Resonant Wave Interaction with Random Forcing and Dissipation

2002 ◽  
Vol 108 (1) ◽  
pp. 123-144 ◽  
Author(s):  
Paul A. Milewski ◽  
Esteban G. Tabak ◽  
Eric Vanden-Eijnden
Keyword(s):  
Wave Interaction ◽  
Random Forcing ◽  
Resonant Wave

scholarly journals Decay Rates of Internal Tides Estimated by an Improved Wave–Wave Interaction Analysis

2018 ◽  
Vol 48 (11) ◽  
pp. 2689-2701 ◽  
Author(s):  
Yohei Onuki ◽  
Toshiyuki Hibiya
Keyword(s):  
Kinetic Equation ◽  
Energy Loss ◽  
Interaction Analysis ◽  
Wave Interaction ◽  
Deep Ocean ◽  
Energy Decay ◽  
Decay Rates ◽  
Internal Tides ◽  
Global Ocean ◽  
Resonant Wave

AbstractRecent numerical and observational studies have reported that resonant wave–wave interaction may be a crucial process for the energy loss of internal tides and the associated vertical water mixing in the midlatitude deep ocean. Special attention has been directed to the remarkable latitudinal dependence of the resonant interaction intensity; semidiurnal internal tides promptly lose their energy to near-inertial motions through parametric subharmonic instability equatorward of the critical latitudes 29°N/S, where half the tidal frequency coincides with the local inertial frequency. This feature contradicts the classical theoretical prediction that resonant wave–wave interaction does not play a major role in the tidal energy loss in the open ocean. By reformulating the kinetic equation for long internal waves and developing its calculation method, we estimate the energy decay rates of the low-vertical-mode semidiurnal internal tides interacting with the “ubiquitous” oceanic internal wave field. The result shows rapid energy decay of the internal tides, typically within O(10) days for the lowest-mode component, near their critical latitudes. This decay time is severalfold shorter than those in the classical studies and, additionally, varies by a factor of 2 depending on the local depth and density structure. We suggest from this study that the numerical integration of the kinetic equation is a more effective approach than recognized to determine the decay parameter of wave energy, which is indispensable for the global ocean models.

scholarly journals Evolution of a Random Directional Wave and Freak Wave Occurrence

2009 ◽  
Vol 39 (3) ◽  
pp. 621-639 ◽  
Author(s):  
Takuji Waseda ◽  
Takeshi Kinoshita ◽  
Hitoshi Tamura
Keyword(s):  
Wave Height ◽  
Wave Interaction ◽  
Northwest Pacific ◽  
Frequency Bandwidth ◽  
Extreme Wave ◽  
Spectral Parameters ◽  
Freak Wave ◽  
Resonant Wave ◽  
Directional Wave ◽  
Wind Sea

Abstract The evolution of a random directional wave in deep water was studied in a laboratory wave tank (50 m long, 10 m wide, 5 m deep) utilizing a directional wave generator. A number of experiments were conducted, changing the various spectral parameters (wave steepness 0.05 < ɛ < 0.11, with directional spreading up to 36° and frequency bandwidth 0.2 < δk/k < 0.6). The wave evolution was studied by an array of wave wires distributed down the tank. As the spectral parameters were altered, the wave height statistics change. Without any wave directionality, the occurrence of waves exceeding twice the significant wave height (the freak wave) increases as the frequency bandwidth narrows and steepness increases, due to quasi-resonant wave–wave interaction. However, the probability of an extreme wave rapidly reduces as the directional bandwidth broadens. The effective Benjamin–Feir index (BFIeff) is introduced, extending the BFI (the relative magnitude of nonlinearity and dispersion) to incorporate the effect of directionality, and successfully parameterizes the observed occurrence of freak waves in the tank. Analysis of the high-resolution hindcast wave field of the northwest Pacific reveals that such a directionally confined wind sea with high extreme wave probability is rare and corresponds mostly to a swell–wind sea mixed condition. Therefore, extreme wave occurrence in the sea as a result of quasi-resonant wave–wave interaction is a rare event that occurs only when the wind sea directionality is extremely narrow.

Viscous Wave Interaction Due to Motion of a Surface Wave Over a Sediment Bed

2006 ◽  
Vol 128 (4) ◽  
pp. 276-279 ◽  
Author(s):  
Mirmosadegh Jamali ◽  
Gregory A. Lawrence
Keyword(s):  
Surface Wave ◽  
Fluidized Bed ◽  
Wave Motion ◽  
Interaction Analysis ◽  
Wave Interaction ◽  
Interfacial Waves ◽  
Viscous Effects ◽  
Sediment Bed ◽  
Resonant Wave ◽  
Determining Factors

The results of a flume experiment and a theoretical study of surface wave motion over a fluidized bed are presented. It is shown that a resonant wave interaction between a surface wave and two interfacial waves at the interface of the fresh water and the fluidized bed is a strong mechanism for instability of the interface and the subsequent mixing of the layers. The interfacial waves are subharmonic to the surface wave and form a standing wave at the interface. The interaction is investigated theoretically using a viscous interaction analysis. It is shown that surface wave height and viscous effects are the determining factors in the instability mechanism. The results indicate that the net effect of viscosity on the interaction is to suppress the interfacial waves.

scholarly journals Far-off-resonant wave interaction in one-dimensional photonic crystals with quadratic nonlinearity

