高雷诺数Taylor-Green流中的涡面场演化

Based on the recently developed theory of the vortex-surface field (VSF) for viscous flows, we study the evolution of VSF in high-Reynolds-number Taylor-Green flows through direct numerical simulations. The VSF theory is based on the Lagrangian representation, which can describe the continuous, timewise evolution of vortical structures, including several important events in vortex dynamics, e.g., vortex reconnection, the formation and roll-up of vortex tubes, vorticity intensification between anti-parallel vortex tubes, and vortex stretching and twisting. However, existing applications based on the VSF theory are only restricted for flows with simple geometry and topology at moderate Reynolds numbers. We extend the applications of the VSF theory for high-Reynolds-number turbulence. In particular, through the quantitative analysis of the geometry and topology of vortex surfaces with the results in turbulence statistics, possible connections between the characteristics of vortical structures and the scaling law in turbulent flows can be found. In addition, we investigate the construction of the initial surrogate VSF in homogenous isotropic turbulence.

基于近期发展的粘性流中的涡面场理论，本项目通过直接数值模拟研究高雷诺数Taylor-Green流中的涡面场演化。该涡面场理论基于拉格朗日方法，可连续追踪涡结构的动力学时间演化过程，包括涡面间的重联、涡管卷并、交叉涡管间的涡量积聚、涡管拉伸与扭曲等重要的涡动力学过程。但是目前该理论的应用仅限于中等雷诺数且具有简单几何与拓扑特性的流动，所以本项目将该理论的应用拓展至高雷诺数湍流。特别是在层流到湍流转捩过程中，通过涡面结构几何特性刻画与湍流统计量的定量分析，揭示涡结构特性与统计标度律之间的联系。此外，本项目将研究均匀各向同性湍流中初始替代涡面场的构造方法。

基于近期发展的粘性流中的涡面场理论，本项目通过直接数值模拟研究高雷诺数Taylor-Green流中的涡面场演化。该涡面场理论基于拉格朗日方法，可连续追踪涡结构的动力学时间演化过程，包括涡面间的重联、涡管卷并、交叉涡管间的涡量积聚、涡管拉伸与扭曲等重要的涡动力学过程。通过涡面几何特征与湍流统计量的定量分析，揭示在层流到湍流转捩过程中轴向拉伸螺旋状涡结构与能谱-5/3统计标度律之间的联系。此外，本项目将先前简单Taylor-Green流中的涡面场与拉格朗日场研究推广至壁流动转捩问题。初步结果揭示转捩中近似涡面由初始平面至典型发卡型结构的涡动力学演化过程。