Spontaneously stochastic solutions in one-dimensional inviscid systems
Spontaneously stochastic solutions in one-dimensional inviscid systems
复制标题
一维无粘系统中的自发随机解
DOI：
10.1088/0951-7715/29/8/2238
复制
发表时间：
2015
期刊：
影响因子：
1.7
通讯作者：
A. Mailybaev
中科院分区：
文献类型：
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作者：
A. Mailybaev
本文研究了湍流Sabra壳模型的无粘极限，它被认为是一维粘性守恒律的一个特例，具有非局部二次通量函数。我们提出了一个理论论证（与详细的数值确认）表明，一个经典的确定性解决方案之前的有限时间爆破，t < tb，必须继续作为一个随机过程后的爆破，t > tb，代表一个独特的物理相关的描述在无粘极限。该理论基于对数时间τ=log τ（t-tb）的动力系统公式，其特征在于无粘Burgers方程的稳定行波解，但Sabra模型的随机行波。后者描述了一个普遍的随机性爆发后立即开始。
In this paper, we study the inviscid limit of the Sabra shell model of turbulence, which is considered as a particular case of a viscous conservation law in one space dimension with a nonlocal quadratic flux function. We present a theoretical argument (with a detailed numerical confirmation) showing that a classical deterministic solution before a finite-time blowup, t < tb, must be continued as a stochastic process after the blowup, t > tb, representing a unique physically relevant description in the inviscid limit. This theory is based on the dynamical system formulation written for the logarithmic time τ=log(t−tb), which features a stable traveling wave solution for the inviscid Burgers equation, but a stochastic traveling wave for the Sabra model. The latter describes a universal onset of stochasticity immediately after the blowup.