Various experimental wave statistics emerging from a single energy spectrum

2021 ◽  
Author(s):  
Maxime Canard ◽  
Guillaume Ducrozet ◽  
Benjamin Bouscasse
Keyword(s):  
Energy Spectrum ◽  
Wave Field ◽  
Wave Energy ◽  
Spatial Dynamics ◽  
Height Distribution ◽  
Sea State ◽  
Wave Statistics ◽  
Wave Basin ◽  
Crest Height

<p>As it strongly impacts the design of offshore structures, the accurate control of experimental wave fields is of great interest for the ocean engineering community. A significant majority of sea keeping tests are based on the stochastic approach. Long duration runs of irregular design sea states are generated at model scale in numerical or experimental wavetanks. The run duration is carefully chosen to observe the emergence of extreme events. The quality of the wavefield at the domain area of interest is assessed thanks to i) the wave energy spectrum and ii) the crest height distribution. The accurate reproduction of those two quantities stands a difficult process. Numerous complex phenomena such as wave breaking or Benjamin Feir (modulational) instabilities strongly impact the wave field. The shapes of i) the wave spectrum and ii) the tail of crest height distributions significantly evolve along the tank depending i) the wave steepness, ii) the spectral width, iii) the water depth and iv) the directional spreading (for directional sea states) [1, 2, 3].</p><p>The vast majority of the work in this area has focused on reproducing realistic wave energy spectra at the location of interest, assuming the indirect control of wave statistics. The present study intends to question such a characterization of a sea state. We address the problem within the framework of long crested irregular deep water waves generated in an experimental wave tank. In this respect, using the Ecole Centrale de Nantes (ECN) towing tank (140m*5m*3m), a narrow banded sea state has been generated at several locations of a long domain. The shape of the spectrum is accurately controlled thanks to a procedure based on wavemaker motion iterative correction [4]. For such nonlinear wave conditions the statistics along the wave propagation in the tank are known to be enhanced by significant spatial dynamics [1, 3]. As a result, configurations characterized by strictly identical wave spectra lead to the emergence of strongly different crest distributions. The data yielded by the study provide convincing evidence that the characterization of the wave field using the sole energy spectrum is insufficient. Particular attention must be given to the spatial dynamics of the wave field in order to control the wave statistics.</p><p>[1] Janssen, P. A. (2003). Nonlinear four-wave interactions and freak waves. <em>Journal of Physical Oceanography</em>, <em>33</em>(4), 863-884.</p><p>[2] Shemer, L., Sergeeva, A., & Liberzon, D. (2010). Effect of the initial spectrum on the spatial evolution of statistics of unidirectional nonlinear random waves. <em>Journal of Geophysical Research: Oceans</em>, <em>115</em>(C12).</p><p>[3] Onorato, M., Cavaleri, L., Fouques, S., Gramstad, O., Janssen, P. A., Monbaliu, J., ... & Trulsen, K. (2009). Statistical properties of mechanically generated surface gravity waves: a laboratory experiment in a three-dimensional wave basin.</p><p>[4] Canard, M., Ducrozet, G., & Bouscasse, B. (2020, August). Generation of 3-hr Long-Crested Waves of Extreme Sea States With HOS-NWT Solver. In <em>International Conference on Offshore Mechanics and Arctic Engineering</em> (Vol. 84386, p. V06BT06A064). American Society of Mechanical Engineers.</p><p> </p>

Wave Distributions and Sampling Variability

2007 ◽  
Author(s):  
O̸istein Hagen
Keyword(s):  
Wave Height ◽  
Extreme Values ◽  
Height Distribution ◽  
Short Term ◽  
Sea State ◽  
Sampling Variability ◽  
Wave Statistics ◽  
Individual Wave ◽  
Wave Heights ◽  
Crest Height

The paper describes the effect of sampling variability on the predicted extreme individual wave height and the predicted extreme individual crests height for long return periods, such as for the 100-year maximum wave height and 100-year maximum crest height. We show that the effect of sampling variability is different for individual crest or wave height as compared to for significant wave height. The short term wave statistics is modeled by the Forristall crest height distribution and the Forristall wave height distribution [3,4]. Samples from the 3-hour Weibull distribution are simulated for 100.000 years period, and the 100-year extreme values for wave heights and crest heights determined for respectively 20 minute and 3 hour sea states. The simulations are compared to results obtained by probabilistic analysis. The paper shows that state of the art analysis approaches using the Forristall distributions give about unbiased estimates for extreme individual crest or wave height if implemented appropriately. Direct application of the Forristall distributions for 3-hour sea state parameters give long term extremes that are biased low, and it is shown how the short term distributions can be modified such that consistent results for 20 minute and 3 hour sea states are obtained. These modified distributions are expected applicable for predictions based on hindcast sea state statistics and for the environmental contour approach.

