scholarly journals A laboratory study of wave crest statistics and the role of directional spreading

2013 ◽  
Vol 469 (2152) ◽  
pp. 20120696 ◽  
Author(s):  
M. Latheef ◽  
C. Swan
Keyword(s):  
Wave Breaking ◽  
Nonlinear Effects ◽  
Wave Crest ◽  
Third Order ◽  
Sea State ◽  
Profound Influence ◽  
Nonlinear Amplification ◽  
Local Wave ◽  
Crest Height

This paper concerns the crest height statistics arising in sea states that are broad banded in both frequency and direction. A new set of laboratory observations are presented and the results compared with the commonly applied statistical distributions. Taken as a whole, the data confirm that the crest-height distributions are critically dependent upon the directionality of the sea state. Although nonlinear effects arising at third order and above are most pronounced in uni-directional seas, the present data show that they are also important in directionally spread seas, provided the seas are sufficiently steep and not too short crested. The data also highlight the limiting effects of wave breaking. With individual breaking events dependent upon the local wave steepness, the directionality of the sea state again plays a significant role. Indeed, the present observations confirm that the two competing processes of nonlinear amplification and wave breaking can have a profound influence on the crest-height distributions leading to significant departures from established theory. In such cases, the key parameters are the sea state steepness and directional spread; the latter acting to counter the former in terms of nonlinear changes in the crest-height distributions.

scholarly journals Laboratory investigation of crest height statistics in intermediate water depths

2019 ◽  
Vol 475 (2229) ◽  
pp. 20190183 ◽  
Author(s):  
I. Karmpadakis ◽  
C. Swan ◽  
M. Christou
Keyword(s):  
Water Depth ◽  
Wave Breaking ◽  
Field Data ◽  
Full Range ◽  
Second Order ◽  
Intermediate Water ◽  
Sea State ◽  
Nonlinear Amplification ◽  
Effective Water ◽  
Water Depths

This paper concerns the statistical distribution of the crest heights associated with surface waves in intermediate water depths. The results of a new laboratory study are presented in which data generated in different experimental facilities are used to establish departures from commonly applied statistical distributions. Specifically, the effects of varying sea-state steepness, effective water depth and directional spread are investigated. Following an extensive validation of the experimental data, including direct comparisons to available field data, it is shown that the nonlinear amplification of crest heights above second-order theory observed in steep deep water sea states is equally appropriate to intermediate water depths. These nonlinear amplifications increase with the sea-state steepness and reduce with the directional spread. While the latter effect is undoubtedly important, the present data confirm that significant amplifications above second order (5–10%) are observed for realistic directional spreads. This is consistent with available field data. With further increases in the sea-state steepness, the dissipative effects of wave breaking act to reduce these nonlinear amplifications. While the competing mechanisms of nonlinear amplification and wave breaking are relevant to a full range of water depths, the relative importance of wave breaking increases as the effective water depth reduces.

Distribution of Crest Amplitudes in Severe Seas With Breaking

1993 ◽  
Vol 115 (1) ◽  
pp. 9-15 ◽  
Author(s):  
D. L. Kriebel ◽  
T. H. Dawson
Keyword(s):  
Theoretical Model ◽  
Probability Distribution ◽  
Wave Breaking ◽  
Laboratory Data ◽  
Selective Reduction ◽  
Wave Crest ◽  
Wave Spectra ◽  
Sea State ◽  
Subsequent Modification ◽  
Nonlinear Increase

A theoretical model is presented for the probability distribution of wave crest amplitudes in severe seas states with wave breaking. As the severity of a sea state increases, nonlinearities cause an increase in the amplitudes of the largest wave crests with a subsequent modification of the distribution of wave crest amplitudes from the linear Rayleigh theory. In this paper, a theory for the probabilities of these nonlinear crest amplitudes is first reviewed based on earlier work. The further limitations on these nonlinear crest amplitudes by wave breaking are then considered. As a result, a theoretical model is presented to account for both: 1) the nonlinear increase in the highest wave crests, and 2) the selective reduction of some fraction of these high crests due to wave breaking. This model is then verified using several sets of laboratory data for severe breaking seas having approximate JONSWAP wave spectra.

