当前位置: X-MOL 学术Phys. Rev. E › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Quasi-Markovian property of strong wave turbulence
Physical Review E ( IF 2.4 ) Pub Date : 2021-05-03 , DOI: 10.1103/physreve.103.052101
Wonjung Lee

This paper is concerned with the reduced-order modeling of the strongly nonlinear wave turbulence system. The motivation for such an attempt comes from the utility of the probabilistic coarse-grained model in facilitating the theoretical and numerical analysis of the true dynamical system model. One typical practice of simplifying the complex physical model is, in the spirit of Brownian motion, to replace the nonlinear interactions by white noise forcing and linear dissipation. For the case of slowly varying longwave, the resulting Markov process is an accurate approximate model. However, this conventional scheme is highly inappropriate for the description of shortwaves because the rapidly varying turbulent signal acquires a significantly non-Markovian character resulting from the poor timescale separation between the relevant mode and the environmental wave field. To resolve the issue, we discuss a simplification technique for which the central concept is the quasi-Markovian property; a non-Markov stochastic process is referred to as quasi-Markovian if it can be represented as a component of Markovian system made by adding a finite number of auxiliary variables. Our contribution in this work is to single out the nontrivial and near resonances from the nonlinear interactions in search of the auxiliary variable. We perform a comparison analysis of the autocorrelation matrices of the true and approximate models, and numerically demonstrate the effectiveness of our Markovian formulation of the inherently non-Markov turbulent signal.

中文翻译:

强波湍流的拟马尔可夫性质

本文涉及强非线性波湍流系统的降阶建模。进行这种尝试的动机来自概率粗粒度模型在促进对真实动力学系统模型进行理论和数值分析方面的实用性。根据布朗运动的精神,简化复杂物理模型的一种典型做法是用白噪声强迫和线性耗散代替非线性相互作用。对于长波缓慢变化的情况,所得的马尔可夫过程是一个精确的近似模型。然而,该常规方案非常不适用于短波的描述,因为快速变化的湍流信号由于相关模式与环境波场之间较差的时标间隔而获得了明显的非马尔可夫特性。为了解决这个问题,我们讨论一种简化技术,其中心概念是准马尔可夫性质。如果非马尔可夫随机过程可以表示为通过添加有限数量的辅助变量而构成的马尔可夫系统的一个组成部分,则该过程称为准马尔可夫过程。我们在这项工作中的贡献是从非线性相互作用中找出非平凡和近乎共振的现象,以寻找辅助变量。我们对真实模型和近似模型的自相关矩阵进行比较分析,
更新日期:2021-05-03
down
wechat
bug