Stochastic Model Construction of Correlated Nonlinear Wave Fields

2015 ◽  
Author(s):  
Fabrice Poirion ◽  
Michel Benoit
Keyword(s):  
Stochastic Model ◽  
Nonlinear Wave ◽  
Vertical Displacement ◽  
Physical Characteristics ◽  
Sea Surface ◽  
Model Construction ◽  
Single Wave ◽  
Wave Fields

The aim of this work is to present a method for constructing simulations of correlated trajectories of sea surface vertical displacement at different locations. It can also be used in order to construct a stochastic model for a single wave with given physical characteristics.

scholarly journals Null modes effect in Rossby wave model

2004 ◽  
Vol 11 (3) ◽  
pp. 281-293
Author(s):  
V. Goncharov ◽  
V. Pavlov
Keyword(s):  
Nonlinear Wave ◽  
Rossby Wave ◽  
Wave Model ◽  
Wave Fields

Abstract. The problem of the null-modes existence and some particularities of their interaction with nonlinear vortex-wave-like structures is discussed. We show that the null-modes are fundamental elements of nonlinear wave fields. The conditions under which null-modes can manifest themselves are elucidated. The Rossby-Hasegawa-Mima (RHM) model is used for the illustration of features of null-modes-waves interactions.

scholarly journals Statistical properties of nonlinear one-dimensional wave fields

2005 ◽  
Vol 12 (5) ◽  
pp. 671-689 ◽  
Author(s):  
D. Chalikov
Keyword(s):  
Surface Waves ◽  
Nonlinear Wave ◽  
High Accuracy ◽  
Statistical Properties ◽  
Statistical Characteristics ◽  
Small Scale ◽  
Sea Waves ◽  
Wave Fields ◽  
Linear Waves ◽  
Stokes Waves

Abstract. A numerical model for long-term simulation of gravity surface waves is described. The model is designed as a component of a coupled Wave Boundary Layer/Sea Waves model, for investigation of small-scale dynamic and thermodynamic interactions between the ocean and atmosphere. Statistical properties of nonlinear wave fields are investigated on a basis of direct hydrodynamical modeling of 1-D potential periodic surface waves. The method is based on a nonstationary conformal surface-following coordinate transformation; this approach reduces the principal equations of potential waves to two simple evolutionary equations for the elevation and the velocity potential on the surface. The numerical scheme is based on a Fourier transform method. High accuracy was confirmed by validation of the nonstationary model against known solutions, and by comparison between the results obtained with different resolutions in the horizontal. The scheme allows reproduction of the propagation of steep Stokes waves for thousands of periods with very high accuracy. The method here developed is applied to simulation of the evolution of wave fields with large number of modes for many periods of dominant waves. The statistical characteristics of nonlinear wave fields for waves of different steepness were investigated: spectra, curtosis and skewness, dispersion relation, life time. The prime result is that wave field may be presented as a superposition of linear waves is valid only for small amplitudes. It is shown as well, that nonlinear wave fields are rather a superposition of Stokes waves not linear waves. Potential flow, free surface, conformal mapping, numerical modeling of waves, gravity waves, Stokes waves, breaking waves, freak waves, wind-wave interaction.

Diffusion of action in some nonlinear wave fields

1978 ◽  
Vol 21 (8) ◽  
pp. 1448
Author(s):  
Bruce J. West
Keyword(s):  
Nonlinear Wave ◽  
Wave Fields

Nonlinear Wave Loads Acting on Cylinder Array Slowly Oscillating in Diffraction and Radiation Wave Fields

2005 ◽  
Author(s):  
Weiguang Bao ◽  
Takeshi Kinoshita ◽  
Motoki Yoshida
Keyword(s):  
Nonlinear Wave ◽  
Perturbation Expansion ◽  
Low Frequency ◽  
Added Mass ◽  
Wave Loads ◽  
Wave Fields ◽  
Wave Drift ◽  
Cylinder Array ◽  
Radiation Wave ◽  
Low Frequency Motion

The problem of a circular cylinder array slowly oscillating in both diffraction and radiation wave fields is considered in the present work. As a result of the interaction between the wave fields and the low-frequency motion, nonlinear wave loads may be separated into the so-called wave-drift added mass and damping. They are force components proportional to the square of the wave amplitude but in phase of the acceleration and velocity of the low-frequency motion respectively. The frequency of the slow oscillation is assumed to be much smaller than the wave frequency. Perturbation expansion based on two time scales and two small parameters is performed to the order to include the effects of the acceleration of the low-frequency motion. Solutions to these higher order potentials are suggested in the present work. Wave loads including the wave drift added mass and damping are evaluated by the integration of the hydrodynamic pressure over the instantaneous wetted body surface.

