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Modelling and Simulation in Engineering
Volume 2011, Article ID 721487, 16 pages
Research Article

New Findings by High-Order DNS for Late Flow Transition in a Boundary Layer

1Mathematics Department, University of TX at Arlington, Arlington, TX 76019, USA
2Aerodynamics Department, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Received 6 October 2010; Accepted 24 November 2010

Academic Editor: Guan Yeoh

Copyright © 2011 Chaoqun Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper serves as a summary of new discoveries by DNS for late stages of flow transition in a boundary layer. The widely spread concept “vortex breakdown” is found theoretically impossible and never happened in practice. The ring-like vortex is found the only form existing inside the flow field. The ring-like vortex formation is the result of the interaction between two pairs of counter-rotating primary and secondary streamwise vortices. Following the first Helmholtz vortex conservation law, the primary vortex tube rolls up and is stretched due to the velocity gradient. In order to maintain vorticity conservation, a bridge must be formed to link two Λ-vortex legs. The bridge finally develops as a new ring. This process keeps going on to form a multiple ring structure. The U-shaped vortices are not new but existing coherent 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 small vortices can be found on the bottom of the boundary layer near the wall surface. It is believed that the small vortices, and thus turbulence, are generated by the interaction of positive spikes and other higher level vortices with the solid wall. The mechanism of formation of secondary vortex, second sweep, positive spike, high shear distribution, downdraft and updraft motion, and multiple ring-circle overlapping is also investigated.