scholarly journals Soliton spectra of random water waves in shallow basins

2018 ◽  
Vol 13 (4) ◽  
pp. 40 ◽  
Author(s):  
J.-P. Giovanangeli ◽  
C. Kharif ◽  
Y.A. Stepanyants
Keyword(s):  
Shallow Water ◽  
Wave Field ◽  
Water Waves ◽  
Wind Waves ◽  
Inverse Scattering Method ◽  
Random Wave ◽  
Scattering Method ◽  
Wave Fields ◽  
Fourier Spectra ◽  
Random Wave Field

Interpretation of random wave field on a shallow water in terms of Fourier spectra is not adequate, when wave amplitudes are not infinitesimally small. A nonlinearity of wave fields leads to the harmonic interactions and random variation of Fourier spectra. As has been shown by Osborne and his co-authors, a more adequate analysis can be performed in terms of nonlinear modes representing cnoidal waves; a spectrum of such modes remains unchanged even in the process of nonlinear mode interactions. Here we show that there is an alternative and more simple analysis of random wave fields on shallow water, which can be presented in terms of interacting Korteweg–de Vries solitons. The data processing of random wave field is developed on the basis of inverse scattering method. The soliton component obscured in a random wave field is determined and a corresponding distribution function of number of solitons on their amplitudes is constructed. The approach developed is illustrated by means of artificially generated quasi-random wave field and applied to the real data interpretation of wind waves generated in the laboratory wind tank.

Large-time evolution of statistical moments of wind–wave fields

2013 ◽  
Vol 726 ◽  
pp. 517-546 ◽  
Author(s):  
Sergei Y. Annenkov ◽  
Victor I. Shrira
Keyword(s):  
Wave Field ◽  
Large Time ◽  
Random Wave ◽  
Wave Spectra ◽  
Large Time Asymptotics ◽  
Wave Fields ◽  
Weakly Nonlinear ◽  
Time Asymptotics ◽  
Random Wave Field ◽  
Skewness And Kurtosis

AbstractWe study the long-term evolution of weakly nonlinear random gravity water wave fields developing with and without wind forcing. The focus of the work is on deriving, from first principles, the evolution of the departure of the field statistics from Gaussianity. Higher-order statistical moments of elevation (skewness and kurtosis) are used as a measure of this departure. Non-Gaussianity of a weakly nonlinear random wave field has two components. The first is due to nonlinear wave–wave interactions. We refer to this component as ‘dynamic’, since it is linked to wave field evolution. The other component is due to bound harmonics. It is non-zero for every wave field with finite amplitude, contributes both to skewness and kurtosis of gravity water waves and can be determined entirely from the instantaneous spectrum of surface elevation. The key result of the work, supported both by direct numerical simulation (DNS) and by the analysis of simulated and experimental (JONSWAP) spectra, is that in generic situations of a broadband random wave field the dynamic contribution to kurtosis is small in absolute value, and negligibly small compared with the bound harmonics component. Therefore, the latter dominates, and both skewness and kurtosis can be obtained directly from the instantaneous wave spectra. Thus, the departure of evolving wave fields from Gaussianity can be obtained from evolving wave spectra, complementing the capability of forecasting spectra and capitalizing on the existing methodology. We find that both skewness and kurtosis are significant for typical oceanic waves; the non-zero positive kurtosis implies a tangible increase of freak wave probability. For random wave fields generated by steady or slowly varying wind and for swell the derived large-time asymptotics of skewness and kurtosis predict power law decay of the moments. The exponents of these laws are determined by the degree of homogeneity of the interaction coefficients. For all self-similar regimes the kurtosis decays twice as fast as the skewness. These formulae complement the known large-time asymptotics for spectral evolution prescribed by the Hasselmann equation. The results are verified by the DNS of random wave fields based on the Zakharov equation. The predicted asymptotic behaviour is shown to be very robust: it holds both for steady and gusty winds.

scholarly journals Nonlinear random wave field in shallow water: variable Korteweg-de Vries framework

2011 ◽  
Vol 11 (2) ◽  
pp. 323-330 ◽  
Author(s):  
A. Sergeeva ◽  
E. Pelinovsky ◽  
T. Talipova
Keyword(s):  
Shallow Water ◽  
Wave Field ◽  
Large Amplitude ◽  
Rogue Waves ◽  
High Amplitude ◽  
Random Wave ◽  
Flat Bottom ◽  
Wave State ◽  
De Vries ◽  
Random Wave Field

Abstract. The transformation of a random wave field in shallow water of variable depth is analyzed within the framework of the variable-coefficient Korteweg-de Vries equation. The characteristic wave height varies with depth according to Green's law, and this follows rigorously from the theoretical model. The skewness and kurtosis are computed, and it is shown that they increase when the depth decreases, and simultaneously the wave state deviates from the Gaussian. The probability of large-amplitude (rogue) waves increases within the transition zone. The characteristics of this process depend on the wave steepness, which is characterized in terms of the Ursell parameter. The results obtained show that the number of rogue waves may deviate significantly from the value expected for a flat bottom of a given depth. If the random wave field is represented as a soliton gas, the probabilities of soliton amplitudes increase to a high-amplitude range and the number of large-amplitude (rogue) solitons increases when the water shallows.

