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.

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.

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.

Wave Height Distribution in Mixed Sea States

2001 ◽  
Vol 124 (1) ◽  
pp. 34-40 ◽  
Author(s):  
German Rodriguez ◽  
C. Guedes Soares ◽  
Mercedes Pacheco ◽  
E. Pe´rez-Martell
Keyword(s):  
Wave Height ◽  
Probabilistic Models ◽  
Simulated Data ◽  
Peak Frequency ◽  
Frequency Separation ◽  
Height Distribution ◽  
Zero Crossing ◽  
Frequency Wave ◽  
Wave Height Distribution ◽  
Wave Heights

The statistical distribution of zero-crossing wave heights in Gaussian mixed sea states is examined by analyzing numerically simulated data. Nine different kinds of bimodal scalar spectra are used to study the effects of the relative energy ratio and the peak frequency separation between the low and high frequency wave fields on the wave height distribution. Observed results are compared with predictions of probabilistic models adopted in practice. Comparisons of the empirical data with relevant probabilistic models reveals that the Rayleigh model systematically overestimates the number of observed wave heights larger than the mean wave height, except for one of the cases analyzed. None of the models used to predict the observed exceedance probabilities is able to characterize adequately all cases of bimodal sea states examined here.

scholarly journals PREDICTION METHOD FOR THE WAVE HEIGHT DISTRIBUTION OEF THE WESTERN COAST OE TAIWAN

1984 ◽  
Vol 1 (19) ◽  
pp. 31 ◽  
Author(s):  
Frederick L.W. Tang ◽  
Jea-Tzyy Juang
Keyword(s):  
Wave Height ◽  
Prediction Method ◽  
Distribution Model ◽  
Western Coast ◽  
Height Distribution ◽  
North West ◽  
The North ◽  
Wave Height Distribution ◽  
Wave Heights ◽  
The Western Pacific

Taiwan Strait locates on the continental shelf of the western Pacific Ocean. The water depth is less than 100 meters. Furthermore, the bathemetry of the eastern side namely the offing of western coast of Taiwan shoals gradually. In consequence, in case of the wind "blows from the north to south, waves in the deeper part of the strait refract to he north west direction while they are approaching the shore and local waves directly generated by the wind still keep the same direction of the wind. The situation is shown in Figure 1. Erom September to April of the next year, anticyclones come from Mongolia causes monsoon in this area. The wind velocity in the monsoon sometimes exceeds 20 meters per second, but it is arround 10 meters per second in general. Howerer, the duration of winds over 5 meters per second has been recorded more than 50 days. Engineering works such as towing caissons for building breakwater as well as dredging offshore have to be done in these days. Furthermore, navigation operations should not be stopped unless the wind is too strong. Of course, waves are forecast every day, however, more precise information about the probability of the occurrence of certain wave height is of great significance. In last conference, the authors submitted a probability density function of wave heights in this area. This distribution model is to be remended by considering energy loss in this paper, and concrete forecasting procedure is submitted for engineering and navigation practice.

scholarly journals WAVE HEIGHT DISTRIBUTION IN CONSTANT AND FINITE DEPTHS

2012 ◽  
Vol 1 (33) ◽  
pp. 15 ◽  
Author(s):  
Sofia Caires ◽  
Marcel R.A. Van Gent
Keyword(s):  
Shallow Water ◽  
Wave Height ◽  
Wave Breaking ◽  
Rayleigh Distribution ◽  
Height Distribution ◽  
High Wave ◽  
Wave Height Distribution ◽  
Individual Wave ◽  
Wave Heights

Several alternatives to the Rayleigh distribution have been proposed for describing individual wave heights in regions where depth-induced wave breaking occurs. The most widely used of these is the so-called Battjes and Groenendijk distribution. This distribution has been derived and validated in a context of a shallow water foreshore waves propagating over a gently sloping shallow region towards the shore. Its validity for waves propagating in regions with shallow flat bottoms is investigated here. It is concluded that the distribution on average underestimates (outside its range of validity) high wave height measurements in shallow flat bottoms by as much as 15%.

