Structures of the vorticity tube segment in turbulence

To address the geometrical properties of the turbulent velocity vector field, a new concept named streamtube segment has been developed recently [L. Wang, “On properties of fluid turbulence along streamlines,” J. Fluid Mech. 648, 183–203 (2010)10.1017/S0022112009993041]. 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. In principle, properties of turbulent fields can be reproduced from those of the decomposed geometrical units with relatively simple structures. A similar idea is implemented to study the turbulent vorticity vector field using the vorticity tube segment structure. Differently from the conventional vortex tubes, vorticity tube segments are space-filling and can be characterized by non-arbitrary parameters, which enables a more quantitative description rather than just an illustrative explanation of turbulence behaviors. From analyzing the direct numerical simulation data, the topological and dynamical properties of vorticity tube segments are explored. The characteristic parameters have strong influence on some conditional statistics, such as the enstrophy production and the probability density function of vorticity stretching. Consequently the common knowledge in turbulence dynamics that vorticity are more stretched than compressed need to be rectified in the vorticity tube segment context.