Extreme Waves in Sea States Crossing an Oblique Current

2010 ◽  
Author(s):  
A. Toffoli ◽  
A. V. Babanin ◽  
F. Ardhuin ◽  
M. Benoit ◽  
E. M. Bitner-Gregersen ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Gravity Waves ◽  
Laboratory Experiments ◽  
Random Wave ◽  
Extreme Waves ◽  
Regular Waves ◽  
Wave Fields ◽  
Surface Gravity Waves ◽  
Directional Wave ◽  
A Current

Laboratory experiments have been carried out in the directional wave tank at Marintek (Norway) to study the nonlinear dynamics of surface gravity waves and the occurrence of extreme events, when the wave field traverses obliquely an ambient current. A condition of partial opposition has been considered. Tests on regular waves have shown that the current can trigger the formation of large amplitude waves. In random wave fields, however, this only results in a weak deviation from the statistical properties observed in absence of a current.

scholarly journals Scattering of surface gravity waves by bottom topography with a current

2007 ◽  
Vol 576 ◽  
pp. 235-264 ◽  
Author(s):  
FABRICE ARDHUIN ◽  
RUDY MAGNE
Keyword(s):  
Gravity Waves ◽  
Bottom Topography ◽  
Wave Spectrum ◽  
Action Spectrum ◽  
Wave Action ◽  
Surface Gravity ◽  
Small Scale ◽  
Surface Gravity Waves ◽  
Reflected Wave ◽  
A Current

A theory is presented that describes the scattering of random surface gravity waves by small-amplitude topography, with horizontal scales of the order of the wavelength, in the presence of an irrotational and almost uniform current. A perturbation expansion of the wave action to order η2 yields an evolution equation for the wave action spectrum, where η = max(h)/H is the small-scale bottom amplitude normalized by the mean water depth. Spectral wave evolution is proportional to the bottom elevation variance at the resonant wavenumbers, representing a Bragg scattering approximation. With a current, scattering results from a direct effect of the bottom topography, and an indirect effect of the bottom through the modulations of the surface current and mean surface elevation. For Froude numbers of the order of 0.6 or less, the bottom topography effects dominate. For all Froude numbers, the reflection coefficients for the wave amplitudes that are inferred from the wave action source term are asymptotically identical, as η goes to zero, to previous theoretical results for monochromatic waves propagating in one dimension over sinusoidal bars. In particular, the frequency of the most reflected wave components is shifted by the current, and wave action conservation results in amplified reflected wave energies for following currents. Application of the theory to waves over current-generated sandwaves suggests that forward scattering can be significant, resulting in a broadening of the directional wave spectrum, while back-scattering should be generally weaker.

scholarly journals Measurement of the dispersion relation for random surface gravity waves

2015 ◽  
Vol 766 ◽  
pp. 326-336 ◽  
Author(s):  
Tore Magnus A. Taklo ◽  
Karsten Trulsen ◽  
Odin Gramstad ◽  
Harald E. Krogstad ◽  
Atle Jensen
Keyword(s):  
Dispersion Relation ◽  
Gravity Waves ◽  
Laboratory Experiments ◽  
Surface Gravity ◽  
Linear Dispersion ◽  
Random Surface ◽  
Zakharov Equation ◽  
Surface Gravity Waves ◽  
Linear Dispersion Relation ◽  
Jonswap Spectrum

AbstractWe report laboratory experiments and numerical simulations of the Zakharov equation, designed to have sufficient resolution in space and time to measure the dispersion relation for random surface gravity waves. The experiments and simulations are carried out for a JONSWAP spectrum and Gaussian spectra of various bandwidths on deep water. It is found that the measured dispersion relation deviates from the linear dispersion relation above the spectral peak when the bandwidth is sufficiently narrow.

