scholarly journals Five-Wave Resonances in Deep Water Gravity Waves: Integrability, Numerical Simulations and Experiments

Fluids ◽  
2021 ◽  
Vol 6 (6) ◽  
pp. 205
Author(s):  
Dan Lucas ◽  
Marc Perlin ◽  
Dian-Yong Liu ◽  
Shane Walsh ◽  
Rossen Ivanov ◽  
...  
Keyword(s):  
Normal Form ◽  
Numerical Simulations ◽  
Gravity Waves ◽  
Deep Water ◽  
Plane Waves ◽  
Surface Elevation ◽  
Wave Interactions ◽  
Frequency Space ◽  
Target Mode ◽  
The Hilbert Transform

In this work we consider the problem of finding the simplest arrangement of resonant deep-water gravity waves in one-dimensional propagation, from three perspectives: Theoretical, numerical and experimental. Theoretically this requires using a normal-form Hamiltonian that focuses on 5-wave resonances. The simplest arrangement is based on a triad of wavevectors K1+K2=K3 (satisfying specific ratios) along with their negatives, corresponding to a scenario of encountering wavepackets, amenable to experiments and numerical simulations. The normal-form equations for these encountering waves in resonance are shown to be non-integrable, but they admit an integrable reduction in a symmetric configuration. Numerical simulations of the governing equations in natural variables using pseudospectral methods require the inclusion of up to 6-wave interactions, which imposes a strong dealiasing cut-off in order to properly resolve the evolving waves. We study the resonance numerically by looking at a target mode in the base triad and showing that the energy transfer to this mode is more efficient when the system is close to satisfying the resonant conditions. We first look at encountering plane waves with base frequencies in the range 1.32–2.35 Hz and steepnesses below 0.1, and show that the time evolution of the target mode’s energy is dramatically changed at the resonance. We then look at a scenario that is closer to experiments: Encountering wavepackets in a 400-m long numerical tank, where the interaction time is reduced with respect to the plane-wave case but the resonance is still observed; by mimicking a probe measurement of surface elevation we obtain efficiencies of up to 10% in frequency space after including near-resonant contributions. Finally, we perform preliminary experiments of encountering wavepackets in a 35-m long tank, which seem to show that the resonance exists physically. The measured efficiencies via probe measurements of surface elevation are relatively small, indicating that a finer search is needed along with longer wave flumes with much larger amplitudes and lower frequency waves. A further analysis of phases generated from probe data via the analytic signal approach (using the Hilbert transform) shows a strong triad phase synchronisation at the resonance, thus providing independent experimental evidence of the resonance.

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.

Spatial versions of the Zakharov and Dysthe evolution equations for deep-water gravity waves

2002 ◽  
Vol 450 ◽  
pp. 201-205 ◽  
Author(s):  
ELIEZER KIT ◽  
LEV SHEMER
Keyword(s):  
Gravity Waves ◽  
Fourth Order ◽  
Deep Water ◽  
Evolution Equations ◽  
Velocity Potential ◽  
Surface Elevation ◽  
Two Dimensional ◽  
Zakharov Equation ◽  
Dimensional Version

A spatial two-dimensional version of the Zakharov equation describing the evolution of deep-water gravity waves is used to derive two fourth-order evolution equations, for the amplitudes of the surface elevation and of the velocity potential. The scaled form of the equations is presented.

Normal Form Transformations and Dysthe’s Equation for the Nonlinear Modulation of Deep-Water Gravity Waves

Water Waves ◽  
2020 ◽  
Author(s):  
Walter Craig ◽  
Philippe Guyenne ◽  
Catherine Sulem
Keyword(s):  
Normal Form ◽  
Gravity Waves ◽  
Deep Water ◽  
Nonlinear Modulation

scholarly journals FREAK WAVE AND WEATHER CONDITION

2011 ◽  
Vol 1 (32) ◽  
pp. 70
Author(s):  
Nobuhito Mori ◽  
Hajime Mase ◽  
Tomohiro Yasuda
Keyword(s):  
Numerical Simulations ◽  
Weather Condition ◽  
The Other ◽  
Surface Elevation ◽  
Fourth Quadrant ◽  
Wave Interactions ◽  
Freak Waves ◽  
Freak Wave

The kurtosis of the surface elevation, Benjamin-Feir Index (BFI) and directional spread are measures of nonlinear four-wave interactions and freak waves. The dependence of kurtosis, BFI and directional spread under typhoon conditions are examined by numerical simulations. The BFI is significantly large in the fourth quadrant of the typhoon while the directional spread is small in the fourth quadrant. It was found that the potentially possible area of freak wave occurrence is the fourth quadrant of the typhoon rather than the other quadrants.

