On steady three-dimensional deep water weakly nonlinear gravity waves

Wave Motion ◽  
1982 ◽  
Vol 4 (2) ◽  
pp. 113-125 ◽  
Author(s):  
Yan-Chow Ma
Keyword(s):  
Gravity Waves ◽  
Deep Water ◽  
Three Dimensional ◽  
Weakly Nonlinear ◽  
Nonlinear Gravity

scholarly journals Oscillatory spatially periodic weakly nonlinear gravity waves on deep water

1988 ◽  
Vol 191 (-1) ◽  
pp. 341 ◽  
Author(s):  
Juana A. Zufiria
Keyword(s):  
Gravity Waves ◽  
Deep Water ◽  
Weakly Nonlinear ◽  
Spatially Periodic ◽  
Nonlinear Gravity

Frequency downshift in three-dimensional wave trains in a deep basin

1997 ◽  
Vol 352 ◽  
pp. 359-373 ◽  
Author(s):  
KARSTEN TRULSEN ◽  
KRISTIAN B. DYSTHE
Keyword(s):  
Gravity Waves ◽  
Deep Water ◽  
Wave Breaking ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Deep Basin ◽  
Weakly Nonlinear ◽  
Wave Trains ◽  
Dimensional Wave

The conservative evolution of weakly nonlinear narrow-banded gravity waves in deep water is investigated numerically with a modified nonlinear Schrödinger equation, for application to wide wave tanks. When the evolution is constrained to two dimensions, no permanent shift of the peak of the spectrum is observed. In three dimensions, allowing for oblique sideband perturbations, the peak of the spectrum is permanently downshifted. Dissipation or wave breaking may therefore not be necessary to produce a permanent downshift. The emergence of a standing wave across the tank is also predicted.

On the subharmonic instabilities of steady three-dimensional deep water waves

1994 ◽  
Vol 262 ◽  
pp. 265-291 ◽  
Author(s):  
Mansour Ioualalen ◽  
Christian Kharif
Keyword(s):  
Gravity Waves ◽  
Deep Water ◽  
Water Waves ◽  
Transverse Direction ◽  
Plane Waves ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Two Dimensional ◽  
Wave Steepness ◽  
Oblique Angle

A numerical procedure has been developed to study the linear stability of nonlinear three-dimensional progressive gravity waves on deep water. The three-dimensional patterns considered herein are short-crested waves which may be produced by two progressive plane waves propagating at an oblique angle, γ, to each other. It is shown that for moderate wave steepness the dominant resonances are sideband-type instabilities in the direction of propagation and, depending on the value of γ, also in the transverse direction. It is also shown that three-dimensional progressive gravity waves are less unstable than two-dimensional progressive gravity waves.

Particle trajectories of nonlinear gravity waves in deep water

2009 ◽  
Vol 36 (5) ◽  
pp. 324-329 ◽  
Author(s):  
Hsien-Kuo Chang ◽  
Yang-Yi Chen ◽  
Jin-Cheng Liou
Keyword(s):  
Gravity Waves ◽  
Deep Water ◽  
Particle Trajectories ◽  
Nonlinear Gravity

scholarly journals On the kurtosis of deep-water gravity waves

2015 ◽  
Vol 782 ◽  
pp. 25-36 ◽  
Author(s):  
Francesco Fedele
Keyword(s):  
Gravity Waves ◽  
Deep Water ◽  
Rogue Waves ◽  
Angular Frequency ◽  
Quasi Equilibrium ◽  
Weakly Nonlinear ◽  
Excess Kurtosis ◽  
Time Dynamic ◽  
Resonant Interactions ◽  
Type Spectrum

