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.

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.

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.

Plain Interpretation of Freak Waves Phenomenon

2018 ◽  
Author(s):  
Dmitry Chalikov ◽  
Alexander V. Babanin
Keyword(s):  
Nonlinear Models ◽  
Modulational Instability ◽  
Wave Interactions ◽  
Freak Waves ◽  
Freak Wave ◽  
One Dimensional ◽  
Linear Waves ◽  
Instability Theory ◽  
Wave Trains ◽  
Integral Probability

An extremely large (‘freak’) wave is a typical though quite a rare phenomenon observed in the sea. Special theories (for example, the modulational instability theory) were developed to explain the mechanics and appearance of freak waves as a result of nonlinear wave-wave interactions. This paper demonstrates that freak wave appearance can be also explained by superposition of linear modes with a realistic spectrum. The integral probability of trough-to-crest waves is calculated by two methods: the first one is based on the results of a numerical simulation of wave field evolution, performed with one-dimensional and two-dimensional nonlinear models. The second method is based on the calculation of the same probability over ensembles of wave fields, constructed as a superposition of linear waves with random phases and a spectrum similar to that used in nonlinear simulations. It is shown that the integral probabilities for nonlinear and linear cases are of the same order of values. One-dimensional model was used for performing thousands of exact short-term simulations of evolution of two superposed wave trains with different steepness and wavenumbers to investigate the effect of wave crests merging. The nonlinear sharpening of merging crests is demonstrated. It is suggested that such effect may be responsible for appearance of typical sharp crests of surface waves, as well as for the wave breaking.

Thin-sheet EM modelling of the Tasman Sea

1989 ◽  
Vol 20 (2) ◽  
pp. 177 ◽  
Author(s):  
G.S. Heinson ◽  
F.E.M. Lilley
Keyword(s):  
Large Scale ◽  
Salt Water ◽  
Thin Sheet ◽  
Three Dimensional ◽  
One Dimensional ◽  
The Earth ◽  
Tasman Sea ◽  
Modelling Techniques ◽  
Tectonic Features ◽  
The University

The Tasman Project of Seafloor Magnetotelluric Exploration (TPSME) took place between December 1983 and April 1984 (Filloux et al., 1985; Ferguson et al., 1985; Lilley etal., 1989). Seven magnetotelluric and two (additional) magnetometer sites spanned a range of tectonic features across the Tasman Sea. Initial analysis by Ferguson (1988) indicated large-scale three-dimensional induction effects to be present in the data. It was concluded that the most probable causes were the continental margin effect and changes in bathymetry.In the present paper, a method is presented of modelling the salt water of the Tasman Sea and adjoining oceans as a thin sheet of variable lateral conductance, which overlies a series of uniform layers representing the solid Earth. The theory and a suitable computer algorithm were developed in a group led by J. T. Weaver at the University of Victoria, B.C., Canada. Many of the features present in the TPSME data are reproduced by this method, and with a greater understanding of induction processes in the ocean which is thus obtained, it is possible to remove three-dimensional effects from observed data. The TPSME data are then solely a measure of the response of the Earth directly beneath the observing sites, and one-dimensional modelling techniques may be used to determine the conductivity structures.

Structure and function of neural networks in the retina

1988 ◽  
Vol 46 ◽  
pp. 26-27
Author(s):  
Peter Sterling
Keyword(s):  
Ganglion Cells ◽  
Three Dimensional ◽  
Structure And Function ◽  
Synaptic Connections ◽  
Visual Axis ◽  
One Dimensional ◽  
Cat Retina ◽  
Ultrathin Sections ◽  
And Function ◽  
Insight Into

The synaptic connections in cat retina that link photoreceptors to ganglion cells have been analyzed quantitatively. Our approach has been to prepare serial, ultrathin sections and photograph en montage at low magnification (˜2000X) in the electron microscope. Six series, 100-300 sections long, have been prepared over the last decade. They derive from different cats but always from the same region of retina, about one degree from the center of the visual axis. The material has been analyzed by reconstructing adjacent neurons in each array and then identifying systematically the synaptic connections between arrays. Most reconstructions were done manually by tracing the outlines of processes in successive sections onto acetate sheets aligned on a cartoonist's jig. The tracings were then digitized, stacked by computer, and printed with the hidden lines removed. The results have provided rather than the usual one-dimensional account of pathways, a three-dimensional account of circuits. From this has emerged insight into the functional architecture.

Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

2008 ◽  
Vol 67 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Stefano Passini
Keyword(s):  
Social Dominance ◽  
Factor Model ◽  
Three Dimensional ◽  
Social Dominance Orientation ◽  
Model Fit ◽  
Regression Analyses ◽  
One Dimensional ◽  
Confirmatory Factor ◽  
The One ◽  
Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

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