scholarly journals Bifurcation Mechanism for Generation of Random Deep-Water Stokes Waves.

2000 ◽  
pp. 27-36
Author(s):  
Kiyohiro IKEDA ◽  
Nobuhito MORI ◽  
Takashi YASUDA
Keyword(s):  
Deep Water ◽  
Bifurcation Mechanism ◽  
Stokes Waves

Oscillatory Third-Order Perturbation Solutions for Sums of Interacting Long-Crested Stokes Waves on Deep Water

1993 ◽  
Vol 37 (04) ◽  
pp. 354-383
Author(s):  
Willard J. Pierson
Keyword(s):  
Free Surface ◽  
Deep Water ◽  
Perturbation Expansion ◽  
The United States ◽  
Order Perturbation ◽  
Naval Academy ◽  
Third Order ◽  
First Order ◽  
Stokes Waves ◽  
Perturbation Solutions

Oscillatory third-order perturbation solutions for sums of interacting long-crested Stokes waves on deep water are obtained. A third-order perturbation expansion of the nonlinear free boundary value problem, defined by the coupled Bernoulli equation and kinematic boundary condition evaluated at the free surface, is solved by replacing the exponential term in the potential function by its series expansion and substituting the equation for the free surface into it. There are second-order changes in the frequencies of the first-order terms at third order. The waves have a Stokes-like form when they are high. The phase speeds are a function of the amplitudes and wave numbers of all of the first-order terms. The solutions are illustrated. A preliminary experiment at the United States Naval Academy is described. Some applications to sea keeping are bow submergence and slamming, capsizing in following seas and bending moments.

Laboratory Observations on the Evolution of Deep-Water Wave Packets

2011 ◽  
Author(s):  
Yuxiang Ma ◽  
Guohai Dong ◽  
Xiaozhou Ma
Keyword(s):  
Experimental Data ◽  
Deep Water ◽  
Wave Breaking ◽  
Water Wave ◽  
Wave Packets ◽  
Local Maximum ◽  
Peak Frequency ◽  
Higher Harmonics ◽  
Stokes Waves ◽  
Deep Water Wave

New experimental data for the evolution of deep-water wave packets has been presented. The present experimental data shows that the local maximum steepness for extreme waves is significantly above the criterion of the limiting Stokes waves. The wavelet spectra of the wave groups around the breaking locations indicate that the energy of higher harmonics can be generated quickly before wave breaking and mainly concentrate at the part of the wave fronts. After wave breaking, however, these higher harmonics energy is dissipated immediately. Furthermore, the variations of local peak frequency have also been examined. It is found that frequency downshift increases with the increase of initial steepness and wave packet size.

Modulated Periodic Stokes Waves in Deep Water

2000 ◽  
Vol 84 (5) ◽  
pp. 887-890 ◽  
Author(s):  
M. J. Ablowitz ◽  
J. Hammack ◽  
D. Henderson ◽  
C. M. Schober
Keyword(s):  
Deep Water ◽  
Stokes Waves

scholarly journals Three-dimensional surface gravity waves of a broad bandwidth on deep water

2021 ◽  
Vol 926 ◽  
Author(s):  
Yan Li
Keyword(s):  
Deep Water ◽  
Water Waves ◽  
Order Approximation ◽  
Three Dimensional ◽  
Finite Depth ◽  
Second Order ◽  
Leading Order ◽  
Broad Bandwidth ◽  
Stokes Waves ◽  
Deep Water Waves

A new nonlinear Schrödinger equation (NLSE) is presented for ocean surface waves. Earlier derivations of NLSEs that describe the evolution of deep-water waves have been limited to a narrow bandwidth, for which the bound waves at second order in wave steepness are described in leading-order approximations. This work generalizes these earlier works to allow for deep-water waves of a broad bandwidth with large directional spreading. The new NLSE permits simple numerical implementations and can be extended in a straightforward manner in order to account for waves on water of finite depth. For the description of second-order waves, this paper proposes a semianalytical approach that can provide accurate and computationally efficient predictions. With a leading-order approximation to the new NLSE, the instability region and energy growth rate of Stokes waves are investigated. Compared with the exact results based on McLean (J. Fluid Mech., vol. 511, 1982, p. 135), predictions by the new NLSE show better agreement than by Trulsen et al. (Phys. Fluids, vol. 12, 2000, pp. 2432–2437). With numerical implementations of the new NLSE, the effects of wave directionality are investigated by examining the evolution of a directionally spread focused wave group. A downward shift of the spectral peak is observed, owing to the asymmetry in the change rate of energy in a more complex manner than that for uniform Stokes waves. Rapid oblique energy transfers near the group at linear focus are observed, likely arising from the instability of uniform Stokes waves appearing in a narrow spectrum subject to oblique sideband disturbances.

scholarly journals Fractional Fourier approximations for potential gravity waves on deep water

2003 ◽  
Vol 10 (6) ◽  
pp. 599-614 ◽  
Author(s):  
V. P. Lukomsky ◽  
I. S. Gandzha
Keyword(s):  
Gravity Waves ◽  
Deep Water ◽  
Basis Functions ◽  
Irregular Waves ◽  
Computational Time ◽  
Stokes Wave ◽  
Decimal Digit ◽  
Stokes Waves ◽  
New Type ◽  
Flow Domain

Abstract. In the framework of the canonical model of hydrodynamics, where fluid is assumed to be ideal and incompressible, waves are potential, two-dimensional, and symmetric, the authors have recently reported the existence of a new type of gravity waves on deep water besides well studied Stokes waves (Lukomsky et al., 2002b). The distinctive feature of these waves is that horizontal water velocities in the wave crests exceed the speed of the crests themselves. Such waves were found to describe irregular flows with stagnation point inside the flow domain and discontinuous streamlines near the wave crests. In the present work, a new highly efficient method for computing steady potential gravity waves on deep water is proposed to examine the character of singularity of irregular flows in more detail. The method is based on the truncated fractional approximations for the velocity potential in terms of the basis functions 1/(1 - exp(y0 - y -  ix))n, y0 being a free parameter. The non-linear transformation of the horizontal scale x = c - g sin c, 0  < g  <  1,  is additionally applied to concentrate a numerical emphasis on the crest region of a wave for accelerating the convergence of the series. For lesser computational time, the advantage in accuracy over ordinary Fourier expansions in terms of the basis functions exp(n(y + ix))  was found to be from one to ten decimal orders for steep Stokes waves and up to one decimal digit for irregular flows. The data obtained supports the following conjecture: irregular waves to all appearance represent a family of sharp-crested waves like the limiting Stokes wave but of lesser amplitude.

The non-linear evolution of Stokes waves in deep water

1971 ◽  
Vol 47 (2) ◽  
pp. 337-351 ◽  
Author(s):  
Vincent H. Chu ◽  
Chiang C. Mei
Keyword(s):  
Deep Water ◽  
Qualitative Agreement ◽  
Nonlinear Evolution ◽  
Frequency Dispersion ◽  
Experimental Measurements ◽  
Modulation Equations ◽  
Dynamical Equilibrium ◽  
Linear Evolution ◽  
Stokes Waves ◽  
Multiple Groups

Based on a set of modulation equations derived in a previous paper, the nonlinear evolution of wave envelope in deep water is studied numerically. It is found that the wave envelope tends to disintegrate to multiple groups of waves each of which approaches a stable permanent envelope representing dynamical equilibrium between the amplitude dispersion and the frequency dispersion. Qualitative agreement with the experimental measurements of Feir (1967) is also observed.

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