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On the identification of a vortex

  • Jinhee Jeong (a1) and Fazle Hussain (a1)

Considerable confusion surrounds the longstanding question of what constitutes a vortex, especially in a turbulent flow. This question, frequently misunderstood as academic, has recently acquired particular significance since coherent structures (CS) in turbulent flows are now commonly regarded as vortices. An objective definition of a vortex should permit the use of vortex dynamics concepts to educe CS, to explain formation and evolutionary dynamics of CS, to explore the role of CS in turbulence phenomena, and to develop viable turbulence models and control strategies for turbulence phenomena. We propose a definition of a vortex in an incompressible flow in terms of the eigenvalues of the symmetric tensor ${\bm {\cal S}}^2 + {\bm \Omega}^2$; here ${\bm {\cal S}}$ and ${\bm \Omega}$ are respectively the symmetric and antisymmetric parts of the velocity gradient tensor ${\bm \Delta}{\bm u}$. This definition captures the pressure minimum in a plane perpendicular to the vortex axis at high Reynolds numbers, and also accurately defines vortex cores at low Reynolds numbers, unlike a pressure-minimum criterion. We compare our definition with prior schemes/definitions using exact and numerical solutions of the Euler and Navier–Stokes equations for a variety of laminar and turbulent flows. In contrast to definitions based on the positive second invariant of ${\bm \Delta}{\bm u}$ or the complex eigenvalues of ${\bm \Delta}{\bm u}$, our definition accurately identifies the vortex core in flows where the vortex geometry is intuitively clear.

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Bisset, D. K., Antonia, R. A. & Browne, L. W. B. 1990 Spatial organization of large structures in the turbulent far wake of a cylinder. J. Fluid Mech. 218, 439.

Blackwelder, R. F.1977On the role of phase information in conditional sampling. Phys. Fluids20, S232.

Bödewadt, U. T.1940Die Drehströmung über festern Grund. Z. Angew. Math. Mech.20, 141.

Cantwell, B. J.1981Organized motion in turbulent flow. Ann. Rev. Fluid Mech.13, 457.

Chong, M. S., Perry, A. E. & Cantwell, B. J.1990A general classification of three-dimensional flow field. Phys. Fluids A 2, 765.

Fiedler, H. E. & Mensing, P. 1985 The plane turbulent shear layer with periodic excitation. J. Fluid Mech. 150, 281.

Hussain, F. 1986 Coherent structures and turbulence. J. Fluid Mech. 173, 303.

Hussain, A. K. M. F. & Hayakawa, M. 1987 Eduction of large-scale organized structure in a turbulent plane wake. J. Fluid Mech. 180, 193.

Hussain, A. K. M. F. & Zaman, K. B. M. Q. 1980 Vortex pairing in a circular jet under controlled excitation. Part 2. Coherent structure dynamics. J. Fluid Mech. 101, 493.

Jimenez, J., Moin, P., Moser, R. & Keefe, L.1988Ejection mechanisms in the sublayer of a turbulent channel. Phys. Fluids31, 1311.

Kida, S., Takaoka, M. & Hussain, F. 1991 Collision of two vortex rings. J. Fluid Mech. 230, 583.

Kim, J.1985Turbulence structures associated with the bursting event. Phys. Fluids.28, 52.

Melander, M. & Hussain, F.1993Polarized vorticity dynamics on a vortex column. Phys. Fluids A 5, 1992.

Moffatt, H. K. 1963 Viscous and resistive eddies near a sharp corner. J. Fluid Mech. 18, 1.

Mumford, J. C. 1982 The structures of the large eddies in fully developed turbulent shear flows. Part 1. The plane jet. J. Fluid Mech. 118, 241.

Park, K., Metcalfe, R. W. & Hussain, F.1994Role of coherent structures in an isothermally reacting mixing layer. Phys. Fluids6, 885.

Shtern, V. & Hussain, F.1993Hysteresis in a swirling jet as a model tornado. Phys. Fluids A 5, 2183.

Tso, J. & Hussain, F. 1989 Organized motions in a fully developed turbulent axisymmetric jet. J. Fluid Mech. 203, 425.

Virk, D., Melander, M. V. & Hussain, F. 1994 Dynamics of a polarized vortex ring. J. Fluid Mech. 260, 23.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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