scholarly journals 2- AND 3-DIMENSIONAL DETERMINISTIC FREAK WAVES

1982 ◽  
Vol 1 (18) ◽  
pp. 43
Author(s):  
Soren Peter Kjeldsen
Keyword(s):  
Dimensional Case ◽  
Linear Wave ◽  
Linear Dispersion ◽  
New Techniques ◽  
Freak Waves ◽  
3 Dimensional ◽  
Non Linear ◽  
Stokes Waves ◽  
First Results ◽  
Wave Trains

The present paper deals with a new non-linear technique for generation of violent breaking freak waves (plunging breakers) at specified positions and times in wave basins. First, results concerning generation of non-linear wave trains, Stokes-waves and wave solitons in deep water are given. Then the technique for generation of non-linear wave transients are given with specified non-linear dispersion properties. Finally, the new techniques are used to obtain collisions between non-linear solitons coming both from the same direction (2-dimensional case), and from different directions (3-dimensional case) leading to generation of steep and violent plunging breakers.

Weakly non-linear, slowly varying waves and their instabilities

1972 ◽  
Vol 72 (1) ◽  
pp. 95-104 ◽  
Author(s):  
R. Grimshaw
Keyword(s):  
Variational Principle ◽  
Gordon Equation ◽  
Transport Equations ◽  
Linear Wave ◽  
Leading Order ◽  
Non Linear ◽  
Klein Gordon ◽  
Wave Trains ◽  
Klein Gordon Equation

AbstractA non-linear Klein–Gordon equation is used to discuss the theory of slowly varying, weakly non-linear wave trains. An averaged variational principle is used to obtain transport equations for the slow variations which incorporate the leading order modulation and non-linear terms. Linearized transport equations are used to discuss instabilities.

Non-Linear Calculation of Tailored Wave Trains for Experimental Investigation of Extreme Structure Behaviour

2004 ◽  
Author(s):  
Gu¨nther F. Clauss ◽  
Janou Hennig ◽  
Christian E. Schmittner ◽  
Walter L. Ku¨hnlein
Keyword(s):  
Experimental Investigation ◽  
Wave Propagation ◽  
Wave Structure ◽  
Linear Wave ◽  
Advantages And Disadvantages ◽  
Non Linear ◽  
Linear Wave Propagation ◽  
Precise Prediction ◽  
Wave Trains ◽  
Wave Models

The experimental investigation of extreme wave/structure interaction scenarios puts high demands on wave generation and calculation. This paper presents different approaches for modelling non-linear wave propagation. Results of numerical simulations from two different numerical wave tanks are compared to models tests. A further approach uses analytical wave models which are combined with empirical terms to allow a fast and precise prediction of non-linear wave propagation for day-to-day use. All approaches can be used either separately or in combination — depending on their particular purpose. As an application, different special wave scenarios — both academic and realistic — are generated and validated by measurements. The advantages and disadvantages of the presented methods are discussed in detail with regard to their appropriate use for investigations of extreme structure behaviour.

Non-linear dispersion of water waves

1967 ◽  
Vol 27 (2) ◽  
pp. 399-412 ◽  
Author(s):  
G. B. Whitham
Keyword(s):  
Water Waves ◽  
Wave Train ◽  
Periodic Wave ◽  
Wave Number ◽  
Amplitude Wave ◽  
Linear Dispersion ◽  
Elliptic Case ◽  
Non Linear ◽  
Wave Trains ◽  
Linear Water Waves

The slow dispersion of non-linear water waves is studied by the general theory developed in an earlier paper (Whitham 1965b). The average Lagrangian is calculated from the Stokes expansion for periodic wave trains in water of arbitrary depth. This Lagrangian can be used for the various applications described in the above reference. In this paper, the crucial question of the ‘type’ of the differential equations for the wave-train parameters (local amplitude, wave-number, etc.) is established. The equations are hyperbolic or elliptic according to whetherkh0is less than or greater than 1.36, wherekis the wave-number per 2π andh0is the undisturbed depth. In the hyperbolic case, changes in the wave train propagate and the characteristic velocities give generalizations of the linear group velocity. In the elliptic case, modulations in the wave train grow exponentially and a periodic wave train will be unstable in this sense; thus, periodic wave trains on water will be unstable ifkh0> 1·36, The instability of deep-water waves,kh0> 1·36, was discovered in a different way by Benjamin (1966). The relation between the two approaches is explained.