Resonant wave interactions in a stratified shear flow

1988 ◽  
Vol 190 ◽  
pp. 357-374 ◽  
Author(s):  
R. Grimshaw
Keyword(s):  
Shear Flow ◽  
Gravity Waves ◽  
Critical Level ◽  
Internal Gravity Waves ◽  
Wave Interactions ◽  
Resonant Wave ◽  
Resonant Interactions ◽  
Stratified Shear Flow ◽  
Weak Resonance ◽  
Background Shear

Resonant interactions between triads of internal gravity waves propagating in a shear flow are considered for the case when the stratification and the background shear flow vary slowly with respect to typical wavelengths. If ωn, kn(n = 1, 2, 3) are the local frequencies and wavenumbers respectively then the resonance conditions are that ω1 + ω2 + ω3 = 0 and k1 + k2 + k3 = 0. If the medium is only weakly inhomogeneous, then there is a strong resonance and to leading order the resonance conditions are satisfied globally. The equations governing the wave amplitudes are then well known, and have been extensively discussed in the literature. However, if the medium is strongly inhomogeneous, then there is a weak resonance and the resonance conditions can only be satisfied locally on certain space-time resonance surfaces. The equations governing the wave amplitudes in this case are derived, and discussed briefly. Then the results are applied to a study of the hierarchy of wave interactions which can occur near a critical level, with the aim of determining to what extent a critical layer can reflect wave energy.

Steep gravity waves in water of arbitrary uniform depth

1977 ◽  
Vol 286 (1335) ◽  
pp. 183-230 ◽  
Keyword(s):  
Gravity Waves ◽  
Deep Water ◽  
Water Waves ◽  
Perturbation Parameter ◽  
Intermediate Energy ◽  
Finite Amplitude ◽  
Wave Profile ◽  
Accurate Calculation ◽  
Theoretical Developments ◽  
Deep Water Waves

Modern applications of water-wave studies, as well as some recent theoretical developments, have shown the need for a systematic and accurate calculation of the characteristics of steady, progressive gravity waves of finite amplitude in water of arbitrary uniform depth. In this paper the speed, momentum, energy and other integral properties are calculated accurately by means of series expansions in terms of a perturbation parameter whose range is known precisely and encompasses waves from the lowest to the highest possible. The series are extended to high order and summed with Padé approximants. For any given wavelength and depth it is found that the highest wave is not the fastest. Moreover the energy, momentum and their fluxes are found to be greatest for waves lower than the highest. This confirms and extends the results found previously for solitary and deep-water waves. By calculating the profile of deep-water waves we show that the profile of the almost-steepest wave, which has a sharp curvature at the crest, intersects that of a slightly less-steep wave near the crest and hence is lower over most of the wavelength. An integration along the wave profile cross-checks the Padé-approximant results and confirms the intermediate energy maximum. Values of the speed, energy and other integral properties are tabulated in the appendix for the complete range of wave steepnesses and for various ratios of depth to wavelength, from deep to very shallow water.