Nonlinear interactions treated by the methods of theoretical physics (with application to the generation of waves by wind)

1967 ◽  
Vol 299 (1456) ◽  
pp. 77-103 ◽  
Keyword(s):  
Gravity Waves ◽  
Theoretical Physics ◽  
Coarse Grained ◽  
Random Wave ◽  
Wave Interactions ◽  
Diagram Method ◽  
Wave Fields ◽  
Fine Grained ◽  
Complete Set ◽  
Particle Interpretation

The ‘Feynman’ diagram method for analysing wave-wave interactions in random wave fields is generalized to include non-conservative interactions between wave fields and external fields. The particle interpretation is no longer applicable, but the transfer expressions can still be conveniently summarized in terms of ‘transfer’ diagrams, which correspond to collision diagrams in the particle picture. The method is applied to interactions between gravity waves and the turbulent atmospheric boundary layer. The complete set of lowest order transfer diagrams contains the Phillips and Miles mechanisms of wave generation and an additional set of wave-turbulence interactions, which have not been considered previously. The closure hypothesis invoked in the derivation of the transfer expressions is discussed briefly in appendix A. It is pointed out that Benney & Saffman’s recent derivation of the transfer expressions without the usual closure hypothesis contradicts the irreversibility of the transfer expressions and is valid only initially. The relevant statistical properties depend on the distinction between coarse grained and fine grained distributions. This is illustrated in appendix B by a discussion of the Gaussian property of linear, random wave fields.

Probability of Occurrence of Extreme Waves in Three Dimensional Mechanically Generated Random Wave Fields: A Comparison With Numerical Simulations

2011 ◽  
Author(s):  
A. Toffoli ◽  
S. Chai ◽  
E. M. Bitner-Gregersen ◽  
F. Pistani
Keyword(s):  
Numerical Simulations ◽  
Quantitative Estimate ◽  
Numerical Models ◽  
Modulational Instability ◽  
Three Dimensional ◽  
Random Wave ◽  
Extreme Waves ◽  
Wave Fields ◽  
Numerical Investigations ◽  
Probability Of Occurrence

Experimental and numerical investigations reveal that nonlinear modulational instability can significantly affect the probability of occurrence of extreme waves, especially if waves are sufficiently steep and narrow banded both in the frequency and directional domain. However, it is not yet completely clear whether numerical simulations can provide an accurate quantitative estimate of experimental results. Here the potential Euler equations are used to assess the ability of numerical models to describe the evolution of statistical properties of mechanically generated directional, random wave fields and in particular the evolution of the kurtosis. Results show that simulations provide a good quantitative estimate of experimental observations within a broad range of wave directional width.

scholarly journals TIDAL INLET CURRENT--OCEAN WAVE INTERACTION

1972 ◽  
Vol 1 (13) ◽  
pp. 33 ◽  
Author(s):  
Lyndell Z. Hales ◽  
John B. Herbich
Keyword(s):  
Gravity Waves ◽  
Functional Relationship ◽  
Three Dimensional ◽  
Wave Interaction ◽  
Tidal Inlet ◽  
Surface Gravity Waves ◽  
Wave Characteristics ◽  
Wave Basin ◽  
Ocean Region ◽  
A Current

An experimental study was conducted in a three-dimensional wave basin to investigate the manner in which surface gravity waves propagating toward a tidal inlet are altered. Dimensional analysis of the pertinent variables indicates that a functional relationship exists between as many as five dimensionless terms, and the functional relationship is displayed in graphical non-dimensional form to apply to all scales. Results indicate the ebb current increases the steepness in the ocean region to such an extent that the wave begins to lose energy by the crest spilling down the front of the wave, and the wave characteristics in the inlet proper may never reach the breaking limit unless factors other than a current alone are involved.

scholarly journals Time Scale for Scour Beneath Pipelines Due to Long-Crested and Short-Crested Nonlinear Random Waves Plus Current

2021 ◽  
Vol 9 (2) ◽  
pp. 114
Author(s):  
Dag Myrhaug ◽  
Muk Chen Ong
Keyword(s):  
Time Scale ◽  
Current Flow ◽  
Irregular Waves ◽  
Wave Crest ◽  
Random Wave ◽  
Random Waves ◽  
Flow Conditions ◽  
Regular Waves ◽  
Nonlinear Random Waves ◽  
2D And 3D

This article derives the time scale of pipeline scour caused by 2D (long-crested) and 3D (short-crested) nonlinear irregular waves and current for wave-dominant flow. The motivation is to provide a simple engineering tool suitable to use when assessing the time scale of equilibrium pipeline scour for these flow conditions. The method assumes the random wave process to be stationary and narrow banded adopting a distribution of the wave crest height representing 2D and 3D nonlinear irregular waves and a time scale formula for regular waves plus current. The presented results cover a range of random waves plus current flow conditions for which the method is valid. Results for typical field conditions are also presented. A possible application of the outcome of this study is that, e.g., consulting engineers can use it as part of assessing the on-bottom stability of seabed pipelines.

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