Impact of Sampling Variability on Sea Surface Characteristics of Nonlinear Waves

2018 ◽  
Author(s):  
Elzbieta M. Bitner-Gregersen ◽  
Odin Gramstad
Keyword(s):  
Wave Model ◽  
Surface Characteristics ◽  
Rogue Waves ◽  
Sea Surface ◽  
Wave Crest ◽  
Linear Wave ◽  
Extreme Wave ◽  
Sampling Variability ◽  
Wave Forecasting ◽  
Jonswap Spectrum

The restricted duration of wave records, usually 20 or 30 minutes, introduces sampling variability, the statistical uncertainty due to limited number of observations, in estimates of sea surface characteristics. This uncertainty may have significant impact on derived wave parameters commonly used in design and marine operations, and quantifying it is also of importance for wave forecasting purposes as well as for investigations of extreme wave events such as rogue waves. The study shows, using numerical simulations, effects of sampling variability on the measures of wave field nonlinearity, the skewness and kurtosis coefficients of sea surface elevation, and on the wave crest. Wave data are simulated by the nonlinear wave model HOSM (Higher Order Spectral Method). The Pierson-Moskowitz and the JONSWAP spectrum with different gamma parameters and different directional energy spreading functions are used in the analysis and their effect on sampling variability estimates is demonstrated. Sea states where rogue waves were recorded in nature are considered. The results are compared with the ones obtained from linear wave model simulations. Consequences of sampling variability on description of sea surface nonlinearity are discussed.

scholarly journals Fully Nonlinear Statistics of Wave Crest Elevation Calculated Using a Spectral Response Surface Method: Applications to Unidirectional Sea States

2007 ◽  
Vol 37 (1) ◽  
pp. 3-15 ◽  
Author(s):  
R. S. Gibson ◽  
C. Swan ◽  
P. S. Tromans
Keyword(s):  
Response Surface ◽  
Response Surface Method ◽  
Time Domain ◽  
Spectral Response ◽  
Wave Model ◽  
Rogue Waves ◽  
Order Theory ◽  
Wave Crest ◽  
Fully Nonlinear ◽  
Surface Method

Abstract This paper concerns the calculation of the probability of exceedance of wave crest elevation. The statistics have been calculated for broadbanded, unidirectional, deep-water sea states by incorporating a fully nonlinear wave model into a spectral response surface method. This is a novel approach to the calculation of statistics and, as all of the calculations are performed in the probability domain, avoids the need for long time-domain simulations. Furthermore, in contrast to theoretical distributions, the broadbanded, fully nonlinear nature of the sea state can be considered. The results have been compared with those of fully nonlinear time-domain simulations and are shown to be in good agreement. The results indicate that in unidirectional seas the crest elevations of the largest waves can be much higher than would be predicted by linear or second-order theory. Hence, the occurrence of locally long crested sea states offers a possible explanation for the formation of freak or rogue waves.

Shape asymmetry of rogue waves

2020 ◽  
Author(s):  
Anna Kokorina ◽  
Alexey Slunyaev
Keyword(s):  
Spectral Characteristics ◽  
Rogue Waves ◽  
Engineering Management ◽  
Wave Crest ◽  
Extreme Wave ◽  
Linear Waves ◽  
Stokes Waves ◽  
Wave Nonlinearity ◽  
The Waves ◽  
Management And Conservation

<p>Direct numerical simulations of the directional sea surface gravity waves are carried out within the framework of the primitive potential equations of hydrodynamics using the High Order Spectral Method. The data obtained for conditions of deep water, the JONSWAP spectrum, and various wave intensities are processed and the results are discussed. The statistical and spectral characteristics of the waves evolve over a long period. The particular asymmetry of the profiles of rogue waves is highlighted. We show that besides the conventional crest-to-trough asymmetry of nonlinear Stokes waves, the extreme events are characterized by a specific combination of the troughs adjacent to the large crest, so that the trough behind the crest is typically deeper than the preceding trough. Surprisingly, the extreme wave crest-to-trough asymmetry and the discrimination between the extreme wave troughs exhibit the tendency to grow when the angle spectrum broadens. This effect contradicts the expectation based on the Benjamin – Feir Index that broad-banded waves should behave similar to linear waves, and hence the asymmetries should diminish.</p><p>                                                                 </p><p>The research is supported by the RSF grant No. 19-12-00253.</p><p> </p><p>A. Kokorina, A. Slunyaev, The effect of wave nonlinearity on the rogue wave lifetimes and shapes. Proc. 14th Int. MEDCOAST Congress on Coastal and Marine Sciences, Engineering, Management and Conservation (Ed. E. Ozhan), Vol. 2, 711-721 (2019).</p>

