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Vortices play a crucial role in fluid dynamics, which is closely related to fluid diffusion mixing, force, heat, and noise. Five widely-used vortex identification criteria, i.e. the -criterion, Q-criterion, -criterion, ci-criterion, and 2-criterion are analyzed, and four of them are compared with each other based on the velocity-gradient-tensor decomposition method. A new quadruple decomposition method (QDM) is introduced for the first time, so far as we know, to decompose fluid motions into four fundamental components: dilatation, axial deformation along the principal axes of the strain-range sensor, planar motion, and pure shearing. This method helps make the kinematic implications of the four vortex identification criteria more clear. It is found that the mean rotation of fluid elements always contains the pure shearing motion. Non-zero mean rotation does not guarantee the existence of the spiraling streamlines, e.g. in a typically parallel shear flow. A positive Q value indicates the strength of the pure rotation of a fluid element in the 2D complex eigenvalue plane on top of the axial deformation, which however is a sufficient but not a necessary condition for the existence of pure rotation. The -criterion can correctly tell the existence of pure rotation, but cannot accurately determine its strength. The ci-value represents the absolute strength of the pure rotation, which is the combined effect of the canonical rotation in the complex eigenvector plane and the pure shearing. The proposed QDM enables us to achieve a deeper understanding of vortices and motions in fluid dynamics.
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Keywords:
- vortex criterion /
- velocity-gradient tensor /
- quadruple-decomposition
[1] Wu J Z, Ma H Y, Zhou M D 1993 Introduction to Vorticity and Vortex Dynamics (Beijing: Higher Education Press) p221 (in Chinese) [吴介之, 马晖扬, 周明德 1993 涡动力学引论(北京: 高等教育出版社)第221 页]
[2] Moffatt H K, Kida S, Ohkitani K 1994 J. Fluid Mech. 259 241
[3] Jiang N, Tang Z Q 2011 Chin. Phy. Lett. 28 054702
[4] Okubo A 1970 Deep-Sea. Res. 17 445
[5] Hunt J C R, Wray A A, Moin P 1988 Center for Turbulence Research, Report CTR-S88 p.193
[6] Weiss J 1991 Physica D 48 273
[7] Cai W H, Li F C, Zhang H N 2011 Chin. Phys. B 20 124702
[8] Chong M S, Perry A E, Cantwell B J 1990 Phys. Fluids A 2 765
[9] ZhouJ, Adrian R J, Balach,ar S, Kendall T M 1999 J. Fluid Mech. 387 353
[10] Jeong J, Hussain F 1995 J. Fluid Mech. 285 69
[11] Chen L, Tang D B, Liu C Q 2011 Acta Phys. Sin. (in Chinese) 60 094702 [陈林, 唐登斌, Chaoqun Liu 2011 60 094702]
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[1] Wu J Z, Ma H Y, Zhou M D 1993 Introduction to Vorticity and Vortex Dynamics (Beijing: Higher Education Press) p221 (in Chinese) [吴介之, 马晖扬, 周明德 1993 涡动力学引论(北京: 高等教育出版社)第221 页]
[2] Moffatt H K, Kida S, Ohkitani K 1994 J. Fluid Mech. 259 241
[3] Jiang N, Tang Z Q 2011 Chin. Phy. Lett. 28 054702
[4] Okubo A 1970 Deep-Sea. Res. 17 445
[5] Hunt J C R, Wray A A, Moin P 1988 Center for Turbulence Research, Report CTR-S88 p.193
[6] Weiss J 1991 Physica D 48 273
[7] Cai W H, Li F C, Zhang H N 2011 Chin. Phys. B 20 124702
[8] Chong M S, Perry A E, Cantwell B J 1990 Phys. Fluids A 2 765
[9] ZhouJ, Adrian R J, Balach,ar S, Kendall T M 1999 J. Fluid Mech. 387 353
[10] Jeong J, Hussain F 1995 J. Fluid Mech. 285 69
[11] Chen L, Tang D B, Liu C Q 2011 Acta Phys. Sin. (in Chinese) 60 094702 [陈林, 唐登斌, Chaoqun Liu 2011 60 094702]
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