Analysis of the vorticity tube segment in fluid turbulence

Abstract

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.