Dynamics and geometry of developing planar jets based on the invariants of the velocity gradient tensor

Based on the direct numerical simulation (DNS), the developing planar jets under different initial conditions, e.g., the conditions of the exit Reynolds number and the exit mean velocity profile, are investigated. We mainly focus on the characteristics of the invariants of the velocity gradient tensor, which provides insights into the evolution of the dynamics and the geometry of the planar jets along with the flow transition. The results show that the initial flow near the jet exit is strongly predominated by the dissipation over the enstrophy, the flow transition is accompanied by a severe rotation and straining of the flow elements, where the vortex structure evolves faster than the fluid element deformation, in the fully-developed state, the irrotational dissipation is dominant and the most probable geometry of the fluid elements should remain between the biaxial stretching and the axisymmetric stretching. In addition, with a small exit Re and a parabolic profile for the exit mean streamwise velocity, the decay of the mean flow field and the magnitude of the turbulent variables will be strengthened in the process of the flow transition, however, a large exit Re will promote the flow transition to the fully-developed state. The cross-impact between the exit Re and the exit mean velocity profile is also observed in the present study.