Bispectral experimental estimation of the nonlinear energy transfer in two-dimensional plasma turbulence

In the present paper, we give a selective review of some very recent works concerning the non-stationary regimes emerging in various one- and two-dimensional models incorporating internal rotators. In one-dimensional models, these regimes are characterized by the intense energy transfer from the outer element, subjected to initial or harmonic excitation, to the internal rotator. As for the two-dimensional models (incorporating internal rotators), we will mainly focus on the two special dynamical states, namely a state of the near-complete energy transfer from longitudinal to lateral vibrations of the outer element as well as the state of a permanent, unidirectional energy locking with mild, spatial energy exchanges. In this review, we will discuss the recent theoretical and experimental advancements in the study of essentially nonlinear mechanisms governing the formation and bifurcations of the regimes of intense energy transfer. The present review is composed of two parts. The first part will be mainly devoted to the emergence of resonant energy transfer states in one-dimensional models incorporating internal rotators, while the second part will be mainly concerned with the manifestation of various energy transfer states in two-dimensional ones. This article is part of the theme issue ‘Nonlinear energy transfer in dynamical and acoustical systems’.

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Technique for the experimental estimation of nonlinear energy transfer in fully developed turbulence

Physics of Plasmas ◽

10.1063/1.871572 ◽

1996 ◽

Vol 3 (11) ◽

pp. 3998-4009 ◽

Cited By ~ 48

Author(s):

J. S. Kim ◽

R. D. Durst ◽

R. J. Fonck ◽

E. Fernandez ◽

A. Ware ◽

...

Keyword(s):

Energy Transfer ◽

Fully Developed Turbulence ◽

Developed Turbulence ◽

Nonlinear Energy Transfer ◽

Experimental Estimation ◽

Nonlinear Energy

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Frequency spectra evolution of two-dimensional focusing wave groups in finite depth water

Journal of Fluid Mechanics ◽

10.1017/jfm.2011.371 ◽

2011 ◽

Vol 688 ◽

pp. 169-194 ◽

Cited By ~ 26

Author(s):

Zhigang Tian ◽

Marc Perlin ◽

Wooyoung Choi

Keyword(s):

Energy Transfer ◽

Wave Breaking ◽

Frequency Region ◽

Breaking Wave ◽

Two Dimensional ◽

Spectral Bandwidth ◽

Frequency Spectra ◽

Wave Groups ◽

Nonlinear Energy Transfer ◽

Nonlinear Energy

AbstractAn experimental and numerical study of the evolution of frequency spectra of dispersive focusing wave groups in a two-dimensional wave tank is presented. Investigations of both non-breaking and breaking wave groups are performed. It is found that dispersive focusing is far more than linear superposition, and that it undergoes strongly nonlinear processes. For non-breaking wave groups, as the wave groups propagate spatial evolution of wave frequency spectra, spectral bandwidth, surface elevation skewness, and kurtosis are examined. Nonlinear energy transfer between the above-peak ($f/ {f}_{p} = 1. 2{{\ndash}}1. 5$) and the higher-frequency ($f/ {f}_{p} = 1. 5\text{{\ndash}} 2. 5$) regions, with ${f}_{p} $ being the spectral peak frequency, is demonstrated by tracking the energy level of the components in the focusing and defocusing process. Also shown is the nonlinear energy transfer to the lower-frequency components that cannot be detected easily by direct comparisons of the far upstream and downstream measurements. Energy dissipation in the spectral peak region ($f/ {f}_{p} = 0. 9\text{{\ndash}} 1. 1$) and the energy gain in the higher-frequency region ($f/ {f}_{p} = 1. 5\text{{\ndash}} 2. 5$) are quantified, and exhibit a dependence on the Benjamin–Feir Index (BFI). In the presence of wave breaking, the spectral bandwidth reduces as much as 40 % immediately following breaking and eventually becomes much smaller than its initial level. Energy levels in different frequency regions are examined. It is found that, before wave breaking onset, a large amount of energy is transferred from the above-peak region ($f/ {f}_{p} = 1. 2\text{{\ndash}} 1. 5$) to the higher frequencies ($f/ {f}_{p} = 1. 5\text{{\ndash}} 2. 5$), where energy is dissipated during the breaking events. It is demonstrated that the energy gain in the lower-frequency region is at least partially due to nonlinear energy transfer prior to wave breaking and that wave breaking may not necessarily increase the energy in this region. Complementary numerical studies for breaking waves are conducted using an eddy viscosity model previously developed by the current authors. It is demonstrated that the predicted spectral change after breaking agrees well with the experimental measurements.

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

10.5194/npg-2018-35 ◽

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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