A CFD Study of Focused Extreme Wave Impact on Decks of Offshore Structures

2014 ◽  
Author(s):  
Xin Lu ◽  
Pankaj Kumar ◽  
Anand Bahuguni ◽  
Yanling Wu
Keyword(s):  
Real World ◽  
Offshore Structures ◽  
Air Gap ◽  
Irregular Waves ◽  
Linear Wave ◽  
Extreme Wave ◽  
Wave Impact ◽  
Loading Test ◽  
Wide Range ◽  
Wave Maker

The design of offshore structures for extreme/abnormal waves assumes that there is sufficient air gap such that waves will not hit the platform deck. Due to inaccuracies in the predictions of extreme wave crests in addition to settlement or sea-level increases, the required air gap between the crest of the extreme wave and the deck is often inadequate in existing platforms and therefore wave-in-deck loads need to be considered when assessing the integrity of such platforms. The problem of wave-in-deck loading involves very complex physics and demands intensive study. In the Computational Fluid Mechanics (CFD) approach, two critical issues must be addressed, namely the efficient, realistic numerical wave maker and the accurate free surface capturing methodology. Most reported CFD research on wave-in-deck loads consider regular waves only, for instance the Stokes fifth-order waves. They are, however, recognized by designers as approximate approaches since “real world” sea states consist of random irregular waves. In our work, we report a recently developed focused extreme wave maker based on the NewWave theory. This model can better approximate the “real world” conditions, and is more efficient than conventional random wave makers. It is able to efficiently generate targeted waves at a prescribed time and location. The work is implemented and integrated with OpenFOAM, an open source platform that receives more and more attention in a wide range of industrial applications. We will describe the developed numerical method of predicting highly non-linear wave-in-deck loads in the time domain. The model’s capability is firstly demonstrated against 3D model testing experiments on a fixed block with various deck orientations under random waves. A detailed loading analysis is conducted and compared with available numerical and measurement data. It is then applied to an extreme wave loading test on a selected bridge with multiple under-deck girders. The waves are focused extreme irregular waves derived from NewWave theory and JONSWAP spectra.

scholarly journals Non-linear wave data assimilation with an ANN-type wind-wave model and Ensemble Kalman Filter (EnKF)

2010 ◽  
Vol 34 (8) ◽  
pp. 1984-1999 ◽  
Author(s):  
Ahmadreza Zamani ◽  
Ahmadreza Azimian ◽  
Arnold Heemink ◽  
Dimitri Solomatine
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Wind Wave ◽  
Wave Model ◽  
Linear Wave ◽  
Wave Data ◽  
Non Linear

scholarly journals Study of the air-sea interactions at the mesoscale: the SEMAPHORE experiment

1996 ◽  
Vol 14 (9) ◽  
pp. 986-1015 ◽  
Author(s):  
L. Eymard ◽  
S. Planton ◽  
P. Durand ◽  
C. Le Visage ◽  
P. Y. Le Traon ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Atmospheric Boundary Layer ◽  
Ocean Circulation ◽  
Wave Model ◽  
Heat Fluxes ◽  
Sea Surface ◽  
Upper Ocean ◽  
Test Model ◽  
Model Simulations ◽  
Drifting Buoys

