Quantification and prediction of extreme events in a one-dimensional nonlinear dispersive wave model
Quantification and prediction of extreme events in a one-dimensional nonlinear dispersive wave model
复制标题
DOI：
10.1016/j.physd.2014.04.012
复制
发表时间：
2014-07-01
影响因子：
4
通讯作者：
Sapsis, Themistoklis P.
中科院分区：
文献类型：
--
作者：
Cousins, Will;Sapsis, Themistoklis P.
本工作的目的是量化和预测的罕见事件的极端强度的非线性波具有广泛的频谱。我们考虑一个一维非线性模型与深水波色散关系，Majda-McLaughlin-Tabak（MMT）模型，在动力学制度，其特征在于由一个宽带谱和强非线性能量转移的发展过程中的间歇性事件与有限的寿命。为了了解在极端事件的发展过程中发生的能量转移，我们通过Gabor变换对能量分布沿沿着不同波数进行空间局部化分析。Gabor系数的统计分析揭示了（i）间歇结构的低维性，（ii）非高斯统计特性和模式之间的非线性能量传递之间的相互作用，以及（iii）临界尺度（或临界Gabor系数），其中临界量的能量可以触发极端事件的形成。我们直接通过系统方程分析了这些特殊局域模的不稳定性，并表明这些间歇性事件是由于系统非线性，波色散和波耗散的相互作用，模仿波破碎。这些局部不稳定性是由空间中能量的随机局部化触发的，由具有随机相位的低振幅波的色散传播产生。基于这些属性，我们设计的低维泛函的这些Gabor系数，允许预测的极端事件之前的非线性相互作用开始发生。(C)© 2014 Elsevier B. V.保留所有权利。
The aim of this work is the quantification and prediction of rare events characterized by extreme intensity in nonlinear waves with broad spectra. We consider a one-dimensional nonlinear model with deep-water waves dispersion relation, the Majda-McLaughlin-Tabak (MMT) model, in a dynamical regime that is characterized by a broadband spectrum and strong nonlinear energy transfers during the development of intermittent events with finite-lifetime. To understand the energy transfers that occur during the development of an extreme event we perform a spatially localized analysis of the energy distribution along different wavenumbers by means of the Gabor transform. A statistical analysis of the Gabor coefficients reveals (i) the low-dimensionality of the intermittent structures, (ii) the interplay between non-Gaussian statistical properties and nonlinear energy transfers between modes, as well as (iii) the critical scales (or critical Gabor coefficients) where a critical amount of energy can trigger the formation of an extreme event. We analyze the unstable character of these special localized modes directly through the system equation and show that these intermittent events are due to the interplay of the system nonlinearity, the wave dispersion, and the wave dissipation which mimics wave breaking. These localized instabilities are triggered by random localizations of energy in space, created by the dispersive propagation of low-amplitude waves with random phase. Based on these properties, we design low-dimensional functionals of these Gabor coefficients that allow for the prediction of the extreme event well before the nonlinear interactions begin to occur. (C) 2014 Elsevier B.V. All rights reserved.