X-Band Radar as a Tool to Determine Spectral and Single Wave Properties

2006 ◽  
Author(s):  
Konstanze Reichert ◽  
Katrin Hessner ◽  
Jens Dannenberg ◽  
Ina Traenkmann
Keyword(s):  
Real Time ◽  
Ocean Waves ◽  
Sea Surface ◽  
Surface Elevation ◽  
Radar Signal ◽  
Sea State ◽  
Single Wave ◽  
Radar Images ◽  
X Band ◽  
Wave Properties

The Wave Monitoring System WaMoS II was developed for real time measurements of directional ocean waves spectra to monitor the sea state from fixed platforms in deep water or coastal areas as well as from moving vessels. The system is based on a standard marine X-Band radar used for navigation and ship traffic control. WaMoS II digitises the analogous radar signal and analyses the sea clutter information to obtain directional wave spectra from the sea surface in real time even under harsh weather conditions and during night. Spectral sea state parameters such as significant wave height, peak wave period and peak wave direction both for wind sea and swell are derived. Within the EU funded project ‘MaxWave’ and the German project ‘SinSee’ new algorithms were developed to determine sea surface elevation maps from radar images which are used to investigate the spatial and temporal evolution of single waves simultaneously. In this paper a short overview describes the calculation of surface elevation maps and the detection of individual waves. Considering two case studies, the results of spatial single wave detection and corresponding temporal single wave properties are compared and discussed. Individual wave parameters derived from radar images are compared to individual waves measured by a buoy. An application of the method to characterise extreme sea states is discussed.

Rogue wave occurrence and dynamics by direct simulations of nonlinear wave-field evolution

2013 ◽  
Vol 720 ◽  
pp. 357-392 ◽  
Author(s):  
Wenting Xiao ◽  
Yuming Liu ◽  
Guangyu Wu ◽  
Dick K. P. Yue
Keyword(s):  
Wave Field ◽  
Linear Theory ◽  
Nonlinear Wave ◽  
Rogue Wave ◽  
Modulational Instability ◽  
Rogue Waves ◽  
Single Wave ◽  
Gaussian Statistics ◽  
Non Gaussian ◽  
Nonlinear Wave Field

AbstractWe study the occurrence and dynamics of rogue waves in three-dimensional deep water using phase-resolved numerical simulations based on a high-order spectral (HOS) method. We obtain a large ensemble of nonlinear wave-field simulations ($M= 3$ in HOS method), initialized by spectral parameters over a broad range, from which nonlinear wave statistics and rogue wave occurrence are investigated. The HOS results are compared to those from the broad-band modified nonlinear Schrödinger (BMNLS) equations. Our results show that for (initially) narrow-band and narrow directional spreading wave fields, modulational instability develops, resulting in non-Gaussian statistics and a probability of rogue wave occurrence that is an order of magnitude higher than linear theory prediction. For longer times, the evolution becomes quasi-stationary with non-Gaussian statistics, a result not predicted by the BMNLS equations (without consideration of dissipation). When waves spread broadly in frequency and direction, the modulational instability effect is reduced, and the statistics and rogue wave probability are qualitatively similar to those from linear theory. To account for the effects of directional spreading on modulational instability, we propose a new modified Benjamin–Feir index for effectively predicting rogue wave occurrence in directional seas. For short-crested seas, the probability of rogue waves based on number frequency is imprecise and problematic. We introduce an area-based probability, which is well defined and convergent for all directional spreading. Based on a large catalogue of simulated rogue wave events, we analyse their geometry using proper orthogonal decomposition (POD). We find that rogue wave profiles containing a single wave can generally be described by a small number of POD modes.

Statistical description of nonlinear wave fields

1975 ◽  
Vol 18 (10) ◽  
pp. 1084-1097 ◽  
Author(s):  
V. E. Zakharov ◽  
V. S. L'vov
Keyword(s):  
Nonlinear Wave ◽  
Wave Fields
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