scholarly journals Generation of 3-hr Long-Crested Waves of Extreme Sea States With HOS-NWT Solver

2020 ◽  
Author(s):  
Maxime Canard ◽  
Guillaume Ducrozet ◽  
Benjamin Bouscasse
Keyword(s):  
Energy Spectrum ◽  
Wave Energy ◽  
Wave Spectrum ◽  
Wave Structure ◽  
Spatial Discretization ◽  
Ocean Engineering ◽  
Sea State ◽  
Wave Condition ◽  
Highly Nonlinear ◽  
Wave Energy Spectrum

Abstract The accurate control of wave fields generated in experiments and numerical simulations is of great interest for the ocean engineering community. In the context of wave-structure interactions, the recommended practices of classification societies are indeed based on the definition of a wave spectrum, that needs to be reproduced. The present work intends to address this problem from the numerical point of view, using a Numerical Wave Tank equipped with a wavemaker and an absorbing beach, based on the High-Order Spectral method (HOS-NWT). The challenging case of the generation of 3-hours long-crested extreme sea states is studied in details. An iterative procedure to reproduce a target wave spectrum at a given distance from the wavemaker is proposed. The quality of the sea state obtained is evaluated using several criteria defined from spectral quantities. A validation is first performed with a highly nonlinear but non-breaking sea-state. Statistical crest distributions obtained are compared with the Forristall and Huang distributions [1,2]. Then, the Gulf of Mexico 1,000 Year Return Period wave condition is generated. This corresponds to an extreme sea state with significant wave breaking occurrence. The numerical solver needs to be able to account for this phenomenon [3]. The Tian breaking model [4, 5] is calibrated to realistically reproduce the dissipation due to breaking, with particular attention paid to the spatial discretization, enlightening its significant effect on breaking model actions. Consequences on the iterative correction process are studied. The computed statistical quantities appear to be significantly different changing the spatial discretization, while the wave energy spectrum stands the same. It questions the relevance of the characterization of a sea state with the sole wave energy spectrum.

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.

Analysis of Short-Term and Long-Term Wave Statistics by Time Domain Simulations Statistics

2017 ◽  
Author(s):  
Øistein Hagen ◽  
Ida Håøy Grue ◽  
Jørn Birknes-Berg ◽  
Gunnar Lian ◽  
Kjersti Bruserud
Keyword(s):  
Wave Height ◽  
Time Domain ◽  
Statistical Distributions ◽  
Short Term ◽  
Sea State ◽  
Wave Statistics ◽  
Individual Wave ◽  
Wave Heights ◽  
Crest Height

In the design of new structures and assessment of existing structures, short- and long term statistical distributions of wave height, crest height and wave periods, as well as joint distributions, are important for structural integrity assessment. It is important to model the statistical distributions accurately to calculate wave design criteria and to assess fatigue life. A detailed study of the wave statistics for an offshore location at the Norwegian Continental Shelf field is carried out. Extensive time domain simulations for the complete scatter diagram of possible sea states are carried out by a second order wave model. Time series of the surface elevation are generated for JONSWAP and Torsethaugen wave spectra, and for several wave spreading models. Statistics for individual wave heights, crest heights and wave periods are established. The simulated results for the short-term statistics are compared with existing short term models that are commonly used, viz. the Forristal, Næss and Rayleigh wave height distributions, and the Forristall 2nd order crest height distribution. Also, parameterized distributions for wave height and for crest height are fitted to the simulated data. The long-term distributions F(H) and F(C) of all simulated individual wave heights H and crest heights C are determined by weighting the simulations with the long-term probability of occurrence of the sea state. Likewise, the long-term distributions F(Hmax) and F(Cmax) of the maximum simulated individual wave heights Hmax and crest heights Cmax in the sea states are determined. The design criteria for return periods R = 1, 10, 100 and 10 000 years are determined from the appropriate quantile levels. The effect of statistical uncertainty is investigated by comparing the confidence intervals for the estimated extreme values results as function of the number N of 3-hour time domain simulations per sea state for 10<N<500.