Retrieval of wave period from altimetry: Deep learning accounting for random wave field dynamics

2021 ◽  
Vol 265 ◽  
pp. 112629
Author(s):  
Jiuke Wang ◽  
Lotfi Aouf ◽  
Sergei Badulin
Keyword(s):  
Deep Learning ◽  
Wave Field ◽  
Wave Period ◽  
Random Wave ◽  
Random Wave Field

scholarly journals Random wave-driven drag forces on near-bed vegetation in shallow water based on deepwater wind conditions

2019 ◽  
Vol 233 (4) ◽  
pp. 1287-1290
Author(s):  
Dag Myrhaug
Keyword(s):  
Shallow Water ◽  
Drag Force ◽  
Wind Waves ◽  
Wave Spectrum ◽  
Random Wave ◽  
Random Waves ◽  
Coastal Zones ◽  
Drag Forces ◽  
Mean Wind Speed ◽  
Wave Induced

This article provides a simple analytical method for giving estimates of random wave-driven drag forces on near-bed vegetation in shallow water from deepwater wind conditions. Results are exemplified using a Pierson–Moskowitz model wave spectrum for wind waves with the mean wind speed at the 10 m elevation above the sea surface as the parameter. The significant value of the drag force within a sea state of random waves is given, and an example typical for field conditions is presented. This method should serve as a useful tool for assessing random wave-induced drag force on vegetation in coastal zones and estuaries based on input from deepwater wind conditions.

Nonlinear Fourier Analysis Algorithm and Models for Water Waves in Terms of Surface Elevation, Amplitude Modulations

2019 ◽  
Author(s):  
Alfred R. Osborne
Keyword(s):  
Synthetic Aperture Radar ◽  
Surface Waves ◽  
Shallow Water ◽  
Wave Field ◽  
Deep Water ◽  
Coherent Structures ◽  
Water Waves ◽  
Surface Elevation ◽  
Synthetic Aperture ◽  
Wave Measurements

Abstract This paper addresses two issues with regard to nonlinear ocean waves. (1) The first issue relates to the often-confused differences between the coordinates used for the measurement and characterization of ocean surface waves: The surface elevation and the complex modulation of a wave field. (2) The second issue relates to the very different kinds of physical wave behavior that occur in shallow and deep water. Both issues come from the known, very different behaviors of deep and shallow water waves. In shallow water one often uses the Korteweg-deVries that describes the wave surface elevation in terms of cnoidal waves and solitons. In deep water one uses the nonlinear Schrödinger equation whose solutions correspond to the complex envelope of a wave field that has Stokes wave and breather solutions. Here I make clear the relationships between the two ways of characterizing surface waves. Furthermore, and more importantly, I address the issues of matching the two types of wave behavior as the wave motion passes from deep to shallow water, or vice versa. For wave measurements we normally obtain the surface elevation with a wave staff, resistance gauge or pressure recorder for getting time series. Remote sensing applications relate to the use of lidar, radar or synthetic aperture radar for obtaining space series. The two types of wave behavior can therefore crucially depend on where the instrument is placed on the “ground track” or “field” over which the lidar or radar measurements are made. Thus the matching problem from deep to shallow water is not only important for wave measurements, but also for wave modeling. Modern wave models [Osborne, 2010, 2018, 2019a, 2019b] that maintain the coherent structures of wave dynamics (solitons, Stokes waves, breathers, superbreathers, vortices, etc.) must naturally pass from deep to shallow water where the nature of the nonlinear physics, and the form of the coherent structures, change. I address these issues and more herein. This paper is directed towards the development of methods for the real time measurement of waves by shipboard radar and for wave measurements by airplane and helicopter using lidar and synthetic aperture radar. Wave modeling efforts are also underway.

scholarly journals On the feasibility of the use of wind SAR to downscale waves on shallow water

Ocean Science ◽  
2016 ◽  
Vol 12 (1) ◽  
pp. 39-49 ◽  
Author(s):  
O. Q. Gutiérrez ◽  
F. Filipponi ◽  
A. Taramelli ◽  
E. Valentini ◽  
P. Camus ◽  
...  
Keyword(s):  
Shallow Water ◽  
Spatial Resolution ◽  
Water Waves ◽  
Wave Climate ◽  
Wind Fields ◽  
Northern Adriatic Sea ◽  
Northern Adriatic ◽  
Wave Fields ◽  
Wind Regimes ◽  
Offshore Wave