Delay stabilization of periodic orbits in coupled oscillator systems

2010 ◽  
Vol 368 (1911) ◽  
pp. 319-341 ◽  
Author(s):  
B. Fiedler ◽  
V. Flunkert ◽  
P. Hövel ◽  
E. Schöll
Keyword(s):  
Normal Form ◽  
Numerical Simulations ◽  
Periodic Orbits ◽  
Coupled Oscillators ◽  
Coupled Oscillator ◽  
Non Invasive ◽  
Coupling Parameters ◽  
Necessary And Sufficient ◽  
Time Delayed Feedback ◽  
Coupled Oscillator Systems

We study diffusively coupled oscillators in Hopf normal form. By introducing a non-invasive delay coupling, we are able to stabilize the inherently unstable anti-phase orbits. For the super- and subcritical cases, we state a condition on the oscillator’s nonlinearity that is necessary and sufficient to find coupling parameters for successful stabilization. We prove these conditions and review previous results on the stabilization of odd-number orbits by time-delayed feedback. Finally, we illustrate the results with numerical simulations.

scholarly journals Emergence of Peregrine solitons in integrable turbulence of deep water gravity waves

2020 ◽  
Vol 5 (8) ◽  
Author(s):  
Guillaume Michel ◽  
Félicien Bonnefoy ◽  
Guillaume Ducrozet ◽  
Gaurav Prabhudesai ◽  
Annette Cazaubiel ◽  
...  
Keyword(s):  
Gravity Waves ◽  
Deep Water

Interaction of surface waves with turbulence: direct numerical simulations of turbulent open-channel flow

1995 ◽  
Vol 286 ◽  
pp. 1-23 ◽  
Author(s):  
Vadim Borue ◽  
Steven A. Orszag ◽  
Ilya Staroselsky
Keyword(s):  
Free Surface ◽  
Numerical Simulations ◽  
Channel Flow ◽  
Gravity Waves ◽  
Open Channel ◽  
Open Channel Flow ◽  
Surface Region ◽  
Direct Numerical Simulations ◽  
Turbulence Production ◽  
Wind Sea

We report direct numerical simulations of incompressible unsteady open-channel flow. Two mechanisms of turbulence production are considered: shear at the bottom and externally imposed stress at the free surface. We concentrate upon the effects of mutual interaction of small-amplitude gravity waves with in-depth turbulence and statistical properties of the near-free-surface region. Extensions of our approach can be used to study turbulent mixing in the upper ocean and wind–sea interaction, and to provide diagnostics of bulk turbulence.

Numerical Simulation of Dynamics of a Spar Type Floating Wind Turbine and Comparison With Laboratory Measurements

2016 ◽  
Author(s):  
Hyunseong Min ◽  
Cheng Peng ◽  
Fei Duan ◽  
Zhiqiang Hu ◽  
Jun Zhang
Keyword(s):  
Numerical Simulation ◽  
Wind Speed ◽  
Numerical Simulations ◽  
Wind Turbine ◽  
Wind Turbines ◽  
Deep Water ◽  
Offshore Wind ◽  
Wind Loads ◽  
Floating Offshore Wind Turbines ◽  
The Cost

Wind turbines are popular for harnessing wind energy. Floating offshore wind turbines (FOWT) installed in relatively deep water may have advantages over their on-land or shallow-water cousins because winds over deep water are usually steadier and stronger. As the size of wind turbines becomes larger and larger for reducing the cost per kilowatt, it could bring installation and operation risks in the deep water due to the lack of track records. Thus, together with laboratory tests, numerical simulations of dynamics of FOWT are desirable to reduce the probability of failure. In this study, COUPLE-FAST was initially employed for the numerical simulations of the OC3-HYWIND, a spar type platform equipped with the 5-MW baseline wind turbine proposed by National Renewable Energy Laboratory (NREL). The model tests were conducted at the Deepwater Offshore Basin in Shanghai Jiao Tong University (SJTU) with a 1:50 Froude scaling [1]. In comparison of the simulation using COUPLE-FAST with the corresponding measurements, it was found that the predicted motions were in general significantly smaller than the related measurements. The main reason is that the wind loads predicted by FAST were well below the related measurements. Large discrepancies are expected because the prototype and laboratory wind loads do not follow Froude number similarity although the wind speed was increased (or decreased) in the tests such that the mean surge wind force matched that predicted by FAST at the nominal wind speed (Froude similarity) in the cases of a land wind turbine [1]. Therefore, an alternative numerical simulation was made by directly inputting the measured wind loads to COUPLE instead of the ones predicted by FAST. The related simulated results are much improved and in satisfactory agreement with the measurements.

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