In this paper, we revisit Janssen’s (J. Phys. Oceanogr., vol. 33 (4), 2003, pp. 863–884) formulation for the dynamic excess kurtosis of weakly nonlinear gravity waves in deep water. For narrowband directional spectra, the formulation is given by a sixfold integral that depends upon the Benjamin–Feir index and the parameter $R={\it\sigma}_{{\it\theta}}^{2}/2{\it\nu}^{2}$, a measure of short-crestedness for the dominant waves, with ${\it\nu}$ and ${\it\sigma}_{{\it\theta}}$ denoting spectral bandwidth and angular spreading. Our refinement leads to a new analytical solution for the dynamic kurtosis of narrowband directional waves described with a Gaussian-type spectrum. For multidirectional or short-crested seas initially homogeneous and Gaussian, in a focusing (defocusing) regime dynamic kurtosis grows initially, attaining a positive maximum (negative minimum) at the intrinsic time scale ${\it\tau}_{c}={\it\nu}^{2}{\it\omega}_{0}t_{c}=1/\sqrt{3R}$, or $t_{c}/T_{0}\approx 0.13/{\it\nu}{\it\sigma}_{{\it\theta}}$, where ${\it\omega}_{0}=2{\rm\pi}/T_{0}$ denotes the dominant angular frequency. Eventually the dynamic excess kurtosis tends monotonically to zero as the wave field reaches a quasi-equilibrium state characterized by nonlinearities mainly due to bound harmonics. Quasi-resonant interactions are dominant only in unidirectional or long-crested seas where the longer-time dynamic kurtosis can be larger than that induced by bound harmonics, especially as the Benjamin–Feir index increases. Finally, we discuss the implication of these results for the prediction of rogue waves.

scholarly journals Phase Domain Walls in Weakly Nonlinear Deep Water Surface Gravity Waves

2018 ◽  
Vol 120 (22) ◽  
Author(s):  
F. Tsitoura ◽  
U. Gietz ◽  
A. Chabchoub ◽  
N. Hoffmann
Keyword(s):  
Gravity Waves ◽  
Deep Water ◽  
Water Surface ◽  
Domain Walls ◽  
Surface Gravity ◽  
Weakly Nonlinear ◽  
Surface Gravity Waves ◽  
Phase Domain

scholarly journals A new type of three-dimensional deep-water wave of permanent form

1980 ◽  
Vol 101 (4) ◽  
pp. 797-808 ◽  
Author(s):  
Philip G. Saffman ◽  
Henry C. Yuen
Keyword(s):  
Deep Water ◽  
Wave Train ◽  
Three Dimensional ◽  
Wave Pattern ◽  
Weakly Nonlinear ◽  
New Class ◽  
Wave Heights ◽  
New Type ◽  
Deep Water Wave ◽  
Permanent Form

A new class of three-dimensional, deep-water gravity waves of permanent form has been found using an equation valid for weakly nonlinear waves due to Zakharov (1968). These solutions appear as bifurcations from the uniform two-dimensional wave train. The critical wave heights are given as functions of the modulation wave vector. The three-dimensional patterns may be skewed or symmetrical. An example of the skewed wave pattern is given and shown to be stable. The results become exact in the limit of very oblique modulations.

On the Bifurcation of a Random Spectrum of Weakly Nonlinear Deep-Water Gravity Waves

1982 ◽  
Vol 66 (2) ◽  
pp. 145-158
Author(s):  
Yan-Chow Ma
Keyword(s):  
Gravity Waves ◽  
Deep Water ◽  
Weakly Nonlinear

Canonical equations for almost periodic, weakly nonlinear gravity waves

Wave Motion ◽  
1985 ◽  
Vol 7 (5) ◽  
pp. 473-485 ◽  
Author(s):  
A.C. Radder ◽  
M.W. Dingemans
Keyword(s):  
Gravity Waves ◽  
Almost Periodic ◽  
Weakly Nonlinear ◽  
Nonlinear Gravity

Three-Dimensional Stability and Bifurcation of Capillary and Gravity Waves on Deep Water

1985 ◽  
Vol 72 (2) ◽  
pp. 125-147 ◽  
Author(s):  
B. Chen ◽  
P. G. Saffman
Keyword(s):  
Gravity Waves ◽  
Deep Water ◽  
Dimensional Stability ◽  
Three Dimensional ◽  
Stability And Bifurcation
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