湍流场中涡线单元的结构分析  

Analysis of the vorticity tube segment in fluid turbulence

作　　者：王利坡[1] WANG LiPo(UM-SJTU Joint Institute,Shanghai Jiao Tong University,Shanghai 200240,China)

机构地区：[1]上海交通大学密西根学院,上海200240

出　　处：《中国科学：物理学、力学、天文学》2020年第4期8-16,共9页Scientia Sinica Physica,Mechanica & Astronomica

基　　金：国家自然科学基金(编号:11172175)资助项目。

摘　　要：与描述湍流速度场的流线管单元[Wang L. On properties of fluid turbulence along streamlines. J Fluid Mech,2010, 648:183–203]的思想类似,为了描述湍流涡矢量场的结构,我们提出了一种新的结构分析方法,即涡线单元,可以用单元尺度和极值点涡量差值来表征.涡线单元与常用的涡管结构的不同可以概括为:涡线单元结构可以定量描述,并且是全空间填充的.在理论上这两个条件是保证我们可以将涡线单元的结构分析与全流场统计规律联系起来的必要前提,帮助理解和重构湍流涡量场.根据直接数值模拟数据,我们研究了涡线单元的统计与结构特性,包括尺度与手性等.根据涡线单元结构可以定量表征精细的条件统计,例如发现涡相关的动力学参数(例如拟涡能耗散率和涡拉伸率)强烈依赖于基于涡线单元结构的条件统计.这样一种结构分析方法为深入研究湍流场提供了新的手段.To address the geometrical properties of the turbulent velocity vector field, a new concept named streamtube segment has been developed [Wang L. On properties of fluid turbulence along streamlines. J Fluid Mech, 2010, 648: 183–203].According to the vectorial topology, the entire velocity field can be partitioned into the so-called streamtube segments,which are organized in a non-overlapping and space-filling manner. A similar idea is implemented to study the turbulent vorticity vector field. Differently from the conventional vortex tubes, vorticity tube segments are space-filling and can be characterized by non-arbitrary parameters. Such structure enables a more quantitative, rather than illustrative, description of turbulence. In principle, these two conditions are the linkage to reproduce the entire turbulent field from decomposed geometrical units with relatively simple structures. From analyzing the direct numerical simulation data, the topological and dynamical properties of vorticity tube segments are explored, such as the scale distribution and chirality. The characteristic parameters have strong influence on the enstrophy production and vorticity stretching. Consequently the common knowledge in turbulence dynamics that vorticity is more stretched than compressed need to be rectified in the vorticity tube segment context.

关 键 词：涡矢量 涡线单元 手性 湍流场结构 

分 类 号：O357.5[理学—流体力学]