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.