Optimum Vessel Performance in Evolving Nonlinear Wave Fields

2012 ◽  
Author(s):  
Robert F. Beck
Keyword(s):  
Nonlinear Wave ◽  
Wave Fields

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.

Particle acceleration in localized nonlinear wave fields

1998 ◽  
Vol 21 (4) ◽  
pp. 619-628 ◽  
Author(s):  
Rudolf A Treumann
Keyword(s):  
Particle Acceleration ◽  
Nonlinear Wave ◽  
Wave Fields

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.

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

Nonlinear phase-resolved reconstruction of irregular water waves

2018 ◽  
Vol 838 ◽  
pp. 544-572 ◽  
Author(s):  
Yusheng Qi ◽  
Guangyu Wu ◽  
Yuming Liu ◽  
Moo-Hyun Kim ◽  
Dick K. P. Yue
Keyword(s):  
Wave Field ◽  
Nonlinear Wave ◽  
Water Waves ◽  
Three Dimensional ◽  
Reconstruction Error ◽  
High Order ◽  
Order Effects ◽  
Wave Fields ◽  
Wave Measurements ◽  
Wave Nonlinearity

We develop and validate a high-order reconstruction (HOR) method for the phase-resolved reconstruction of a nonlinear wave field given a set of wave measurements. HOR optimizes the amplitude and phase of $L$ free wave components of the wave field, accounting for nonlinear wave interactions up to order $M$ in the evolution, to obtain a wave field that minimizes the reconstruction error between the reconstructed wave field and the given measurements. For a given reconstruction tolerance, $L$ and $M$ are provided in the HOR scheme itself. To demonstrate the validity and efficacy of HOR, we perform extensive tests of general two- and three-dimensional wave fields specified by theoretical Stokes waves, nonlinear simulations and physical wave fields in tank experiments which we conduct. The necessary $L$, for general broad-banded wave fields, is shown to be substantially less than the free and locked modes needed for the nonlinear evolution. We find that, even for relatively small wave steepness, the inclusion of high-order effects in HOR is important for prediction of wave kinematics not in the measurements. For all the cases we consider, HOR converges to the underlying wave field within a nonlinear spatial-temporal predictable zone ${\mathcal{P}}_{NL}$ which depends on the measurements and wave nonlinearity. For infinitesimal waves, ${\mathcal{P}}_{NL}$ matches the linear predictable zone ${\mathcal{P}}_{L}$, verifying the analytic solution presented in Qi et al. (Wave Motion, vol. 77, 2018, pp. 195–213). With increasing wave nonlinearity, we find that ${\mathcal{P}}_{NL}$ contains and is generally greater than ${\mathcal{P}}_{L}$. Thus ${\mathcal{P}}_{L}$ provides a (conservative) estimate of ${\mathcal{P}}_{NL}$ when the underlying wave field is not known.

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.

Efficient Fourier-collocation method for full scattering data of Zakharov-Shabat periodic problem

2021 ◽  
Author(s):  
Ilya Mullyadzhanov ◽  
Rustam Mullyadzhanov ◽  
Andrey Gelash
Keyword(s):  
Wave Field ◽  
Collocation Method ◽  
Nonlinear Wave ◽  
Periodic Problem ◽  
Physical Review ◽  
Scattering Data ◽  
Eigenvalue Spectrum ◽  
Plane Wave Solution ◽  
Wave Fields ◽  
Fourier Collocation

<p>The one-dimensional nonlinear Schrodinger equation (NLSE) serves as a universal model of nonlinear wave propagation appearing in different areas of physics. In particular it describes weakly nonlinear wave trains on the surface of deep water and captures up to certain extent the phenomenon of rogue waves formation. The NLSE can be completely integrated using the inverse scattering transform method that allows transformation of the wave field to the so-called scattering data representing a nonlinear analogue of conventional Fourier harmonics. The scattering data for the NLSE can be calculated by solving an auxiliary linear system with the wave field playing the role of potential – the so-called Zakharov-Shabat problem. Here we present a novel efficient approach for numerical computation of scattering data for spatially periodic nonlinear wave fields governed by focusing version of the NLSE. The developed algorithm is based on Fourier-collocation method and provides one an access to full scattering data, that is main eigenvalue spectrum (eigenvalue bands and gaps) and auxiliary spectrum (specific phase parameters of the nonlinear harmonics) of Zakharov-Shabat problem. We verify the developed algorithm using a simple analytic plane wave solution and then demonstrate its efficiency with various examples of large complex nonlinear wave fields exhibiting intricate structure of bands and gaps. Special attention is paid to the case when the wave field is strongly nonlinear and contains solitons which correspond to narrow gaps in the eigenvalue spectrum, see e.g. [1], when numerical computations may become unstable [2]. Finally we discuss applications of the developed approach for analysis of numerical and experimental nonlinear wave fields data.</p><p>The work was supported by Russian Science Foundation grant No. 20-71-00022.</p><p>[1] A. A. Gelash and D. S. Agafontsev, Physical Review E 98, 042210 (2018).</p><p>[2] A. Gelash and R. Mullyadzhanov, Physical Review E 101, 052206 (2020).</p>

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