Toward investigation of local vortex line topology in turbulence

Current vortex identification methods employ $Q$ or $\lambda_2$ criterion to investigate vortical structures in turbulent flows. We propose an alternate method to examine the local vortex structure. Specifically, we construct the vorticity vector field ($\vec\omega$) and compute the vorticity gradient tensor ($J_{ik}\equiv \partial\omega_i/\partial x_k$). The tensor ($J_{ik}$), similar to the velocity gradient tensor ($A_{ij}\equiv\partial u_i/\partial x_j$), is trace free. In a manner similar to streamline topology analysis using the second and third invariants of $A_{ij}$, the second ($Q_\omega$) and third ($R_\omega$) invariants of $J_{ik}$ are used to develop the topological description of local vortex line structure. Such a representation is not only useful for investigation of the local vortex-line structure but is also useful in identifying key turbulence phenomena such as vortex line reconnection. Direct numerical simulation (DNS) data of incompressible forced isotropic turbulence and perturbation-evolution in plane-Poiseuille flow are analysed in this study. We investigate the following: (i) distribution in these two key canonical turbulent flows; and (ii) the formation of hair-pin vortices in transitioning plane Poiseuille flow using the aforementioned method.