DNS study on Λ-vortex and vortex ring formation in flow transition at Mach number 0.5

Large vortex structure in late boundary layer transition with an inflow Mach number of 0.5 is studied by DNS (Direct Numerical Simulation) in this paper. First, we found that there are no Λ-vortex tubes, contradicting to what the existing literatures and textbooks addressed. The so-called Λ-vortex is always open on head, which has a different shape from Λ. Λ-vortex is really a pair of open rotation cores with a lower half of the Λ shape. It is also found that the Λ-vortex and ring-like vortex are formed separately and independently. There is no such a process that the Λ-vortex self-deforms to a hairpin vortex at the tip as many literatures indicated. Λ-vortex and ring-like vortex can be visualised by the iso-surface of λ2. However, the iso-surfaces of λ2 only represent rotation cores but not necessarily vortex tubes. In fact, many spanwise vortex filaments can easily penetrate the so-called Λ-vortex (iso-surface of λ2), change the direction toward the streamwise direction, and then leave the iso-surface of λ2. The vortex ring is not part of the original Λ-vortex but is formed separately. The Λ-vortex cores were originated from the 2D and 3D T-S waves, amplified and became strong by attracting neighbouring spanwise vortex filaments from the boundary shear layer. As the Λ-vortex becomes strong, a strong shear layer is formed above the Λ-vortex roots, which is caused by ejection of the Λ-vortex rotation to bring low speed flow from the bottom of the boundary layer to form an olive-like low speed zone. As a result, the instability of the shear layer leads to the formation of new ring-like vortex tubes one by one.