Non-linear dispersion of Stokes waves

1969 ◽  
Vol 3 (1) ◽  
pp. 45-54 ◽  
Author(s):  
H. W. Hoogstraten
Keyword(s):  
Linear Dispersion ◽  
Non Linear ◽  
Stokes Waves

scholarly journals On the Deterministic Prediction of Water Waves

Fluids ◽  
2020 ◽  
Vol 5 (1) ◽  
pp. 9 ◽  
Author(s):  
Marco Klein ◽  
Matthias Dudek ◽  
Günther F. Clauss ◽  
Sören Ehlers ◽  
Jasper Behrendt ◽  
...  
Keyword(s):  
Water Waves ◽  
Linear Wave ◽  
Wave Steepness ◽  
Forecast Horizon ◽  
Linear Dispersion ◽  
Similarity Parameter ◽  
Linear Solution ◽  
Basic Module ◽  
Wave Prediction ◽  
Non Linear

This paper discusses the potential of deterministic wave prediction as one basic module for decision support of offshore operations. Therefore, methods of different complexity—the linear wave solution, the non-linear Schrödinger equation (NLSE) of two different orders and the high-order spectral method (HOSM)—are presented in terms of applicability and limitations of use. For this purpose, irregular sea states with varying parameters are addressed by numerical simulations as well as model tests in the controlled environment of a seakeeping basin. The irregular sea state investigations focuses on JONSWAP spectra with varying wave steepness and enhancement factor. In addition, the influence of the propagation distance as well as the forecast horizon is discussed. For the evaluation of the accuracy of the prediction, the surface similarity parameter is used, allowing an exact, quantitative validation of the results. Based on the results, the pros and cons of the different deterministic wave prediction methods are discussed. In conclusion, this paper shows that the classical NLSE is not applicable for deterministic wave prediction of arbitrary irregular sea states compared to the linear solution. However, the application of the exact linear dispersion operator within the linear dispersive part of the NLSE increased the accuracy of the prediction for small wave steepness significantly. In addition, it is shown that non-linear deterministic wave prediction based on second-order NLSE as well as HOSM leads to a substantial improvement of the prediction quality for moderate and steep irregular wave trains in terms of individual waves and prediction distance, with the HOSM providing a high accuracy over a wider range of applications.

The Average Shape of Large Waves in the Norwegian Sea: Is Non-Linear Physics Important?

2019 ◽  
Author(s):  
Tianning Tang ◽  
Margaret J. Yelland ◽  
Thomas A. A. Adcock
Keyword(s):  
Field Data ◽  
Wave Theory ◽  
Linear Wave ◽  
Wave Problem ◽  
Linear Dispersion ◽  
Norwegian Sea ◽  
Linear Wave Theory ◽  
Average Shape ◽  
Non Linear ◽  
Average Wave

Abstract Linear wave theory predicts that in a random sea, the shape of the average wave is given by the scaled autocorrelation function — the “NewWave”. However, the gravity wave problem is non-linear. Numerical simulations of waves on deep water have suggested that their average shape can become modified in a number of ways, including the largest wave in a group tending to move to the front of the group through non-linear dispersion. In this paper we examine whether this occurs for waves in the Norwegian Sea. Field data measured from the weather ship Polarfront is analysed for the period 2000 to 2009. We find that, at this location, the effect of non-linearity is small due to the moderate steepness of the sea-states.

Nonlinear Fourier Analysis with Sine Wave, Stokes Wave and Rogue Wave Basis Functions: A Paradigm Change in the Understanding of Nonlinear Waves

2020 ◽  
Author(s):  
Alfred Osborne
Keyword(s):  
Fourier Series ◽  
Fourier Analysis ◽  
Rogue Wave ◽  
Random Phase ◽  
Stokes Wave ◽  
Random Wave ◽  
Linear Dispersion ◽  
Wide Range ◽  
Stokes Waves ◽  
Wave Trains

