Parallel DNS for vortex structure of late stages of flow transition

A new DNS using compact high order scheme and MPI parallel computation has been conducted with 1920 × 241 × 128 grid points for non-linear stages of flow transition. The coherent vortex structure of the late flow transition stages and the mechanism of formation of single vortex ring, multiple vortex rings, and small length scales are discussed. The ring-like vortex formation from the Λ-vortex is the result of the interaction of two pairs of counter-rotating primary and secondary streamwise vortices. The formation of the multiple ring structure follows the first Helmholtz vortex conservation law. A bridge must be formed to link two Λ-vortex legs. The bridge finally develops as a new ring. This process keeps going onto form a multiple ring structure. The U-shaped vortices are part of existing coherent large vortex structure. Actually, the U-shaped vortex, which is a third level vortex, serves as a second neck to supply vorticity to the multiple rings. The multiple ring-like vortex structure is found quite stable and can travel for a long distance. The “hairpin vortex breakdown” does not happen. The small vortices can be found on the bottom of the boundary layer near the wall surface. It is believed that the small vortices are generated by the interaction of higher level vortices with the solid wall, but not by the “vortex breakdown”.