Maximum Wave Height Distribution in a Sea State: Effects of Record Length and Spectral Peakedness

2004 ◽  
Author(s):  
Germa´n Rodri´guez ◽  
Mercedes Pacheco ◽  
Carlos Guedes Soares
Keyword(s):  
Probability Distribution ◽  
Wave Height ◽  
Spectral Shape ◽  
Height Distribution ◽  
Sea State ◽  
Maximum Wave Height ◽  
Record Length ◽  
State Duration ◽  
Long Duration ◽  
Wave Height Distribution

The probability distribution of the maximum wave height in a sea state is examined in terms of the spectral peakedness and the sea state duration. The study is based on the analysis of numerically simulated gaussian wave records with given target spectra to fulfill the long duration and stationarity jointly required conditions, seldom found in nature. Results indicate a clear dependence of the probability distribution structure and location on the record length and the spectral shape.

scholarly journals WAVE HEIGHT DISTRIBUTION AND WAVE GROUPING IN SURF ZONE

1982 ◽  
Vol 1 (18) ◽  
pp. 4 ◽  
Author(s):  
Hajime Mase ◽  
Yuichi Iwagaki
Keyword(s):  
Wave Height ◽  
Surf Zone ◽  
Irregular Waves ◽  
Wave Transformation ◽  
Height Distribution ◽  
Frequency Distributions ◽  
Irregular Wave ◽  
Wave Height Distribution ◽  
Wave Heights ◽  
Deep Water Wave

The main purpose of this paper is to propose a model for prediction of the spatial distributions of representative wave heights and the frequency distributions of wave heights of irregular waves in shallow-water including the surf zone. In order to examine the validity of the model, some experiments of irregular wave transformation have been made. In addition, an attempt has been made to clarify the spatial distribution of wave grouping experimentally. Especially the present paper focuses finding the effects of the bottom slope and the deep-water wave steepness on the wave height distribution and wave grouping.

scholarly journals ATTENUATION OF WAVE INDUCED OSCILLATION IN PORTS BY IMPROVING THE CONDITIONS AT THE HARBOR ENTRANCE

1984 ◽  
Vol 1 (19) ◽  
pp. 196
Author(s):  
M. Kubo ◽  
S. Aoki ◽  
J.J. Avitia Segura
Keyword(s):  
Numerical Method ◽  
Wave Height ◽  
Arbitrary Shape ◽  
Height Distribution ◽  
Remarkable Effect ◽  
Wave Height Distribution ◽  
Wave Heights ◽  
Wave Induced

The authors developed the numerical method to calculate the wave height distribution around a pair of breakwaters with arbitrary shape of the edge. The effect of the resonators equipped in the breakwaters on the diffracted wave height is simulated by using this method. Simulated results show that the resonators have remarkable effect to reduce wave heights in a harbor. However, in the experiments, resonators are not so effective as predicted by the theory.

scholarly journals Modeling extreme wave heights from laboratory experiments with the nonlinear Schrödinger equation

2013 ◽  
Vol 1 (5) ◽  
pp. 5261-5293 ◽  
Author(s):  
H. D. Zhang ◽  
C. Guedes Soares ◽  
Z. Cherneva ◽  
M. Onorato
Keyword(s):  
Schrödinger Equation ◽  
Numerical Simulations ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Laboratory Experiments ◽  
Nonlinear Schrodinger Equation ◽  
Extreme Wave ◽  
Nonlinear Schrödinger ◽  
Wave Basin ◽  
Wave Heights

Abstract. Spatial variation of nonlinear wave groups with different initial envelope shapes is theoretically studied first, confirming that the simplest nonlinear theoretical model is capable of describing the evolution of propagating wave packets in deep water. Moreover, three groups of laboratory experiments run in the wave basin of CEHIPAR are systematically compared with the numerical simulations of the nonlinear Schrödinger equation. Although a small overestimation is detected, especially in the set of experiments characterized by higher initial wave steepness, the numerical simulations still display a high degree of agreement with the laboratory experiments. Therefore, the nonlinear Schrödinger equation catches the essential characteristics of the extreme waves and provides an important physical insight into their generation. The modulation instability, resulted by the quasi-resonant four wave interaction in a unidirectional sea state, can be indicated by the coefficient of kurtosis, which shows an appreciable correlation with the extreme wave height and hence is used in the modified Edgeworth-Rayleigh distribution. Finally, some statistical properties on the maximum wave heights in different sea states have been related with the initial Benjamin-Feir Index.

Correction for Bias in Return Values of Wave Heights Caused by Hindcast Uncertainty

2011 ◽  
Author(s):  
Ed Mackay
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Case Studies ◽  
Wave Height ◽  
Error Distribution ◽  
Height Distribution ◽  
Wave Height Distribution ◽  
Wave Heights ◽  
Measured Distribution ◽  
Iterative Deconvolution

Hindcasts of wave conditions can be subject to large uncertainties, especially in storms. Even if estimates of extremes are unbiased on average, the variance of the errors can lead to a bias in estimates of extremes derived from hindcast data. The convolution of the error distribution and wave height distribution causes a stretching of the measured distribution. This can lead to substantial positive biases in estimates of return values. An iterative deconvolution procedure is proposed to estimate the size of the bias, based on the measured distribution and knowledge of the error distribution. The effectiveness of the procedure is illustrated in several case studies using Monte Carlo simulation.

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