Invariants of velocity gradient tensor in supersonic turbulent pipe, nozzle, and diffuser flows

Velocity gradient tensor (VGT) analysis of high-order accurate direct numerical simulation data of supersonic pipe, nozzle, and diffuser flows at computationally moderate Reynolds numbers is performed. Joint probability density functions of second and third invariants of the VGT conditioned on positive and negative dilatation levels are presented in the near-wall viscous layer, buffer layer, log layer, and core region of these flows. For flow regions with positive dilatation, there is a preference for unstable flow topologies, while regions with negative dilatation show a preference for stable flow topologies.