2008 ◽  
Vol 77 (2) ◽  
Author(s):  
Johannes-Geert Hagmann ◽  
Lasha Tkeshelashvili ◽  
Kurt Busch ◽  
Guido Schneider
Keyword(s):  
Photonic Crystals ◽  
Wave Interaction ◽  
Quadratic Nonlinearity ◽  
One Dimensional ◽  
Resonant Wave

scholarly journals Route to thermalization in the α-Fermi–Pasta–Ulam system

2015 ◽  
Vol 112 (14) ◽  
pp. 4208-4213 ◽  
Author(s):  
Miguel Onorato ◽  
Lara Vozella ◽  
Davide Proment ◽  
Yuri V. Lvov
Keyword(s):  
Wave Interaction ◽  
Discrete Systems ◽  
Interaction Theory ◽  
Random Waves ◽  
Wave Interactions ◽  
Weakly Nonlinear ◽  
Time Dynamics ◽  
Resonant Wave ◽  
Resonant Interactions ◽  
The One

We study the original α-Fermi–Pasta–Ulam (FPU) system with N = 16, 32, and 64 masses connected by a nonlinear quadratic spring. Our approach is based on resonant wave–wave interaction theory; i.e., we assume that, in the weakly nonlinear regime (the one in which Fermi was originally interested), the large time dynamics is ruled by exact resonances. After a detailed analysis of the α-FPU equation of motion, we find that the first nontrivial resonances correspond to six-wave interactions. Those are precisely the interactions responsible for the thermalization of the energy in the spectrum. We predict that, for small-amplitude random waves, the timescale of such interactions is extremely large and it is of the order of 1/ϵ8, where ϵ is the small parameter in the system. The wave–wave interaction theory is not based on any threshold: Equipartition is predicted for arbitrary small nonlinearity. Our results are supported by extensive numerical simulations. A key role in our finding is played by the Umklapp (flip-over) resonant interactions, typical of discrete systems. The thermodynamic limit is also briefly discussed.

scholarly journals Level III Reliability Design of an Armor Block of Rubble Mound Breakwater Using Probabilistic Model of Wave Height Optimized for the Korean Sea Wave Conditions and Non-Gaussian Wave Slope Distribution

2021 ◽  
Vol 9 (2) ◽  
pp. 223
Author(s):  
Yong Jun Cho
Keyword(s):  
Wave Height ◽  
Gaussian Distribution ◽  
Wave Interaction ◽  
Numerical Results ◽  
Controversial Issues ◽  
Reliability Design ◽  
Resonant Wave ◽  
Wave Slope ◽  
Rubble Mound ◽  
Non Gaussian

In this study, a Level III reliability design of an armor block of rubble mound breakwater was developed using the optimized probabilistic wave height model for the Korean marine environment and Van der Meer equation. To demonstrate what distinguishes this study from the others, numerical simulation was first carried out, assuming that wave slope follows Gaussian distribution recommended by PIANC. Numerical results showed that Gaussian wave slope distribution overpredicted the failure probability of armor block, longer and shorter waves, and on the contrary, underpredicted waves of the medium period. After noting the limitations of Gaussian distribution, some efforts were made to develop an alternative for Gaussian distribution. As a result, non-Gaussian wave slope distribution was analytically derived from the joint distribution of wave amplitude and period by Longuet–Higgins using the random variables transformation technique. Numerical results showed that non-Gaussian distribution could effectively address the limitations of Gaussian distribution due to its capability to account for the nonlinear resonant wave–wave interaction and its effects on the wave slope distribution that significantly influences the armor block’s stability. Therefore, the non-Gaussian wave slope distribution presented in this study could play an indispensable role in addressing controversial issues such as whether or not enormous armor blocks like a Tetrapod of 100 t frequently mentioned in developing countermeasures against rough seas due to climate change is too conservatively designed.

Viscous Wave Interaction Due to Motion of a Surface Wave Over a Sediment Bed

2004 ◽  
Author(s):  
Mirmosadegh Jamali ◽  
Greg A. Lawrence
Keyword(s):  
Surface Wave ◽  
Fluidized Bed ◽  
Wave Motion ◽  
Interaction Analysis ◽  
Wave Interaction ◽  
Interfacial Waves ◽  
Viscous Effects ◽  
Sediment Bed ◽  
Resonant Wave ◽  
Determining Factors

The results of a flume investigation of surface wave motion over a fluidized bed are presented. It is shown that a resonant wave interaction between a surface wave and two interfacial waves at the interface of the fresh water and the fluidized bed is a strong mechanism for instability of the interface and the subsequent mixing of the layers. The interfacial waves are subharmonic to the surface wave and form a standing wave at the interface. The interaction is investigated theoretically using a fully viscous interaction analysis. It is shown that surface wave height and viscous effects are the determining factors in the instability mechanism. The results indicate that the net effect of viscosity on the interaction process is to suppress the interfacial waves.

scholarly journals Interplay of Resonant and Quasi-Resonant Interaction of the Directional Ocean Waves

2009 ◽  
Vol 39 (9) ◽  
pp. 2351-2362 ◽  
Author(s):  
Takuji Waseda ◽  
Takeshi Kinoshita ◽  
Hitoshi Tamura
Keyword(s):  
Wave Interaction ◽  
Ocean Waves ◽  
Resonant Interaction ◽  
Wave System ◽  
Spectral Evolution ◽  
Relative Significance ◽  
Freak Wave ◽  
Recent Experimental Study ◽  
Resonant Wave ◽  
Insight Into

Abstract Recent experimental study of the evolution of random directional gravity waves in deep water provides new insight into the nature of the spectral evolution of the ocean waves and the relative significance of resonant and quasi-resonant wave interaction. When the directional angle containing half the total energy is broader than ∼20°, the spectrum evolves following the energy transfer that can be described by the four-wave resonant interaction alone. In contrast, in the case of a directionally confined spectrum, the effect of quasi-resonant wave–wave interaction becomes important, and the wave system becomes unstable. When the temporal change of the spectral shape due to quasi resonance becomes irreversible owing to energetic breaking dissipation, the spectrum rapidly downshifts. Under such extreme conditions, the likelihood of a freak wave is high.

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