Deterministic and Wind/Wave Modeling: A Comprehensive Approach to Deterministic and Probabilistic Descriptions of Ocean Waves

2012 ◽  
Author(s):  
Alfred R. Osborne
Keyword(s):  
Wind Wave ◽  
Rogue Wave ◽  
Ocean Waves ◽  
Rogue Waves ◽  
Deterministic Equation ◽  
Wave Interactions ◽  
Zakharov Equation ◽  
Wave Modeling ◽  
Discrete Interaction ◽  
Interaction Approximation

Deterministic Modeling of ocean surface rogue waves is often done with highly complex spectral codes for the nonlinear Schrödinger equation and its higher order versions, the Zakharov equation or the full Euler equations in two-space and one-time dimensions. Wind/Wave Modeling is normally conducted with a kinetic equation derived from a deterministic equation: the nonlinear four wave interactions are normally computed with the Discrete Interaction Approximation (DIA) algorithm, the Webb-Resio-Tracy (WRT) algorithm or the full Boltzmann integral. I give an overview of these methods and show how a fully self-consistent approach can simultaneously yield all of these methods while computing a multidimensional Fourier series that contains rogue wave packets as “coherent structures” or “nonlinear Fourier components” in the theory. The methods also lead to hyperfast codes in which deterministic evolution is millions of times faster than traditional spectral codes on a large multicore computer. This method could lead the way to an ideal future in which there are single codes that can simultaneously compute the deterministic and probabilistic evolution of surface waves.

scholarly journals Role of Nonlinear Four-Wave Interactions Source Term on the Spectral Shape

2020 ◽  
Vol 8 (4) ◽  
pp. 251 ◽  
Author(s):  
Sonia Ponce de León ◽  
Alfred R. Osborne
Keyword(s):  
Power Spectrum ◽  
Ocean Waves ◽  
Central Peak ◽  
Spectral Shape ◽  
Wave Interactions ◽  
Standard Code ◽  
Discrete Interaction ◽  
Interaction Approximation ◽  
Very High

The goal of this paper is to investigate the importance of the four-wave nonlinear interactions (SNL4) on the shape of the power spectrum of ocean waves. To this end, the following results are discussed: a number of authors have conducted modern experimental measurements of ocean waves over the past decades and found that the measured power spectrum has (a) a very high central peak (characterized by the parameter γ, developed in the 1970s in the JONSWAP program) and (b) enhanced high-frequency channels which lead to the phenomenon of “bimodality”, also a well-known phenomenon. We discuss how a numerical hindcast of the Draupner storm (1995) with the standard code WAVEWATCH-III with full Boltzmann interactions also reflects these previously experimentally determined spectral shapes. Our results suggest that the use of the full Boltzmann interactions (as opposed to the discrete interaction approximation often employed for forecasting/hindcasting) is important for obtaining this characteristic physical spectral shape of the power spectrum.

scholarly journals Real-world rogue wave probabilities

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Dion Häfner ◽  
Johannes Gemmrich ◽  
Markus Jochum
Keyword(s):  
Real World ◽  
Rogue Wave ◽  
Ocean Waves ◽  
Rogue Waves ◽  
Order Theory ◽  
Linear Superposition ◽  
Sea State ◽  
Single Wave ◽  
The Common ◽  
A Minor

AbstractRogue waves are dangerous ocean waves at least twice as high as the surrounding waves. Despite an abundance of studies conducting simulations or wave tank experiments, there is so far no reliable forecast for them. In this study, we use data mining and interpretable machine learning to analyze large amounts of observational data instead (more than 1 billion waves). This reveals how rogue wave occurrence depends on the sea state. We find that traditionally favored parameters such as surface elevation kurtosis, steepness, and Benjamin–Feir index are weak predictors for real-world rogue wave risk. In the studied regime, kurtosis is only informative within a single wave group, and is not useful for forecasting. Instead, crest-trough correlation is the dominating parameter in all studied conditions, water depths, and locations, explaining about a factor of 10 in rogue wave risk variation. For rogue crests, where bandwidth effects are unimportant, we find that skewness, steepness, and Ursell number are the strongest predictors, in line with second-order theory. Our results suggest that linear superposition in bandwidth-limited seas is the main pathway to “everyday” rogue waves, with nonlinear contributions providing a minor correction. This casts some doubt whether the common rogue wave definition as any wave exceeding a certain height threshold is meaningful in practice.

