scholarly journals Numerical experiments of nonlinear energy transfer within the oceanic internal wave spectrum

1998 ◽  
Vol 103 (C9) ◽  
pp. 18715-18722 ◽  
Author(s):  
Toshiyuki Hibiya ◽  
Yoshihiro Niwa ◽  
Kayo Fujiwara
Keyword(s):  
Energy Transfer ◽  
Internal Wave ◽  
Numerical Experiments ◽  
Wave Spectrum ◽  
Nonlinear Energy Transfer ◽  
Oceanic Internal Wave ◽  
Nonlinear Energy

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.

Nonlinear energy transfer and the energy balance of the internal wave field in the deep ocean

1976 ◽  
Vol 74 (2) ◽  
pp. 375-399 ◽  
Author(s):  
Dirk J. Olbers
Keyword(s):  
Energy Transfer ◽  
Energy Balance ◽  
Internal Wave ◽  
Wave Field ◽  
Wave Spectrum ◽  
Fluid Motion ◽  
Deep Ocean ◽  
Nonlinear Interactions ◽  
Nonlinear Energy Transfer ◽  
Spectral Models

The source function describing the energy transfer between the components of the internal wave spectrum due to nonlinear interactions is derived from the Lagrangian of the fluid motion and evaluated numerically for the spectral models of Garrett & Munk (1972a, 1975). The characteristic time scales of the transfer are found to be typically of the order of some days, so that nonlinear interactions will play an important role in the energy balance of the wave field. Thus implications of the nonlinear transfer within the spectrum for generation and dissipation processes are considered.

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.

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