Abstract. The SEMAPHORE (Structure des Echanges Mer-Atmosphère, Propriétés des Hétérogénéités Océaniques: Recherche Expérimentale) experiment has been conducted from June to November 1993 in the Northeast Atlantic between the Azores and Madeira. It was centered on the study of the mesoscale ocean circulation and air-sea interactions. The experimental investigation was achieved at the mesoscale using moorings, floats, and ship hydrological survey, and at a smaller scale by one dedicated ship, two instrumented aircraft, and surface drifting buoys, for one and a half month in October-November (IOP: intense observing period). Observations from meteorological operational satellites as well as spaceborne microwave sensors were used in complement. The main studies undertaken concern the mesoscale ocean, the upper ocean, the atmospheric boundary layer, and the sea surface, and first results are presented for the various topics. From data analysis and model simulations, the main characteristics of the ocean circulation were deduced, showing the close relationship between the Azores front meander and the occurrence of Mediterranean water lenses (meddies), and the shift between the Azores current frontal signature at the surface and within the thermocline. Using drifting buoys and ship data in the upper ocean, the gap between the scales of the atmospheric forcing and the oceanic variability was made evident. A 2 °C decrease and a 40-m deepening of the mixed layer were measured within the IOP, associated with a heating loss of about 100 W m-2. This evolution was shown to be strongly connected to the occurrence of storms at the beginning and the end of October. Above the surface, turbulent measurements from ship and aircraft were analyzed across the surface thermal front, showing a 30% difference in heat fluxes between both sides during a 4-day period, and the respective contributions of the wind and the surface temperature were evaluated. The classical momentum flux bulk parameterization was found to fail in low wind and unstable conditions. Finally, the sea surface was investigated using airborne and satellite radars and wave buoys. A wave model, operationally used, was found to get better results compared with radar and wave-buoy measurements, when initialized using an improved wind field, obtained by assimilating satellite and buoy wind data in a meteorological model. A detailed analysis of a 2-day period showed that the swell component, propagating from a far source area, is underestimated in the wave model. A data base has been created, containing all experimental measurements. It will allow us to pursue the interpretation of observations and to test model simulations in the ocean, at the surface and in the atmospheric boundary layer, and to investigate the ocean-atmosphere coupling at the local and mesoscales.

scholarly journals Relation between orbital velocities, pressure and surface elevation in non-linear nearshore water waves

2021 ◽  
Author(s):  
Kévin Martins ◽  
Philippe Bonneton ◽  
David Lannes ◽  
Hervé Michallet
Keyword(s):  
Free Surface ◽  
Surface Energy ◽  
Water Waves ◽  
Energy Levels ◽  
Sea Surface ◽  
Surface Elevation ◽  
Linear Wave ◽  
Free Surface Elevation ◽  
High Frequencies ◽  
Non Linear

AbstractThe inability of the linear wave dispersion relation to characterize the dispersive properties of non-linear shoaling and breaking waves in the nearshore has long been recognised. Yet, it remains widely used with linear wave theory to convert between sub-surface pressure, wave orbital velocities and the free surface elevation associated with non-linear nearshore waves. Here, we present a non-linear fully dispersive method for reconstructing the free surface elevation from sub-surface hydrodynamic measurements. This reconstruction requires knowledge of the dispersive properties of the wave field through the dominant wavenumbers magnitude κ, representative in an energy-averaged sense of a mixed sea-state composed of both free and forced components. The present approach is effective starting from intermediate water depths - where non-linear interactions between triads intensify - up to the surf zone, where most wave components are forced and travel approximately at the speed of non-dispersive shallow-water waves. In laboratory conditions, where measurements of κ are available, the non-linear fully dispersive method successfully reconstructs sea-surface energy levels at high frequencies in diverse non-linear and dispersive conditions. In the field, we investigate the potential of a reconstruction that uses a Boussinesq approximation of κ, since such measurements are generally lacking. Overall, the proposed approach offers great potential for collecting more accurate measurements under storm conditions, both in terms of sea-surface energy levels at high frequencies and wave-by-wave statistics (e.g. wave extrema). Through its control on the efficiency of non-linear energy transfers between triads, the spectral bandwidth is shown to greatly influence non-linear effects in the transfer functions between sub-surface hydrodynamics and the sea-surface elevation.

