TY - JOUR

T1 - On the identification of a vortex

AU - JEong, Jinhee

AU - Hussain, Fazle

N1 - Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.

PY - 1995/2

Y1 - 1995/2

N2 - 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 S2+122; here S and Q are respectively the symmetric and antisymmetric parts of the velocity gradient tensor ∇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 ∇u or the complex eigenvalues of ∇u. our definition accurately identifies the vortex core in flows where the vortex geometry is intuitively clear.

AB - 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 S2+122; here S and Q are respectively the symmetric and antisymmetric parts of the velocity gradient tensor ∇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 ∇u or the complex eigenvalues of ∇u. our definition accurately identifies the vortex core in flows where the vortex geometry is intuitively clear.

UR - http://www.scopus.com/inward/record.url?scp=0029252670&partnerID=8YFLogxK

U2 - 10.1017/S0022112095000462

DO - 10.1017/S0022112095000462

M3 - Article

AN - SCOPUS:0029252670

VL - 285

SP - 69

EP - 94

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -