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DNS Study on Vortex and Vorticity in Late Boundary Layer Transition

Part of: Basic methods in fluid mechanics Turbulence Incompressible viscous fluids

Published online by Cambridge University Press:  21 June 2017

Yiqian Wang ,
Yong Yang ,
Guang Yang  and
Chaoqun Liu
Yiqian Wang*
Affiliation:
Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA School of Aerospace Engineering, Tsinghua University, Beijing 100084, China
Yong Yang*
Affiliation:
Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA
Guang Yang*
Affiliation:
Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA Beihang University, Beijing 100191, China
Chaoqun Liu*
Affiliation:
Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA
*
*Corresponding author. Email addresses:yqwang@nuaa.edu.cn (Y. Wang), yong.yang@mavs.uta.edu (Y. Yang), guang.yang@uta.edu (G. Yang), cliu@uta.edu (C. Liu)
*Corresponding author. Email addresses:yqwang@nuaa.edu.cn (Y. Wang), yong.yang@mavs.uta.edu (Y. Yang), guang.yang@uta.edu (G. Yang), cliu@uta.edu (C. Liu)
*Corresponding author. Email addresses:yqwang@nuaa.edu.cn (Y. Wang), yong.yang@mavs.uta.edu (Y. Yang), guang.yang@uta.edu (G. Yang), cliu@uta.edu (C. Liu)
*Corresponding author. Email addresses:yqwang@nuaa.edu.cn (Y. Wang), yong.yang@mavs.uta.edu (Y. Yang), guang.yang@uta.edu (G. Yang), cliu@uta.edu (C. Liu)
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Abstract

Vortex and vorticity are two correlated but fundamentally different concepts which have been the central issues in fluid mechanics research. Vorticity has rigorous mathematical definition (curl of velocity), but no clear physical meaning. Vortex has clear physical meaning (rotation) but no rigorous mathematical definition. For a long time, many people treat them as a same thing. However, based on our high-order direct numerical simulation (DNS), we found that first, “vortex” is not “vorticity tube” or “vortex tube” which is widely defined as a bundle of vorticity lines without any vorticity line leak. Actually, vortex is an open area for vorticity line penetration. Second, vortex is not necessarily congregation of vorticity lines, but dispersion in many 3-dimensional cases. Some textbooks say that vortex cannot end inside the flow field but must end on the solid wall (and/or boundaries). Our DNS observation and many other numerical results show almost all vortices are ended inside the flow field. Finally, a more theoretical study shows that neither vortex nor vorticity line can attach to the solid wall and they must be detached from the wall.

Keywords

Vortexvorticityvorticity linevorticity tube∧-vortexhairpin vortexDNSflow transitionturbulence

MSC classification

Secondary: 76F06: Transition to turbulence 76F40: Turbulent boundary layers 76M23: Vortex methods 76D17: Viscous vortex flows
Type
Research Article
Information
Communications in Computational Physics , Volume 22 , Issue 2 , August 2017 , pp. 441 - 459
Copyright
Copyright © Global-Science Press 2017 

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