scholarly journals The choice of optimal Discrete Interaction Approximation to the kinetic integral for ocean waves

2003 ◽  
Vol 10 (4/5) ◽  
pp. 425-434 ◽  
Author(s):  
V. G. Polnikov
Keyword(s):  
Kinetic Equation ◽  
Water Waves ◽  
Wave Spectrum ◽  
Ocean Waves ◽  
Interaction Processes ◽  
Wave Forecast ◽  
Long Time ◽  
Discrete Interaction ◽  
The One ◽  
Interaction Approximation

Abstract. A lot of discrete configurations for the four-wave nonlinear interaction processes have been calculated and tested by the method proposed earlier in the frame of the concept of Fast Discrete Interaction Approximation to the Hasselmann's kinetic integral (Polnikov and Farina, 2002). It was found that there are several simple configurations, which are more efficient than the one proposed originally in Hasselmann et al. (1985). Finally, the optimal multiple Discrete Interaction Approximation (DIA) to the kinetic integral for deep-water waves was found. Wave spectrum features have been intercompared for a number of different configurations of DIA, applied to a long-time solution of kinetic equation. On the basis of this intercomparison the better efficiency of the configurations proposed was confirmed. Certain recommendations were given for implementation of new approximations to the wave forecast practice.

scholarly journals A Two-Scale Approximation for Efficient Representation of Nonlinear Energy Transfers in a Wind Wave Spectrum. Part I: Theoretical Development

2008 ◽  
Vol 38 (12) ◽  
pp. 2801-2816 ◽  
Author(s):  
Donald T. Resio ◽  
William Perrie
Keyword(s):  
Wind Wave ◽  
Wave Spectrum ◽  
Estimation Method ◽  
Finite Depth ◽  
Theoretical Development ◽  
Wave Interactions ◽  
Transfer Rates ◽  
Energy Transfers ◽  
Total Integral ◽  
Discrete Interaction

Abstract A new method for estimating the transfer rates in wind wave spectra is derived and tested, based on a two-scale approximation (TSA) to the total integral for quadruplet wave–wave interactions. Comparisons of this new estimation method to the full integral are given for several idealized spectra, including Joint North Sea Wave Project spectra with different peakednesses, a finite depth case, and cases with perturbations added to underlying parametric spectra. In particular, these comparisons show that the TSA is a significant improvement over the discrete interaction approximation (DIA) in deep water and an even greater improvement in shallow water.

scholarly journals The Fast Discrete Interaction Approximation Concept

2020 ◽  
Author(s):  
Vladislav Polnikov
Keyword(s):  
Numerical Calculation ◽  
World Wide ◽  
Wind Wave ◽  
Nonlinear Evolution ◽  
Wave Model ◽  
Discrete Interaction ◽  
Wave Models ◽  
Active Implementation ◽  
Interaction Approximation ◽  
Approximation Concept

Hasselmann and coauthors proposed the discrete interaction approximation (DIA) as the best tool replacing the nonlinear evolution term in a numerical wind-wave model. Much later, Polnikov and Farina radically improved the original DIA by means of location all the interacting four wave vectors, used in the DIA configuration, exactly at the nodes of the numerical frequency-angular grid. This provides nearly two-times enhancing the speed of numerical calculation for the nonlinear evolution term in a wind-wave model. For this reason, the proposed version of the DIA was called as the fast DIA (FDIA). In this paper we demonstrate all details of the FDIA concept for several frequency-angular numerical grids of high resolution, with the aim of active implementation the FDIA in modern versions of world-wide used wind-wave models.

Occurrence Frequency of a Triple Rogue Wave Group in the Ocean

2020 ◽  
Author(s):  
Elzbieta M. Bitner-Gregersen ◽  
Odin Gramstad ◽  
Anne Karin Magnusson ◽  
Pierre C. Sames
Keyword(s):  
Rogue Wave ◽  
Single Point ◽  
Forecast Model ◽  
Ocean Waves ◽  
Rogue Waves ◽  
Occurrence Frequency ◽  
Wave Group ◽  
Wave Forecast ◽  
Wind Sea ◽  
Three Sisters

