scholarly journals Emergence of non-stationary regimes in one- and two-dimensional models with internal rotators

2018 ◽  
Vol 376 (2127) ◽  
pp. 20170134 ◽  
Author(s):  
K. Vorotnikov ◽  
M. Kovaleva ◽  
Y. Starosvetsky
Keyword(s):  
Energy Transfer ◽  
Harmonic Excitation ◽  
Two Dimensional ◽  
Theme Issue ◽  
One Dimensional ◽  
Lateral Vibrations ◽  
Nonlinear Energy Transfer ◽  
Energy Exchanges ◽  
Dimensional Models ◽  
Nonlinear Energy

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’.

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

2011 ◽  
Vol 688 ◽  
pp. 169-194 ◽  
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.

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.

Mine Impact Burial Prediction From One to Three Dimensions

2008 ◽  
Vol 62 (1) ◽  
Author(s):  
Peter C. Chu
Keyword(s):  
Three Dimensional ◽  
Time History ◽  
Three Dimensions ◽  
Vertical Position ◽  
Burial Depth ◽  
Prediction Errors ◽  
Two Dimensional ◽  
Dimensional Model ◽  
One Dimensional ◽  
Dimensional Models

The Navy’s mine impact burial prediction model creates a time history of a cylindrical or a noncylindrical mine as it falls through air, water, and sediment. The output of the model is the predicted mine trajectory in air and water columns, burial depth/orientation in sediment, as well as height, area, and volume protruding. Model inputs consist of parameters of environment, mine characteristics, and initial release. This paper reviews near three decades’ effort on model development from one to three dimensions: (1) one-dimensional models predict the vertical position of the mine’s center of mass (COM) with the assumption of constant falling angle, (2) two-dimensional models predict the COM position in the (x,z) plane and the rotation around the y-axis, and (3) three-dimensional models predict the COM position in the (x,y,z) space and the rotation around the x-, y-, and z-axes. These models are verified using the data collected from mine impact burial experiments. The one-dimensional model only solves one momentum equation (in the z-direction). It cannot predict the mine trajectory and burial depth well. The two-dimensional model restricts the mine motion in the (x,z) plane (which requires motionless for the environmental fluids) and uses incorrect drag coefficients and inaccurate sediment dynamics. The prediction errors are large in the mine trajectory and burial depth prediction (six to ten times larger than the observed depth in sand bottom of the Monterey Bay). The three-dimensional model predicts the trajectory and burial depth relatively well for cylindrical, near-cylindrical mines, and operational mines such as Manta and Rockan mines.

scholarly journals Evaluation of Spatial Variation of Nonlinear Energy Transfer by Use of Turbulence Diagnostic Simulator

2013 ◽  
Vol 8 (0) ◽  
pp. 2403070-2403070 ◽  
Author(s):  
Naohiro KASUYA ◽  
Satoru SUGITA ◽  
Makoto SASAKI ◽  
Shigeru INAGAKI ◽  
Masatoshi YAGI ◽  
...  
Keyword(s):  
Energy Transfer ◽  
Spatial Variation ◽  
Nonlinear Energy Transfer ◽  
Nonlinear Energy

scholarly journals Influence of Accuracy Improvement of Nonlinear Energy Transfer in Wave Model

2009 ◽  
Vol 65 (1) ◽  
pp. 171-175
Author(s):  
Noriaki HASHIMOTO ◽  
Koji KAWAGUCHI ◽  
Katsuyuki SUZUYAMA ◽  
Masaru YAMASHIRO ◽  
Mitsuyoshi KODAMA
Keyword(s):  
Energy Transfer ◽  
Wave Model ◽  
Accuracy Improvement ◽  
Nonlinear Energy Transfer ◽  
Nonlinear Energy

Preliminary Ship Design Using One and Two-Dimensional Models

1999 ◽  
Vol 36 (02) ◽  
pp. 102-112
Author(s):  
Michael D. A. Mackney ◽  
Carl T. F. Ross
Keyword(s):  
Finite Element ◽  
Dimensional Analysis ◽  
Three Dimensional ◽  
Two Dimensional ◽  
One Dimensional ◽  
Dimensional Finite Element ◽  
Dimensional Models ◽  
Support Conditions ◽  
The One ◽  
Three Dimensional Finite Element

Computational studies of hull-superstructure interaction were carried out using one-, two-and three-dimensional finite element analyses. Simplification of the original three-dimensional cases to one- and two-dimensional ones was undertaken to reduce the data preparation and computer solution times in an extensive parametric study. Both the one- and two-dimensional models were evaluated from numerical and experimental studies of the three-dimensional arrangements of hull and superstructure. One-dimensional analysis used a simple beam finite element with appropriately changed sections properties at stations where superstructures existed. Two-dimensional analysis used a four node, first order quadrilateral, isoparametric plane elasticity finite element, with a corresponding increase in the grid domain where the superstructure existed. Changes in the thickness property reflected deck stiffness. This model was essentially a multi-flanged beam with the shear webs representing the hull and superstructure sides, and the flanges representing the decks One-dimensional models consistently and uniformly underestimated the three-dimensional behaviour, but were fast to create and run. Two-dimensional models were also consistent in their assessment, and considerably closer in predicting the actual behaviours. These models took longer to create than the one-dimensional, but ran in very much less time than the refined three-dimensional finite element models Parametric insights were accomplished quickly and effectively with the simplest model and processor, but two-dimensional analyses achieved closer absolute measure of the displacement behaviours. Although only static analysis with simple loading and support conditions were presented, it is believed that similar benefits would be found for other loadings and support conditions. Other engineering components and structures may benefit from similarly judged simplification using one- and two-dimensional models to reduce the time and cost of preliminary design.

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