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Lecture:DNS Study on Relation between Vorticity and Vortex
publishing time:2016-07-28 reading times:742

Date:9:30 am, Aug 4th, 2016

Place: 1st Office Building of Faculty of Energy and Power Engineering room 201

Reporter:Professor Liu Chaoqun, The University of Texas at Arlington , USA


Vorticity, vorticity line, vorticity tube have rigorous mathematical definition, but the rigorous definition of vortex is still an open question. However, for long time until now, in many research papers and text books, vortex is defined as vorticity tube confined by vorticity lines without vorticity line leakage. Vortex is also considered as congregation of vorticity lines with larger vorticity. Our DNS study shows that vortex is not a vortex tube but open for vorticity line penetration, is not a congregation of vorticity lines but a dispersion of vorticity lines, is not a concentration of vorticity with larger vorticity but with smaller vorticity in most 3-D cases. In general, vortex is an intuitive concept of rotation core with weak dissipation, e.g. zero dissipation when it becomes rigid rotation. In addition, vortex is not a vorticity tube, being different from what suggested by many research papers and textbooks. At the laminar boundary layer, vorticity is large but we have no vortex. A core with 2 nearly pure rotations per second, where vorticity is small, is a vortex, but a core with 10000 strongly sheared rotation, where vorticity is very large but deformation is very large as well, may not be a vortex.  Therefore, vorticity magnitude and vortex are irrelevant.   Unlike solid body, vortex is always a mixture of vorticity and deformation and vortex is really defined as an open area (not tube) where deformation is weak and vorticity is dominant.  A function so-called “Omega” is defined to identify the vortex and Omega=0.52 well represents the vortex area boundary. Vortex is mathematically defined as Omega >0.5 which means a place where vorticity overtakes deformation. The minimum gradient of “Omega” is well representing the vortex axis. Several examples including DNS for late flow transition and LES for shock vortex interaction have been tested and the outcome is promising.

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