At the late stage of transitional boundary layers, the nonlinear evolution of the ring-like vortices and spike structures and their effects on the surrounding flow were studied by means of direct numerical simulation with high order accuracy. A spatial transition of the flat-plate boundary layers in the compressible flow was conducted. Detailed numerical results with high resolution clearly represented the typical vortex structures, such as ring-like vortices and so on, and induced ejection and sweep events. It was verified that the formation of spike structures in transitional boundary layers had close relationship with ring-like vortices. Especially, compared to the newly observed positive spike structure in the experiments, the same structure was found in the present numerical simulations, and the mechanism was also studied and analyzed. boundary layer transition, ring-like vortices, spike structure, direct numerical simulation PACS: 47.27.Cn, 47.27.ekThe main stages of the boundary layer transition include receptivity, linear instability, weakly nonlinear instability, formation of complex vortex structures (late stage of the transition) and breakdown to turbulences. Experiments have proved that at the late-stage of the transition similar characteristic vortex structures can be found in the turbulence boundary layers. After more than a century of studies, the early stages of the transition process, such as linear theory, weakly nonlinear and secondary instability theory, are well understood. But the late-stage of the transition is still unclear and takes further investigation, such as the formation of ring-like vortices, and appearance of the spikes which are very intensive local streamwise velocity fluctuations.The formation of ring-like vortices is one of the important issues in the transition process. Kachnaov [1] suggested the existence of the chain of ring-like vortices based on hot-film measurement. Lee et al. [2] showed their clear pictures of real ring-like vortices. The appearance and development of high-frequency spike structures is an important stage of the boundary layer transition, yet the mechanism of production and the physical nature of spike structure remains unclear. Recent years have seen more progress on the investigation of the formation of ring-like vortices and spike structure. Bake et al. [3] studied the structures of turbulence development in periodic Klebanoff boundary layer transition, and found that ring-like vortices would induce highfrequency streamwise velocity fluctuations called spikes. Borodulin et al. [4] studied the late-stage transition mechanism in the boundary layers using numerical and experimental methods, and analyzed relative vortices and spike structure. They proposed that the formation of ring-like vortices was due to self-induction. Meyer et al. [5] by investigating the flow randomization process in a transitional boundary layer found that Λ-vortices and ring-like vortices

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Formation and evolution of secondary streamwise vortices in the compressible transitional boundary layers over a flat plate are studied using a direct numerical simulation method with high-order accuracy and highly effective non-reflecting characteristic boundary conditions. Generation and development processes of the secondary streamwise vortices in the complicated transitional boundary flow are clearly analyzed based on the of numerical results, and the effects on the formation of the ring-like vortex that is vital to the boundary layer transition are explored. A new mechanism forming the ring-like vortex through the mutual effect of the primary and secondary streamwise vortices is expressed.