scholarly journals On the physical constraints for the exceeding probability of deep water rogue waves

2021 ◽  
Author(s):  
Saulo Mendes ◽  
Alberto Scotti ◽  
Paul Stansell
Keyword(s):  
Sample Size ◽  
Rogue Wave ◽  
Probability Distributions ◽  
Rogue Waves ◽  
Uneven Distribution ◽  
Large Set ◽  
Sea State ◽  
Sampling Variability ◽  
The North ◽  
Wave Heights

<p><strong>(manuscript accepted into Applied Ocean Research https://www.researchgate.net/publication/344786014)</strong></p><p><strong>Abstract</strong></p><p>Nearly four decades have elapsed since the first efforts to obtain a realistic narrow-banded model for extreme wave crests and heights were made, resulting in a couple of dozen different exceeding probability distributions. These models reflect results of numerical simulations and storm records measured from oil platforms, buoys, and more recently, satellite data. Nevertheless, no consensus has been achieved in either deterministic or operational approaches. Typically, distributions found in the literature analyze a very large set of waves with large variations in sea-state parameters while neglecting homogeneous smaller samples, such that we lack a suitable definition for the sample size and homogeneity of sea variables, also known as sampling variability (Bitner-Gregersen et al., 2020). Naturally, a possible consequence of such sample size inconsistency is the apparent disagreement between several studies regarding the prediction of rogue wave occurrence, as some studies can report less rogue wave heights while others report more rogue waves or the same statistics predicted by Longuet-Higgins (1952), sometimes a combination of the three in the very same study (Stansell, 2004; Cherneva et al., 2005). In this direction, we have obtained a dimensionless parameter capable of measuring how large the deviations in sea state variables can be so that accuracy in wave statistics is preserved.  In particular, we have defined which samples are too heterogeneous to create an accurate description of the uneven distribution of rogue wave likelihood among different storms (Stansell, 2004). Though the literature is rich in physical bounds for single waves, here we describe empirical physical limits for the ensemble of waves (such as the significant steepness) devised to bound these variables within established and prospective wave distributions. Furthermore, this work supplies a combination of sea state parameters that provide guidance on the influence of sea states influence on rogue wave occurrence. Based on these empirical limits, we conjecture a mathematical model for the dependence of the expected maximum of normalized wave heights and crests on the sea state parameters, thus explaining the uneven distribution of rogue wave likelihood among different storms collected by infrared laser altimeters of the North Alwyn oil platform discussed in Stansell (2004). Finally, we demonstrate that for heights and crests beyond 90% of their thresholds (H>2H<sub>1/3</sub> for heights), the exceeding probability becomes stratified, i.e. they resemble layers of probability curves according to each sea state, suggesting the existence of a dynamical definition for rogue waves rather than purely statistical.</p><p> </p><p><strong>References</strong></p><p>Bitner-Gregersen, E. M., Gramstad, O., Magnusson, A., Malila, M., 2020. Challenges in description of nonlinear waves due to sampling variability. J. Mar. Sci. Eng. 8, 279.</p><p>Longuet-Higgins, M., 1952. On the statistical distribution of the heights of sea waves. Journal of Marine Research 11, 245–265.</p><p>Stansell, P., 2004. Distribution of freak wave heights measured in the north sea. Appl. Ocean Res. 26, 35–48.</p><p>Cherneva, Z., Petrova, P., Andreeva, N., Guedes Soares, C., 2005. Probability distributions of peaks, troughs and heights of wind waves measured in the black sea coastal zone. Coastal Engineering 52, 599–615.</p>

scholarly journals Slope distribution in front-back asymmetric stochastic Lagrange time waves

2010 ◽  
Vol 42 (02) ◽  
pp. 489-508 ◽  
Author(s):  
G. Lindgren
Keyword(s):  
Particle Velocity ◽  
Random Fields ◽  
Wave Model ◽  
Linear Wave ◽  
Multivariate Normal ◽  
Ocean Engineering ◽  
Expected Number ◽  
Measuring Station ◽  
Predetermined Level ◽  
The Waves

