论文标题
湍流的随机模型中的大波动
Large Fluctuations in Stochastic Models of Turbulence
论文作者
论文摘要
该论文讨论了三种湍流模型中的互齿现象，在随机过程的分析中采用了分析和数值技术，以及它们诱导的概率分布。最初的章节介绍了对湍流的统计理论和用于脱离平衡物理学的领域的统计理论。主要文本的两章通过Martin-Siggia-Rose-Janssen-de Dominicis（MSRJD）功能方法研究了RFD模型和Burgers模型。在这两个模型中，对与Instanton周围波动相对应的扰动校正进行了分析。最后一章列出了一个固定的一维随机过程，作为拉格朗日伪驱散波动的模型。在数值上验证了此过程具有对数正态概率分布和远程幂律相关性。
This dissertation discusses the intermitency phenomenon in three models of turbulence, employing analytical and numerical techniques in the analysis of stochastic processes and the probability distributions which they induce. The initial chapters present a review of the statistical theory of turbulence and of statistical theory of fields as applied to out of equilibrium physics. Two chapters of the main text investigate the RFD model and the Burgers model through the Martin-Siggia-Rose-Janssen-de Dominicis (MSRJD) functional method. An analysis of the perturbative corrections corresponding to fluctuations around the instanton in both models is undertaken. The last chapter presents a stationary one-dimensional stochastic process as a model of Lagrangian pseudo-dissipation fluctuations. It is numerically verified that this process has a lognormal probability distribution and long range power-law correlations.
