壁湍流转捩中的拉格朗日场与涡面场演化及多尺度分析

项目名称： 壁湍流转捩中的拉格朗日场与涡面场演化及多尺度分析

项目编号： No.11472015

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 杨越

作者单位： 北京大学

项目金额： 88万元

中文摘要： 基于近期发展的拉格朗日场与涡面场理论，本项目通过直接数值模拟与多尺度几何分析方法研究壁湍流转捩中的拉格朗日与涡面结构演化。首先，拉格朗日场与涡面场方法将推广到壁湍流，特别是槽道流时间转捩与平板边界层空间转捩问题，这一研究将用涡面连续时间演化的统一理论框架解释边界层中转捩现象。然后结合多尺度几何分析，建立壁湍流转捩中拉格朗日物质曲面/涡面几何结构与剪切流主要统计特性之间的联系，从而将原先对壁湍流中拟序结构演化的定性描述提升为定量刻画。此外，通过演化结构中的定量结果可提炼壁湍流减阻与控制中的简化涡模型或低维动力系统模型。

中文关键词： 壁湍流；边界层转捩；拟序结构；多尺度分析；涡动力学

英文摘要： Based on the recently developed theory of Lagrangian and vortex-surface fields, we study the evolution of Lagrangian and vortex-surface structures in the laminar-turbulent transition in wall-bounded flows through direct numerical simulations and multi-scale geometric analysis. First, the methodology of Lagrangian and vortex-surface fields is extended to wall-bounded turbulent flows, in particular, the temporal transition in channel flow and the spatial transition in turbulent boundary layer. This is aimed to clarify the mechanism of transitions in boundary layers using a universal theoretical framework with the continuous temporal evolution of vortex surfaces. Then, the evolutionary geometry of the Lagrangian and vortex-surface structures can be related to the major statistics in shear flows via the multi-scale geometric analysis, so that quantitative characterizations for the evolution of coherent structures can be developed instead of the qualitative descriptions in previous studies. In addition, the quantitative results can be helpful to develop simplified vortex models or low-dimensional dynamical models for drag reduction and flow control in wall-bounded turbulence.

英文关键词： Wall-bounded turbulence;Transition in boundary layer;Coherent strcture;Multi-scale analysis;Vortex dynamics