标题： 湍流的快速合成与多尺度相干涡旋 显示英文标题

标题： Fast synthesis of turbulence with multi-scale coherent vortices

摘要： 湍流合成方法往往难以同时再现相干涡旋并捕捉关键的统计特征。 我们引入了一种快速的合成湍流方法来生成瞬时湍流场（称为“编织湍流”），该方法结合了分数维模型和相干结构的优点，具有多尺度涡旋。 该方法基于分数布朗桥构造的随机中心线生成多尺度Burgers涡管。 最大的涡和最小的涡分别控制积分尺度和耗散尺度，从而能够精确控制能量谱在能量包含范围、惯性范围和耗散范围内的分布。 可调的涡密度允许在速度统计中实现定制的间歇性。 值得注意的是，编织湍流的计算成本极低，与网格点总数成正比。 对于Taylor-Reynolds数大于200的情况，其计算成本比直接数值模拟（DNS）低五个数量级以上。 与DNS数据的对比验证表明，在能量谱、速度概率分布和间歇性标度方面具有良好的一致性。 与先前的方法不同，编织湍流同时再现了高斯速度场、能量谱的Kolmogorov五分之三缩放规律以及类似真实湍流的相互缠绕的相干涡旋。 这种方法不仅弥合了结构性湍流建模和统计性湍流建模之间的差距，还为需要逼真湍流场的应用提供了一个高效的工具。 显示英文摘要

摘要： Turbulence synthesis methods often struggle to reproduce coherent vortices while capturing key statistical features. We introduce a fast synthetic turbulence method to generate instantaneous turbulent fields (termed `woven turbulence') with multi-scale vortices, combining the advantages of fractal models and coherent structures. The method generates multi-scale Burgers vortex tubes based on stochastic centerlines constructed by the fractional Brownian bridge. The largest and smallest vortices govern the integral and dissipation scales, respectively, enabling precise control over the energy spectrum across the energy-containing, inertial, and dissipation ranges. The adjustable vortex density allows tailored intermittency in velocity statistics. Remarkably, the woven turbulence achieves an extremely low computational cost, proportional to the total number of grid points. For the Taylor-Reynolds number larger than 200, its computational cost is over five orders of magnitude lower than that of direct numerical simulation (DNS). Validation against DNS data demonstrates excellent agreement in energy spectra, velocity probability distributions, and intermittency scaling. Unlike prior methods, woven turbulence simultaneously reproduces Gaussian velocity fields, Kolmogorov's five-thirds scaling for the energy spectrum, and intertwined coherent vortices akin to real turbulence. This approach not only bridges the gap between structural and statistical turbulence modelling, but also offers an efficient tool for applications requiring realistic turbulent fields.