标题： 通过瞬子气体近似生成合成湍流 显示英文标题

标题： Synthetic Turbulence via an Instanton Gas Approximation

摘要： 将合成湍流场作为直接数值模拟（DNS）的计算可行替代方法，在各种应用中是一个重要的实际问题，并允许测试我们对真实湍流主要特征的物理理解。 再现高阶欧拉相关函数以及拉格朗日粒子统计，需要在合成湍流场中准确表示流动的相干结构。 为此，本文提出了一种基于相干结构的系统性方法，用于采样合成随机场，该方法基于从湍流的场论公式中得到的瞬子配置的叠加——一种瞬子气体。 我们讨论了瞬子集合的采样策略，包括有相互作用和无相互作用的情况，以及它们周围的高斯涨落。 结果的欧拉和拉格朗日统计通过数值计算并与DNS结果以及缺乏相干结构的高斯和对数正态级联模型进行比较。 本文通过一维Burgers湍流的例子说明了瞬子气体方法，并表明即使是没有涨落的非相互作用瞬子的规范系综也能很好地再现DNS统计。 最后，我们概述了该方法向更高维度的扩展，特别是用于未来宇宙射线传播的磁流体动力学湍流。 显示英文摘要

摘要： Sampling synthetic turbulent fields as a computationally tractable surrogate for direct numerical simulations (DNS) is an important practical problem in various applications, and allows to test our physical understanding of the main features of real turbulent flows. Reproducing higher-order Eulerian correlation functions, as well as Lagrangian particle statistics, requires an accurate representation of coherent structures of the flow in the synthetic turbulent fields. To this end, we propose in this paper a systematic coherent-structure based method for sampling synthetic random fields, based on a superposition of instanton configurations - an instanton gas - from the field-theoretic formulation of turbulence. We discuss sampling strategies for ensembles of instantons, both with and without interactions and including Gaussian fluctuations around them. The resulting Eulerian and Lagrangian statistics are evaluated numerically and compared against DNS results, as well as Gaussian and log-normal cascade models that lack coherent structures. The instanton gas approach is illustrated via the example of one-dimensional Burgers turbulence throughout this paper, and we show that already a canonical ensemble of non-interacting instantons without fluctuations reproduces DNS statistics very well. Finally, we outline extensions of the method to higher dimensions, in particular to magnetohydrodynamic turbulence for future applications to cosmic ray propagation.