Comparison of Distributions of Wave Heights From Nonlinear Schröedinger Equation Simulations and Laboratory Experiments

2013 ◽  
Author(s):  
Huidong Zhang ◽  
Zhivelina Cherneva ◽  
C. Guedes Soares ◽  
Miguel Onorato
Keyword(s):  
Numerical Simulations ◽  
Wave Height ◽  
Laboratory Experiments ◽  
Height Distribution ◽  
Nls Equation ◽  
Sea State ◽  
Wave Height Distribution ◽  
Wave Basin ◽  
Wave Heights ◽  
Deep Water Wave

Numerical simulations of the nonlinear Schrödinger (NLS) equation are performed by using random initial wave conditions characterized by the JONSWAP spectrum and compared with four different sea states generated in the deep water wave basin of Marintek. The comparisons show that the numerical simulations have a high degree of agreement with the laboratory experiments although a little overestimation can be observed, especially in the severe sea state. Thus the simulations still catch the main characteristics of the extreme waves and provide an important physical insight into their generation. The coefficient of kurtosis λ40 presents a similar spatial evolution trend with the abnormal wave density and the nonlinear Gram-Charlier (GC) model is used to predict the wave height distribution. It is demonstrated again that the theoretical approximation based on the GC expansion can describe the larger wave heights reasonably well in most cases. However, if the sea state is severe, wave breaking can significantly decrease the tail of wave height distribution in reality and the discrepancy occurs comparing with the numerical simulation. Moreover, the number of waves also plays an important role on the prediction of extreme wave height.

Comparison of Distributions of Wave Heights From Nonlinear Schröedinger Equation Simulations and Laboratory Experiments

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Huidong Zhang ◽  
Zhivelina Cherneva ◽  
Carlos Guedes Soares ◽  
Miguel Onorato
Keyword(s):  
Numerical Simulations ◽  
Wave Height ◽  
Laboratory Experiments ◽  
Height Distribution ◽  
Sea State ◽  
Large Wave ◽  
Wave Height Distribution ◽  
Wave Basin ◽  
Free Surface Displacement ◽  
Wave Heights

Numerical simulations of the nonlinear Schrödinger (NLS) equation are performed by imposing randomly synthesized free surface displacement at the wave maker characterized by the Joint North Sea Wave Project (JONSWAP) spectrum and compared with four different sea states generated in the deepwater wave basin of Marintek. The comparisons show that the numerical simulations have a high degree of agreement with the laboratory experiments although a little overestimation can be observed, especially in the severe sea state. Thus, the simulations still catch the main characteristics of extreme waves and provide an important physical insight into their generation. The coefficient of kurtosis λ40 presents a similar spatial evolution trend with the abnormal wave density, and the nonlinear Gram–Charlier (GC) model is used to predict the wave height distribution. It is demonstrated again that the theoretical approximation based on the GC expansion can describe large wave heights reasonably well in most cases. However, if the sea state is severe, wave breaking can significantly decrease the actual tail of wave height distribution, and discrepancy occurs when comparing with the numerical simulation. Moreover, the number of waves also plays an important role on the prediction of extreme wave height.

scholarly journals The Underlying Order Induced by Orthogonality and the Quantum Speed Limit

2021 ◽  
Vol 3 (3) ◽  
pp. 376-388
Author(s):  
Francisco J. Sevilla ◽  
Andrea Valdés-Hernández ◽  
Alan J. Barrios
Keyword(s):  
Energy Spectrum ◽  
Energy Distribution ◽  
Finite Time ◽  
Complete Characterization ◽  
Comprehensive Analysis ◽  
Orthogonality Condition ◽  
Speed Limit ◽  
Physical Quantities

We perform a comprehensive analysis of the set of parameters {ri} that provide the energy distribution of pure qutrits that evolve towards a distinguishable state at a finite time τ, when evolving under an arbitrary and time-independent Hamiltonian. The orthogonality condition is exactly solved, revealing a non-trivial interrelation between τ and the energy spectrum and allowing the classification of {ri} into families organized in a 2-simplex, δ2. Furthermore, the states determined by {ri} are likewise analyzed according to their quantum-speed limit. Namely, we construct a map that distinguishes those ris in δ2 correspondent to states whose orthogonality time is limited by the Mandelstam–Tamm bound from those restricted by the Margolus–Levitin one. Our results offer a complete characterization of the physical quantities that become relevant in both the preparation and study of the dynamics of three-level states evolving towards orthogonality.

Characterization of Ni/C Multilayers with Fluorescence XAFS Experiments at Fixed Standing Wave Field Positions

1996 ◽  
Vol 228-231 ◽  
pp. 511-518 ◽  
Author(s):  
D.C. Meyer ◽  
T. Holz ◽  
R. Krawietz ◽  
K. Richter ◽  
B. Wehner ◽  
...  
Keyword(s):  
Wave Field ◽  
Standing Wave ◽  
Standing Wave Field ◽  
Fluorescence Xafs

The cylindrical wave field of wave energy converters

2013 ◽  
Vol 3-4 ◽  
pp. e26-e39 ◽  
Author(s):  
J. Cameron McNatt ◽  
Vengatesan Venugopal ◽  
David Forehand
Keyword(s):  
Wave Field ◽  
Wave Energy ◽  
Cylindrical Wave ◽  
Wave Energy Converters ◽  
Energy Converters
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