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.

Efficient Computation of Nonlinear Crest Distributions for Irregular Stokes Waves

2016 ◽  
Vol 19 (4) ◽  
pp. 881-903
Author(s):  
Ying-Guang Wang
Keyword(s):  
Numerical Algorithm ◽  
Computer Code ◽  
Transformation Model ◽  
Wave Crest ◽  
Efficient Computation ◽  
Distribution Models ◽  
Sea State ◽  
Model Match ◽  
Stokes Waves ◽  
Crest Height

AbstractThis paper concerns the computation of nonlinear crest distributions for irregular Stokes waves, and a numerical algorithm based on the Fast Fourier Transform (FFT) technique has been developed for carrying out the nonlinear computations. In order to further improve the computational efficiency, a new Transformed Rayleigh procedure is first proposed as another alternative for computing the nonlinear wave crest height distributions, and the corresponding computer code has also been developed. In the proposed Transformed Rayleigh procedure, the transformation model is chosen to be a monotonic exponential function, calibrated such that the first three moments of the transformed model match the moments of the true process. The numerical algorithm based on the FFT technique and the proposed Transformed Rayleigh procedure have been applied for calculating the wave crest distributions of a sea state with a Bretschneider spectrum and a sea statewith the surface elevation datameasured at the Poseidon platform. It is demonstrated in these two cases that the numerical algorithm based on the FFT technique and the proposed Transformed Rayleigh procedure can offer better predictions than those from using the empirical wave crest distribution models. Meanwhile, it is found that our proposed Transformed Rayleigh procedure can compute nonlinear crest distributions more than 25 times faster than the numerical algorithm based on the FFT technique.

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 Methodology for Calculating Wave Crest Enhancement in Extreme Seas

2013 ◽  
Author(s):  
Bruce Martin ◽  
Oriol Rijken
Keyword(s):  
Enhancement Factor ◽  
Wave Train ◽  
Irregular Waves ◽  
Wave Crest ◽  
Local Enhancement ◽  
Sea State ◽  
Incoming Wave ◽  
Numerical Predictions ◽  
Very High ◽  
Crest Height

The deck height of a tension leg platform or semi-submersible depends in large part on the expected crest height. This expected crest height is the result of the sea state, i.e. the incoming wave train, and local enhancement due to the vessels diffraction of the wave train. These local enhancements are usually determined by a combination of numerical computations and model tests. Quite often a crest enhancement factor is defined which takes into consideration these local amplification effects. Extrapolating the enhancement factor from extreme conditions to survival conditions may lead to significantly large crests and result in a very high deck elevation. Many studies, including the CresT JIP address the characteristics of the crests within a given sea state and in the absence of a vessel. This paper addresses the effect of the presence of a vessel on the crest heights, and in particular the high crests which will ultimately determine deck height. The paper is based on experimental measurements of wave elevations underneath and around various tension leg platforms and semi submersibles. The investigated sea states comprise of a series of long crested irregular waves, generated in a model basin, which describe extreme and survival conditions in the Gulf of Mexico. The crest heights underneath the vessel are measured and compared with crests which occur without the presence of the vessel. Numerical predictions of the local amplification are also made, based on 1st order diffraction analysis and the as-measured incident wave train. A narrative is provided on the differences in crest height and observed phenomena.

