Modulational Instability in Directional Wave Fields, and Extreme Wave Events

2011 ◽  
Author(s):  
Alexander V. Babanin ◽  
Takuji Waseda ◽  
Igor Shugan ◽  
Hwung-Hweng Hwung
Keyword(s):  
Modulational Instability ◽  
Wave Train ◽  
Three Dimensional ◽  
Breaking Waves ◽  
Two Dimensional ◽  
Wave Fields ◽  
Linear Evolution ◽  
Individual Wave ◽  
Wave Trains ◽  
Directional Wave

The paper is based on review of research articles by the authors, with the purpose to demonstrate that the modulational-instability mechanism is active in typical directional wave fields. If so, possible limits for the wave height due to such mechanism can be outlined. The modulational instability can lead to occurrence of very high waves, which either proceed to the breaking or appear as rogue events, but it was derived for and is usually associated with two-dimensional wave trains. There exists argument, both analytical and experimental, that this kind of instability is impaired or even suppressed in three-dimensional (directional) wave systems. The first part of the paper demonstrates indirect experimental evidences which relate the wave breaking in oceanic conditions to features of two-dimensional breaking waves due to modulational instability. The second section is dedicated to direct measurements of such instability-caused breaking in a directional wave tank with directional spread and mean steepness typical of those in the field. The last section provides conclusions on what is maximal height of an individual wave, depending on the mean wave steepness in a wave train/field, that can be achieved due to such non-linear evolution of wave trains.

scholarly journals Occurrence of extreme waves in three-dimensional mechanically generated wave fields propagating over an oblique current

2011 ◽  
Vol 11 (3) ◽  
pp. 895-903 ◽  
Author(s):  
A. Toffoli ◽  
L. Cavaleri ◽  
A. V. Babanin ◽  
M. Benoit ◽  
E. M. Bitner-Gregersen ◽  
...  
Keyword(s):  
Modulational Instability ◽  
Three Dimensional ◽  
Wave Direction ◽  
Subsequent Increase ◽  
Wave Fields ◽  
Wave Trains ◽  
Directional Wave ◽  
The Mean ◽  
Wave Maker ◽  
Non Gaussian

Abstract. Laboratory experiments were performed to study the dynamics of three- dimensional mechanically generated waves propagating over an oblique current in partial opposition. The flow velocity varied along the mean wave direction of propagation with an increasing trend between the wave-maker and the centre of the tank. Tests with regular wave packets traversing the area of positive current gradient showed that the concurrent increase of wave steepness triggered modulational instability on otherwise stable wave trains and hence induced the development of very large amplitude waves. In random directional wave fields, the presence of the oblique current resulted in a weak reinforcement of wave instability with a subsequent increase of the probability of occurrence of extreme events. This seems to partially compensate the suppression of strongly non-Gaussian properties due to directional energy distribution.

Numerical and laboratory investigation of breaking of steep two-dimensional waves in deep water

2010 ◽  
Vol 644 ◽  
pp. 433-463 ◽  
Author(s):  
ALEXANDER V. BABANIN ◽  
DMITRY CHALIKOV ◽  
I. R. YOUNG ◽  
IVAN SAVELYEV
Keyword(s):  
Modulational Instability ◽  
Three Dimensional ◽  
Breaking Waves ◽  
Strong Wind ◽  
Two Dimensional ◽  
Fourier Space ◽  
Theoretical Predictions ◽  
Steep Waves ◽  
Wave Properties

The paper extends a pilot study into a detailed investigation of properties of breaking waves and processes responsible for breaking. Simulations of evolution of steep to very steep waves to the point of breaking are undertaken by means of the fully nonlinear Chalikov–Sheinin model. Particular attention is paid to evolution of nonlinear wave properties, such as steepness, skewness and asymmetry, in the physical, rather than Fourier space, and to their interplay leading to the onset of breaking. The role of superimposed wind is also investigated. The capacity of the wind to affect the breaking onset is minimal unless the wind forcing is very strong. Wind is, however, important as a source of energy for amplification of the wave steepness and ultimately altering the breaking statistics. A detailed laboratory study is subsequently described. The theoretical predictions are verified and quantified. In addition, some features of the nonlinear development not revealed by the model (i.e. reduction of the wave period which further promotes an increase in steepness prior to breaking) are investigated. Physical properties of the incipient breaker are measured and examined, as well as characteristics of waves both preceding and following the breaker. The experiments were performed both with and without a superimposed wind, the role of which is also investigated. Since these idealized two-dimensional results are ultimately intended for field applications, tentative comparisons with known field data are considered. Limitations which the modulational instability mechanism can encounter in real broadband three-dimensional environments are highlighted. Also, substantial examination of existing methods of breaking onset detection are discussed and inconsistencies of existing measurements of breaking rates are pointed out.

scholarly journals NATURAL WAVE TRAINS: DESCRIPTION AND REPRODUCTION

1978 ◽  
Vol 1 (16) ◽  
pp. 16 ◽  
Author(s):  
H. Lundgren ◽  
S.E. Sand
Keyword(s):  
Numerical Models ◽  
Wave Train ◽  
Three Dimensional ◽  
Correct Description ◽  
Linear Superposition ◽  
Natural Wave ◽  
Wave Trains ◽  
Steep Waves ◽  
Deterministic Description ◽  
The Waves

In many applications there is a great need for a correct description of the natural, irregular three-dimensional sea and its reproduction in physical and numerical models. Because of the tremendous difficulties inherent in the nonlinearities, the science of coastal engineering is still very far from this ultimate goal. Indeed, the scope of this paper is comparatively very modest: To describe and reproduce natural, irregular two-dimensional waves, i.e. waves propagating in one direction in a flume. In addition, this scope is fulfilled only by assuming linear superposition of Fourier terms. As opposed to the usual spectral description, the deterministic description presented here does not eliminate the phase information in the wave train recorded. Because of the nonlinearities, however, the linear deterministic description invariably degenerates with the distance travelled by the waves. It appears though from the present paper that the degeneration is fairly slow even for rather steep waves.

