On the identification of a vortex

Journal of Fluid Mechanics - Tập 285 - Trang 69-94 - 1995
Jinhee Jeong1, Fazle Hussain2
1[Univ. of Houston]
2Department of Mechanical Engineering, University of Houston, Houston, TX 77204-4792, USA

Tóm tắt

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.

Từ khóa


Tài liệu tham khảo

Courant, R. & Hilbert, D. 1953 Methods of Mathematical Physics , vol. 1. Interscience.

10.1007/978-3-642-71435-1_11

10.1017/S0022112095003223

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

10.7551/mitpress/3014.001.0001

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

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

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

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

Tso, j. 1983 coherent structures in a fully-developed turbulent axisymmetric jet. PhD dissertation, johns hopkins university.

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

10.1007/978-3-642-67220-0_32

Ferré, J. A. & Giralt, F. 1989 Pattern recognition analysis of the velocity field in plane turbulent wakes. J. Fluid Mech. 198, 27.

Lamb, H. 1945 Hydrodynamics. Dover.

Hunt, J. C. R. , Wray, A. A. & Moin, P. 1988 Eddies, stream, and convergence zones in turbulent flows. Center for Turbulence Research Report CTR-S88 , p. 193.

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

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

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.

Batchelor, G. K. 1967 Introduction to Fluid Dynamics. Cambridge University Press.

Schoppa, W. , Husain, H. & Hussain, F. 1993 Nonlinear instability of free shear layers: subharmonic resonance and three-dimensional vortex dynamics. IUTAM Symp on Nonlinear Instability of Nonparallel Flows (ed. S. P. Lin et al.), 26–30 July 1993, Clarkson University, pp. 251–280.

Melander, M. V. , Hussain, F. & Basu, A. 1991 Breakdown of a circular jet into turbulence. In Turbulent Shear Flows 8, Munich , pp. 15.5.1–15.5.6.

Blackwelder, R. F. 1977 On the role of phase information in conditional sampling. Phys. Fluids 20, S232.

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.

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.

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

Hunt, J. C. R. 1987 Vorticity and vortex dynamics in complex turbulent flows. In Proc. CANCAM, Trans. Can. Soc. Mech. Engrs 11, 21.

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

Husain, H. S. & Hussain, F. 1993 Elliptic jets. Part 3. Dynamics of preferred mode coherent structure. J. Fluid Mech. 248, 315.

Cantwell, B. J. & Coles, D. 1983 An experimental study of entrainment and transport in the turbulent near wake of a circular cylinder. J. Fluid Mech. 136, 321.

Truesdell, C. 1953 The Kinematics of Vorticity. Indiana University.

Panton, R. L. 1984 Incompressible Flow. Wiley.

Park, K. , Metcalfe, R. W. & Hussain, F. 1994 Role of coherent structures in an isothermally reacting mixing layer. Phys. Fluids 6, 885.

Robinson, S. K. 1991 The kinetics of turbulent boundary layer structure. PhD Dissertation, Stanford University.

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

Jimenez, J. , Moin, P. , Moser, R. & Keefe, L. 1988 Ejection mechanisms in the sublayer of a turbulent channel. Phys. Fluids 31, 1311.

Jeong, J. 1994 A theoretical and numerical study of coherent structures. PhD dissertation, University of Houston.

Melander, M. V. & Hussain, F. 1988 Cut-and-connect of two antiparallel vortex tubes. Center for Turbulence Research Rep. CTR-S88 , pp. 257–286.

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

10.1007/3-540-10289-2_30

10.1007/978-1-4612-2792-2_11

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

10.1016/B978-0-12-493240-1.50017-X