Identifying the tangle of twisted vortex tubes in homogeneous isotropic turbulence

We apply the vortex-surface field (VSF) to the direct numerical simulation of homogeneous isotropic turbulence. The VSF is constructed from a given vorticity field and its isosurface is a vortex surface consisting of vortex lines. The VSF construction involves pseudo-transport in frozen vorticity and local optimization for compromising satisfactory VSF deviation and smoothness of VSF solutions. In the visualization of VSF isosurfaces with the fixed zero isocontour level, stretched spiral vortex tubes constitute a complex network in isotropic turbulence at moderate Reynolds numbers, and the tangle of vortex tubes appears to be an attractor in the chaotic vorticity system. The VSF isosurface reveals physically reasonable vortex dynamics, such as twisting of vortex tubes and rolling-up of vortex sheets, instead of the visual vortex ‘breakdown’ identified by the isosurface of vorticity magnitude. The successful construction of VSFs in isotropic turbulence implies that the VSF can be constructed in arbitrary flow fields.