scholarly journals Role of Nonlinear Energy Transfer on Wave spectrum in the Equilibrium Range

2013 ◽  
Vol 69 (2) ◽  
pp. I_121-I_125
Author(s):  
Hitoshi TAMURA ◽  
Takuji WASEDA ◽  
Yasumasa MIYAZAWA
Keyword(s):  
Energy Transfer ◽  
Wave Spectrum ◽  
Nonlinear Energy Transfer ◽  
Equilibrium Range ◽  
Nonlinear Energy

scholarly journals Current-Induced Modulation of the Ocean Wave Spectrum and the Role of Nonlinear Energy Transfer

2008 ◽  
Vol 38 (12) ◽  
pp. 2662-2684 ◽  
Author(s):  
Hitoshi Tamura ◽  
Takuji Waseda ◽  
Yasumasa Miyazawa ◽  
Kosei Komatsu
Keyword(s):  
Energy Transfer ◽  
Numerical Simulations ◽  
The Self ◽  
Current Field ◽  
Nonlinear Energy Transfer ◽  
Nonlinear Transfer ◽  
Stabilization Effect ◽  
Self Stabilization ◽  
Nonlinear Energy

Abstract Numerical simulations were performed to investigate current-induced modulation of the spectral and statistical properties of ocean waves advected by idealized and realistic current fields. In particular, the role of nonlinear energy transfer among waves in wave–current interactions is examined. In this type of numerical simulation, it is critical to treat the nonlinear transfer function (Snl) properly, because a rigorous Snl algorithm incurs a huge computational cost. However, the applicability of the widely used discrete interaction approximation (DIA) method is strictly limited for complex wave fields. Therefore, the simplified RIAM (SRIAM) method is implemented in an operational third-generation wave model. The method approximates an infinite resonant quadruplet with 20 optimized resonance configurations. The performance of the model is assessed by applying it to fetch-limited wave growth and wave propagation against a shear current. Numerical simulations using the idealized current field revealed that the Snl retained spectral form by redistributing the refracted wave energy; this suggests that energy concentration due to ray focusing is dispersed via the self-stabilization effect of nonlinear transfer. A hindcast simulation using wind and current reanalysis data indicated that the difference in the average monthly wave height was substantial and that instantaneous wave–current interactions were highly sensitive to small current structures. Spectral shape was also modulated, and the spatial distributions of the directional bandwidth with or without current data were completely different. Moreover, the self-stabilization effect of the Snl was also confirmed in a realistic situation. These results indicate that a realistic representation of the current field is crucial for high-resolution wave forecasting.

scholarly journals Nonlinear energy transfer to short gravity waves in the presence of long waves

1995 ◽  
Vol 289 ◽  
pp. 199-226 ◽  
Author(s):  
H. S. Ölmez ◽  
J. H. Milgram
Keyword(s):  
Energy Transfer ◽  
Gravity Waves ◽  
Wave Spectrum ◽  
Nonlinear Interactions ◽  
Physical Reason ◽  
Transfer Rates ◽  
Nonlinear Energy Transfer ◽  
Long Wave ◽  
Direct Numerical Method ◽  
Nonlinear Energy

Existing theories for calculating the energy transfer rates to gravity waves due to resonant nonlinear interactions among wave components whose lengths are long in comparison to wave elevations have been verified experimentally and are well accepted. There is uncertainty, however, about prediction of energy transfer rates within a set of waves having short to moderate lengths when these are present simultaneously with a long wave whose amplitude is not small in comparison to the short wavelengths. Here we implement both a direct numerical method that avoids small-amplitude approximations and a spectral method which includes perturbations of high order. These are applied to an interacting set of short- to intermediate-length waves with and without the presence of a large long wave. The same cases are also studied experimentally. Experimentally and numerical results are in reasonable agreement with the finding that the long wave does influence the energy transfer rates. The physical reason for this is identified and the implications for computations of energy transfer to short waves in a wave spectrum are discussed.

On the Nonlinear Energy Interactions in Harmonically Excited Post-Buckled Flexible Inverted Pendulum in the Presence of Friction

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Vishal Vyas ◽  
Prasanna Gandhi
Keyword(s):  
Energy Transfer ◽  
Inverted Pendulum ◽  
Resonant Mode ◽  
Friction Model ◽  
Low Friction ◽  
Nonlinear Energy Transfer ◽  
Input Side ◽  
Harmonic Resonance ◽  
Nonlinear Energy

Nonlinear energy interaction is a fascinating feature of nonlinear oscillators and has been drawing the attention of researchers since the last few decades. Omnipresent friction in mechanical systems can play a crucial role in modifying these interactions. Using post-buckled flexible inverted pendulum as a candidate system we characterize here, theoretically and experimentally, significant changes in the nonlinear energy transfer in the presence of friction at the input side. Particularly, even with relatively low friction, the energy gets transferred in the higher harmonics of excitation close to a resonant mode as against the transfer to higher modes reported previously. We term this new phenomenon as “excitation harmonic resonance locking.” Theoretical modeling and simulations, considering large deformations, based on assumed modes method, and using a simple friction model reasonably capture the experimental observation. In summary, the paper explicates the role of friction in shifting energy transfer frequencies and can be useful in understanding and designing of oscillators and nonlinear vibrating systems.

scholarly journals Asymptotes of the nonlinear transfer and wave spectrum in the frame of the kinetic equation solution

2018 ◽  
Author(s):  
Vladislav G. Polnikov ◽  
Fangli Qiao ◽  
Yong Teng
Keyword(s):  
Energy Transfer ◽  
Kinetic Equation ◽  
Wave Spectrum ◽  
Low Frequency ◽  
Peak Frequency ◽  
Two Dimensional ◽  
Equation Solution ◽  
Nonlinear Energy Transfer ◽  
The Difference ◽  
Nonlinear Energy

Abstract. The kinetic equation for a gravity wave spectrum is solved numerically to study the high frequencies asymptotes for the one-dimensional nonlinear energy transfer and the variability of spectrum parameters that accompany the long-term evolution of nonlinear waves. The cases of initial two-dimensional spectra S(ω,θ) of modified JONSWAP type with the frequency decay-law S(ω) ~ ω−n (for n = 6, 5, 4 and 3.5) and various initial functions of the angular distribution are considered. It is shown that at the first step of the kinetic equation solution, the nonlinear energy transfer asymptote has the power-like decay-law, Nl(ω) ~ ω−p, with values p ≤ n − 1, valid in cases when n ≥ 5, and the difference, n-p, changes significantly when n approaches 4. On time scales of evolution greater than several thousands of initial wave periods, in every case, a self-similar spectrum Ssf(ω,θ) is established with the frequency decay-law of form S(ω) ~ ω−4. Herein, the asymptote of nonlinear energy transfer becomes negative in value and decreases according to the same law (i.e., Nl(ω) ~ −ω−4). The peak frequency of the spectrum, ωp(t), migrates in time t to the low-frequency region such that the angular and frequency characteristics of the two-dimensional spectrum Ssf(ω,θ) remain constant. However, these characteristics depend on the degree of angular anisotropy of the initial spectrum. The solutions obtained are interpreted, and their connection with the analytical solutions of the kinetic equation by Zakharov and co-authors for gravity waves in water is discussed.

Sign in / Sign up

Export Citation Format

Share Document