Effect of Short-Crestedness on Extreme Wave Impact: A Summary of Findings From the Joint Industry Project “ShorTCresT”

2015 ◽  
Author(s):  
Janou Hennig ◽  
Jule Scharnke ◽  
Chris Swan ◽  
Øistein Hagen ◽  
Kevin Ewans ◽  
...  
Keyword(s):  
Wave Breaking ◽  
Good Description ◽  
Spectral Characteristics ◽  
Offshore Structures ◽  
Wave Crest ◽  
Extreme Waves ◽  
Extreme Wave ◽  
Wave Impact ◽  
Directional Model

Long-crested waves are typically used in the design of offshore structures. However, the corresponding statistics, kinematics and loading are significantly different in short-crested waves and up to date, there is no state-of-the-art methodology to apply short-crested models instead. The objective of the “ShortCresT” Joint Industry Project was to take into account short-crestedness in the design of offshore structures against extreme waves based on a good description of their spectral characteristics, statistics, kinematics, breaking and loading and to deliver (empirical) design recommendations and methods. This paper gives an overview of the findings of ShorTCresT regarding wave crest and height distributions, a comparison of basin and field data, the role of wave breaking, the most realistic directional model, hindcast models as well as the related platform loading.

scholarly journals Assessment of Numerical Methods for Plunging Breaking Wave Predictions

2021 ◽  
Vol 9 (3) ◽  
pp. 264
Author(s):  
Shanti Bhushan ◽  
Oumnia El Fajri ◽  
Graham Hubbard ◽  
Bradley Chambers ◽  
Christopher Kees
Keyword(s):  
Solitary Wave ◽  
Wave Breaking ◽  
Large Scale ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Wave Crest ◽  
Breaking Wave ◽  
Rans Turbulence Models ◽  
Run Up ◽  
Better Than

This study evaluates the capability of Navier–Stokes solvers in predicting forward and backward plunging breaking, including assessment of the effect of grid resolution, turbulence model, and VoF, CLSVoF interface models on predictions. For this purpose, 2D simulations are performed for four test cases: dam break, solitary wave run up on a slope, flow over a submerged bump, and solitary wave over a submerged rectangular obstacle. Plunging wave breaking involves high wave crest, plunger formation, and splash up, followed by second plunger, and chaotic water motions. Coarser grids reasonably predict the wave breaking features, but finer grids are required for accurate prediction of the splash up events. However, instabilities are triggered at the air–water interface (primarily for the air flow) on very fine grids, which induces surface peel-off or kinks and roll-up of the plunger tips. Reynolds averaged Navier–Stokes (RANS) turbulence models result in high eddy-viscosity in the air–water region which decays the fluid momentum and adversely affects the predictions. Both VoF and CLSVoF methods predict the large-scale plunging breaking characteristics well; however, they vary in the prediction of the finer details. The CLSVoF solver predicts the splash-up event and secondary plunger better than the VoF solver; however, the latter predicts the plunger shape better than the former for the solitary wave run-up on a slope case.

scholarly journals A Unified Mathematical Formalism for First to Third Order Dielectric Response of Matter: Application to Surface-Specific Two-Colour Vibrational Optical Spectroscopy

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 153 ◽  
Author(s):  
Christophe Humbert ◽  
Thomas Noblet
Keyword(s):  
Dielectric Response ◽  
Structure And Properties ◽  
Linear Optics ◽  
Third Order ◽  
Mathematical Functions ◽  
Sum Frequency ◽  
Non Linear Optics ◽  
Non Linear ◽  
Light Excitation

To take advantage of the singular properties of matter, as well as to characterize it, we need to interact with it. The role of optical spectroscopies is to enable us to demonstrate the existence of physical objects by observing their response to light excitation. The ability of spectroscopy to reveal the structure and properties of matter then relies on mathematical functions called optical (or dielectric) response functions. Technically, these are tensor Green’s functions, and not scalar functions. The complexity of this tensor formalism sometimes leads to confusion within some articles and books. Here, we do clarify this formalism by introducing the physical foundations of linear and non-linear spectroscopies as simple and rigorous as possible. We dwell on both the mathematical and experimental aspects, examining extinction, infrared, Raman and sum-frequency generation spectroscopies. In this review, we thus give a personal presentation with the aim of offering the reader a coherent vision of linear and non-linear optics, and to remove the ambiguities that we have encountered in reference books and articles.

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