The stochastic Lagrange wave model is a realistic alternative to the Gaussian linear wave model, which has been successfully used in ocean engineering for more than half a century. In this paper we present the slope distributions and other characteristic distributions at level crossings for asymmetric Lagrange time waves, i.e. what can be observed at a fixed measuring station, thereby extending results previously given for space waves. The distributions are given as expectations in a multivariate normal distribution, and they have to be evaluated by simulation or numerical integration. Interesting characteristic variables are the slope in time, the slope in space, and the vertical particle velocity when the waves are observed close to instances when the water level crosses a predetermined level. The theory has been made possible by recent generalizations of Rice's formula for the expected number of marked crossings in random fields.

Effect of Spectrum Tail Length on Modulational Instability and Freak Wave Occurrence in JONSWAP Sea States

2019 ◽  
Author(s):  
Cagil Kirezci ◽  
Alexander V. Babanin
Keyword(s):  
High Frequency ◽  
Modulational Instability ◽  
Wave Spectrum ◽  
Tail Length ◽  
Shape Parameters ◽  
Extreme Wave ◽  
Freak Wave ◽  
Nonlinear Phase ◽  
Wave Forecasting ◽  
Quantitative Indicators

Abstract In this study, probability of freak wave occurrence due to modulational instability in JONSWAP sea states are investigated. This investigation has been conducted based on the quantitative indicators of instability in wave spectrum, which are two Benjamin-Feir index (BFI) [1,2] with different spectral bandwidth definitions and Π number [3]. Evolution of wave field are simulated using fully nonlinear phase-resolving Chalikov-Sheinin (CS) numerical model [4,5]. Initial sea surface is controlled with JONSWAP shape parameters (α and γ) and random initial phases. Effect of high frequency end of spectrum on modulational instability and freak wave evolution are discussed by considering 4 different tail lengths. According to simulation results, all parameters that are considered here perform as an indicator for the occurrence of extreme events which makes it possible to define a certain interval for indicators, where freak wave occurrence probability is the highest and potentially dangerous, to be possibly used in extreme wave forecasting. Another key finding is that, modulational instability increases when high frequency part of spectrum is present (longer tail) as expected. Nevertheless, after certain nonlinearity, modulational instability is more prone to result in breaking which significantly decreases the probability of occurrence of freak events. Therefore, spectra with shorter tail length result in more dangerous sea states.

scholarly journals Far-Field Characteristics of Linear Water Waves Generated by a Submerged Landslide over a Flat Seabed

2020 ◽  
Vol 8 (3) ◽  
pp. 196
Author(s):  
Haixiao Jing ◽  
Yanyan Gao ◽  
Changgen Liu ◽  
Jingming Hou
Keyword(s):  
Shallow Water ◽  
Water Depth ◽  
Water Waves ◽  
Wave Model ◽  
Linear Wave ◽  
Far Field ◽  
Constant Depth ◽  
Low Froude Number ◽  
Dispersive Model ◽  
Wave Models

Understanding the propagation of landslide-generated water waves is of great help against tsunami hazards. In order to investigate the effects of landslide shapes on the far-field leading wave generated by a submerged landslide at a constant depth, three linear wave models with different degrees of dispersive properties are employed in this study. The linear fully dispersive model is then validated by comparing the results against the experimental data available for landslides with a low Froude number. Three simplified shapes of landslides with the same volume, which are unnatural for a body of incoherent material, are used to investigate the effects of landslide shapes on the far-field properties of the generated leading wave over a flat seabed. The results show that the far-field leading crest over a constant depth is independent of the exact landslide shape and is invalid at a shallow water depth. Therefore, the most popular non-dispersive model (also called the shallow water wave model) cannot be used to reproduce the phenomenon. The weakly dispersive wave model can predict this phenomenon well. If only the leading wave is considered, this model is accurate up to at least μ = h0/Lc = 0.6, where h0 is the water depth and Lc denotes the characteristic length of the landslide.

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