Abstract. In recent years, wave reanalyses have become popular as a powerful source of information for wave climate research and engineering applications. These wave reanalyses provide continuous time series of offshore wave parameters; nevertheless, in coastal areas or shallow water, waves are poorly described because spatial resolution is not detailed. By means of wave downscaling, it is possible to increase spatial resolution in high temporal coverage simulations, using forcing from wind and offshore wave databases. Meanwhile, the reanalysis wave databases are enough to describe the wave climate at the limit of simulations; wind reanalyses at an adequate spatial resolution to describe the wind structure near the coast are not frequently available. Remote sensing synthetic aperture radar (SAR) has the ability to detect sea surface signatures and estimate wind fields at high resolution (up to 300 m) and high frequency. In this work a wave downscaling is done on the northern Adriatic Sea, using a hybrid methodology and global wave and wind reanalysis as forcing. The wave fields produced were compared to wave fields produced with SAR winds that represent the two dominant wind regimes in the area: the bora (ENE direction) and sirocco (SE direction). Results show a good correlation between the waves forced with reanalysis wind and SAR wind. In addition, a validation of reanalysis is shown. This research demonstrates how Earth observation products, such as SAR wind fields, can be successfully up-taken into oceanographic modeling, producing similar downscaled wave fields when compared to waves forced with reanalysis wind.

Observations of freak waves in random wave field in 2D experimental wave flume

2013 ◽  
Vol 27 (5) ◽  
pp. 659-670 ◽  
Author(s):  
Jin-xuan Li ◽  
Peng-fei Li ◽  
Shu-xue Liu
Keyword(s):  
Wave Field ◽  
Random Wave ◽  
Freak Waves ◽  
Wave Flume ◽  
Random Wave Field

Modeling the presence of wave groups in a random wave field

1978 ◽  
Vol 83 (C8) ◽  
pp. 4117 ◽  
Author(s):  
E. Mollo-Christensen ◽  
A. Ramamonjiarisoa
Keyword(s):  
Wave Field ◽  
Random Wave ◽  
Wave Groups ◽  
Random Wave Field

Nonlinear phase-resolved reconstruction of irregular water waves

2018 ◽  
Vol 838 ◽  
pp. 544-572 ◽  
Author(s):  
Yusheng Qi ◽  
Guangyu Wu ◽  
Yuming Liu ◽  
Moo-Hyun Kim ◽  
Dick K. P. Yue
Keyword(s):  
Wave Field ◽  
Nonlinear Wave ◽  
Water Waves ◽  
Three Dimensional ◽  
Reconstruction Error ◽  
High Order ◽  
Order Effects ◽  
Wave Fields ◽  
Wave Measurements ◽  
Wave Nonlinearity

We develop and validate a high-order reconstruction (HOR) method for the phase-resolved reconstruction of a nonlinear wave field given a set of wave measurements. HOR optimizes the amplitude and phase of $L$ free wave components of the wave field, accounting for nonlinear wave interactions up to order $M$ in the evolution, to obtain a wave field that minimizes the reconstruction error between the reconstructed wave field and the given measurements. For a given reconstruction tolerance, $L$ and $M$ are provided in the HOR scheme itself. To demonstrate the validity and efficacy of HOR, we perform extensive tests of general two- and three-dimensional wave fields specified by theoretical Stokes waves, nonlinear simulations and physical wave fields in tank experiments which we conduct. The necessary $L$, for general broad-banded wave fields, is shown to be substantially less than the free and locked modes needed for the nonlinear evolution. We find that, even for relatively small wave steepness, the inclusion of high-order effects in HOR is important for prediction of wave kinematics not in the measurements. For all the cases we consider, HOR converges to the underlying wave field within a nonlinear spatial-temporal predictable zone ${\mathcal{P}}_{NL}$ which depends on the measurements and wave nonlinearity. For infinitesimal waves, ${\mathcal{P}}_{NL}$ matches the linear predictable zone ${\mathcal{P}}_{L}$, verifying the analytic solution presented in Qi et al. (Wave Motion, vol. 77, 2018, pp. 195–213). With increasing wave nonlinearity, we find that ${\mathcal{P}}_{NL}$ contains and is generally greater than ${\mathcal{P}}_{L}$. Thus ${\mathcal{P}}_{L}$ provides a (conservative) estimate of ${\mathcal{P}}_{NL}$ when the underlying wave field is not known.

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