Abstract At 18:20 November 30, 2018, a triple rogue wave group was recorded in the central North Sea. These three consecutive rogue waves, subsequently called “Justine Three Sisters”, were recorded at a single point by a SAAB REX radar. The Norwegian Meteorological Institute’s operational wave forecast model and WAMOS marine radar’s measurements show that they appeared in a crossing sea condition with angle between wind sea and swell being 60 degrees, with swell energy much lower than the wind sea energy but with approximately the same peak frequency. We use the nonlinear wave model HOSM (Higher Order Spectral Method) to investigate frequency of occurrence of such an event in the ocean. Input to the simulations has been a wave frequency-directional spectrum generated by the operational wave forecast model of the Norwegian Meteorological Institute having 4 km resolution. The investigations show that occurrence of three consecutive rogue waves at a single point is a very seldom event in the ocean, which can, however, be reproduced in time domain HOSM simulations if sufficient number of realizations is performed. With the HOSM model being able to capture essential physics of ocean waves, we can assume to predict occurrence frequency from simulations. The study demonstrates also the effect of sampling variability on sea surface elevation and illustrates limitation of single point measurements, using the sea state in which “Justine Three Sisters” occurred as an example. Importance of using spacetime statistics in description of ocean waves as well as in design and operations of marine structures is also discussed.

scholarly journals The Fast Discrete Interaction Approximation Concept

Fluids ◽  
2020 ◽  
Vol 5 (4) ◽  
pp. 176
Author(s):  
Vladislav Polnikov
Keyword(s):  
Numerical Calculation ◽  
World Wide ◽  
Wind Wave ◽  
Nonlinear Evolution ◽  
Wave Model ◽  
Discrete Interaction ◽  
Wave Models ◽  
Active Implementation ◽  
Interaction Approximation ◽  
Approximation Concept

Hasselmann and coauthors proposed the discrete interaction approximation (DIA) as the best tool replacing the nonlinear evolution term in a numerical wind–wave model. Much later, Polnikov and Farina radically improved the original DIA by means of location all the interacting four wave vectors, used in the DIA configuration, exactly at the nodes of the numerical frequency–angular grid. This provides a nearly two-times enhancement of the speed of numerical calculation for the nonlinear evolution term in a wind–wave model. For this reason, the proposed version of the DIA was called as the fast DIA (FDIA). In this paper, we demonstrate all details of the FDIA concept for several frequency–angular numerical grids of high-resolution with the aim of active implementation of the FDIA in modern versions of world-wide used wind–wave models.

Advances in Nonlinear Waves With Emphasis on Aspects for Ship Design and Wave Forensics

2013 ◽  
Author(s):  
Alfred R. Osborne
Keyword(s):  
Nonlinear Waves ◽  
Water Waves ◽  
Structural Damage ◽  
Rogue Wave ◽  
Ocean Waves ◽  
Rogue Waves ◽  
Two Dimensions ◽  
Lateral Instability ◽  
Highly Nonlinear ◽  
Directional Sea States

Prof. D. Faulkner emphasized the importance of the study of extreme/rogue waves when he noted that the use of sine waves for computing pressures in the design of ships was no longer tenable, primarily because of the large number of cases where extreme structural damage has been encountered due to highly nonlinear large waves. This perspective resulted in the creation of the European program MaxWave and the subsequent program Extreme Seas soon followed. Recently my own studies of nonlinear effects in water waves at Nonlinear Waves Research Corporation (NWRC) have resulted in a number of successes with regard to the fundamental physical understanding of rogue waves. These studies enlarge our ability to understand the requisite impact of extreme waves on the design of ships. Some of these advances are: (1) The determination of analytical techniques for describing rogue wave packets in two dimensions for random sea states which are directionally spread. (2) The description of wave overturning and breaking in directional sea states with the Type II (lateral) instability. (3) The development of hyperfast computer models for the deterministic simulation of directional sea states. (4) The development of a fast approach for computing the full Boltzmann integral (FBI) for the nonlinear wave/wave interactions in wind/wave models. (5) The identification of the actual physical location in the power spectrum for the nonlinear Fourier rogue wave components. (6) The development of nonlinear Fourier techniques for analyzing times series of ocean waves for the presence of rogue wave states. (7) The development of fully nonlinear directional spectra (in terms of frequency and direction) from arrays of instruments. (8) The development of hindcasting and predicting capability for the assessment of the onset of a rogue sea. I also discuss a number of future developments now underway at NWRC.

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