platform. The analyses also indicate that nonlinear effects are active during the crest event, second-order effects being particular strong and indicating phase-locking of high frequency waves to freely-propagating waves with frequencies close to the spectral peak. These nonlinear effects appear to be strong only in the vicinity of the extreme.

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