Rortex based velocity gradient tensor decomposition

Recently, a vector named Rortex was proposed to represent the local fluid rotation [C. Liu et al., "Rortex-A new vortex vector definition and vorticity tensor and vector decompositions," Phys. Fluids 30, 035103 (2018)]. In this paper, a universal Rortex based velocity gradient tensor decomposition is proposed and the relevant local velocity increment decomposition is provided. Vortex structures in boundary layer transition on a flat plate are analyzed to quantify the local rotational, compression-stretching, and shearing effects. The results demonstrate that vorticity is shearing-dominant, while the rotational part or Rortex in general occupies a small part of vorticity in most areas of this case. In other words, vorticity is a quality representing shearing rather than rotation or vortex in most regions of this case.