SCIENCE CHINA Physics, Mechanics & Astronomy © Science China Press and Springer-Verlag Berlin Heidelberg 2010 phys.scichina.com www.springerlink.com *Corresponding author (email: tangdbin@163.com) • Research Paper • March 2010 Vol.53 No.3: 514–520 doi: 10.1007/s11433-010-0129-7 Evolution of the ring-like vortices and spike structure in transitional boundary layers CHEN Lin 1 , TANG DengBin 1* , LIU XiaoBing 2 , OLIVEIRA Maria 3 & LIU ChaoQun 3 1 Department of Aerodynamics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China; 2 Wind Engineering Research Center of Hunan University, Changsha 410082, China; 3 Department of Mathematics, University of Texas at Arlington, Arlington, Texas 76010, USA Received July 22, 2009; accepted September 25, 2009 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 tran- sition 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.ek The 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 charac- teristic 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 un- clear 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 impor- tant 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 pic- tures of real ring-like vortices. The appearance and devel- opment 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 re- mains 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 transi- tion, and found that ring-like vortices would induce high- frequency streamwise velocity fluctuations called spikes. Borodulin et al. [4] studied the late-stage transition mecha- nism in the boundary layers using numerical and experi- mental methods, and analyzed relative vortices and spike structure. They proposed that the formation of ring-like vor- tices was due to self-induction. Meyer et al. [5] by investi- gating the flow randomization process in a transitional boundary layer found that Λ-vortices and ring-like vortices