Diffraction and Instability of Short-Crested Limited-Length One-Dimensional Coherent Wave Trains

2015 ◽  
Author(s):  
Alexander V. Babanin ◽  
Takuji Waseda
Keyword(s):  
Modulational Instability ◽  
Three Dimensional ◽  
Lateral Spread ◽  
Wave Tank ◽  
One Dimensional ◽  
Coherent Wave ◽  
Limited Length ◽  
Lateral Extent ◽  
Wave Trains ◽  
The University

Alternative representations of the wave field (as opposed to superposition of Fourier components) are possible. In this paper, behaviour of short-crested limited-length one-dimensional coherent wave trains is investigated. Experiments were conducted in the three-dimensional wave tank of the University of Tokyo. Description of the directional wave tank and its capacity to generate short-crested coherent wave trains, including those concurrent, superposed and directionally-superposed is provided. If the crest is shorter than the lateral extent of the wave tank, diffraction tends to redistribute the wave energy into clear surfaces, and thus energy of the wave trains is reduced and the modulational instability bandwidth changes correspondingly. Rates of such nonlinear lateral spread are estimated, and they are proportional to mean wave steepness. To avoid the diffraction, in further tests concurrent trains were mechanically generated, each of which occupied half of the lateral width of the wave tank and had the same energy as another half. The trains had the same frequency, and in order to keep them separate phase shift of 180 degrees was used. Sideband growth was significantly impaired by comparison with the long-crested evolution of the train with the same steepness.

Modulational instability of electrostatic ion cyclotron wave in a two-electron-temperature plasma

1980 ◽  
Vol 24 (3) ◽  
pp. 445-452 ◽  
Author(s):  
M. Lisak
Keyword(s):  
Modulational Instability ◽  
Three Dimensional ◽  
Reductive Perturbation Method ◽  
Two Dimensional ◽  
Cold Electron ◽  
Temperature Plasma ◽  
Ion Acoustic Wave ◽  
Ion Cyclotron ◽  
Free Plasma ◽  
Two Temperature

A three-dimensional nonlinear Schrüdinger equation for an electrostatic ion cyclotron wave coupled to an ion-acoustic wave in a collision-free plasma consisting of cold ions and two-temperature electrons is derived using the reductive perturbation method. It is shown that a range of wavenumbers corresponding to the instability of a plane electrostatic ion cyclotron wave against a two-dimensional modulation depends on the ratio of temperature of hot and cold electron components.

scholarly journals A new model of shoaling and breaking waves - Wave trains and two-dimensional applications

2020 ◽  
Author(s):  
Arnaud DURAN ◽  
Benoît FABREGES ◽  
Maria KAZAKOVA ◽  
Gaël Loïc RICHARD
Keyword(s):  
Breaking Waves ◽  
Two Dimensional ◽  
New Model ◽  
Wave Trains

Wave Breaking in Directional Fields

2011 ◽  
Vol 41 (1) ◽  
pp. 145-156 ◽  
Author(s):  
A. V. Babanin ◽  
T. Waseda ◽  
T. Kinoshita ◽  
A. Toffoli
Keyword(s):  
Wave Breaking ◽  
Modulational Instability ◽  
Primary Wave ◽  
Angular Domain ◽  
Instability Mechanism ◽  
Wave Fields ◽  
Directional Distribution ◽  
Directional Wave ◽  
Directional Distributions ◽  
The University

Abstract Wave breaking is observed in a laboratory experiment with waves of realistic average steepness and directional spread. It is shown that a modulational-instability mechanism is active in such circumstances and can lead to the breaking. Experiments were conducted in the directional wave tank of the University of Tokyo, and the mechanically generated wave fields consisted of a primary wave with sidebands in the frequency domain, with continuous directional distribution in the angular domain. Initial steepness of the primary wave and sidebands, as well as the width of directional distributions varied in a broad range to determine the combination of steepness/directional-spread properties that separates modulational-instability breaking from the linear-focusing breaking.

Calculation of complete seismograms for an explosive source in a layered medium

Geophysics ◽  
1980 ◽  
Vol 45 (2) ◽  
pp. 197-203 ◽  
Author(s):  
Michel Bouchon
Keyword(s):  
Elastic Wave ◽  
Layered Medium ◽  
Plane Waves ◽  
Three Dimensional ◽  
Synthetic Seismograms ◽  
Two Dimensional ◽  
Wave Fields ◽  
Source Radiation ◽  
Explosive Source ◽  
Periodic Arrangement

We apply the method of discrete wavenumber representation of elastic wave fields of Bouchon and Aki (1977) to the computation of synthetic seismograms for an explosive source in a layered medium. The method is based on the representation of the source radiation by a superposition of plane waves propagating in discrete directions. This discretization is exact and results from a periodic arrangement of sources. The two‐dimensional (2-D) and three‐dimensional (3-D) problems are described, and some examples of calculation are presented. They show that very complex seismograms can be obtained for rather simple geologic structures.

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.

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