<p>I give a new perspective for the description of nonlinear water wave trains using mathematical methods I refer to as nonlinear Fourier analysis (NLFA). I discuss how this approach holds for one-space and one time dimensions (1+1) and for two-space and one time dimensions (2+1) to all orders of approximation. I begin with the nonlinear Schroedinger (NLS) equation in 1+1 dimensions: Here the NLFA method is derived from the complete integrability of the equation by the periodic inverse scattering transform. I show how to compute the nonlinear Fourier series that exactly solve 1+1 NLS. I then show how to extend the order of 1+1 NLS to the Dysthe and the extended Dysthe equations. I also show how to include directional spreading in the formulation so that I can address the 2+1 NLS, the 2+1 Dysthe and the 2+1 Trulsen-Dysthe equations. This hierarchy of equations extends formally all the way to the Zakharov equations in the infinite order limit. Each order and extension from 1+1 to 2+1 dimensions is characterized by its own modulational dispersion relation that is required at each order of the NLFA formalism. NLFA is characterized by its own fundamental nonlinear Fourier series, which has particular nonlinear Fourier modes: sine waves, Stokes waves and breather trains. We are all familiar with sine waves (known for centuries) and Stokes waves (known since the Stokes paper in 1847). Breather trains have become known over the past three decades as a major source of rogue or freak waves in the ocean: Breather packets are known to pulse up and down during their evolution. At the moment of the maximum amplitude the largest wave in a breather packet is often referred to as a “rogue” or “freak” wave. Such extreme packets are known to be “coherent structures" so that pure linear dispersion does not occur as in a linear packet. Instead the breather packets have components that are phase locked with each other and hence remain coherent and are “long lived” just as vortices do in classical turbulence. Because the breathers live for a long time, the notion of risk based upon linear dispersion, as used in the oil and shipping industries, must be revised upwards. I discuss how to apply NLFA to (1) nonlinearly Fourier analyze time series, (2) to analyze wave fields from radar, lidar and synthetic aperture radar measurements, (3) how to treat NLFA to describe nonlinear, random wave trains using a kind of nonlinear random phase approximation and (4) how to compute the nonlinear power spectrum in terms of the parameters used to describe the rogue wave Fourier modes in a random wave train. Thus the emphasis here is to discuss a number of new tools for nonlinear Fourier analysis in a wide range of problems in the field of ocean surface waves.</p>

Serial thin sectioning for pre- and post-embedding immunohistochemistry: Achieving consistent and reliable results for a 3-D reconstruction

1993 ◽  
Vol 51 ◽  
pp. 328-329
Author(s):  
Antonia M. Milroy
Keyword(s):  
Nervous System ◽  
Computer Assisted ◽  
Serial Sectioning ◽  
Electron Microscopic ◽  
High Quality ◽  
New Techniques ◽  
3 Dimensional ◽  
Multiple User ◽  
Thin Sectioning ◽  
Subcellular Level

In recent years many new techniques and instruments for 3-Dimensional visualization of electron microscopic images have become available. Higher accelerating voltage through thicker sections, photographed at a tilt for stereo viewing, or the use of confocal microscopy, help to analyze biological material without the necessity of serial sectioning. However, when determining the presence of neurotransmitter receptors or biochemical substances present within the nervous system, the need for good serial sectioning (Fig. 1+2) remains. The advent of computer assisted reconstruction and the possibility of feeding information from the specimen viewing chamber directly into a computer via a camera mounted on the electron microscope column, facilitates serial analysis. Detailed information observed at the subcellular level is more precise and extensive and the complexities of interactions within the nervous system can be further elucidated.We emphasize that serial ultra thin sectioning can be performed routinely and consistently in multiple user electron microscopy laboratories. Initial tissue fixation and embedding must be of high quality.

scholarly journals Excitation Forces Estimation for Non-linear Wave Energy Converters: A Neural Network Approach

2020 ◽  
Vol 53 (2) ◽  
pp. 12334-12339
Author(s):  
M. Bonfanti ◽  
F. Carapellese ◽  
S.A. Sirigu ◽  
G. Bracco ◽  
G. Mattiazzo
Keyword(s):  
Neural Network ◽  
Wave Energy ◽  
Linear Wave ◽  
Network Approach ◽  
Neural Network Approach ◽  
Wave Energy Converters ◽  
Non Linear ◽  
Energy Converters
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