Distinguished material surfaces and coherent structures in three-dimensional fluid flows

Physica D: Nonlinear Phenomena

Volumn 149, Issue 4, 2001, Pages 248-277

  Haller, G ^a  

^a BROWN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; LAGRANGE MULTIPLIERS; LYAPUNOV METHODS; MIXING; TENSORS; THEOREM PROVING;

FINITE-TIME LYAPUNOV EXPONENTIALS; VELOCITY GRADIENT TENSORS;

UNSTEADY FLOW;

EID: 0034823558     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(00)00199-8     Document Type: Article

References (43)

1. H.D.I. Abarbanel, Analysis of Observed Chaotic Data, Springer, New York, 1996.
2. P.D. Anderson, O.S. Galaktionov, G.W. Peters, F.N. Van De Vosse, H.E.H. Meijer, Analysis of mixing in three-dimensional time-periodic cavity flows, J. Fluid Mech. 386 (1999) 149-166.
3. V.I. Arnold, B.A. Khesin, Topological Methods in Hydrodynamics, Springer, New York, 1998.
4. K. Bajer, H.K. Moffatt, F.H. Nex, Steady confined Stokes flows with chaotic streamlines, in: H.K. Moffatt, A. Tsinober (Eds.), Topological Fluid Mechanics, Cambridge University Press, Cambridge, 1990.
5. K.P. Bowman, Manifold geometry and mixing in observed atmospheric flows, Preprint, 1999.
6. B.J. Cantwell, Exact solution of a restricted Euler equation for the velocity gradient tensor, Phys. Fluids A 4 (1992) 782-793.
7. C.Q. Cheng, Y.S. Sun, Existence of invariant tori in 3D measure-preserving mappings, Cel. Mech. 47 (1990) 275-292.
8. M.S. Chong, A.E. Perry, B.J. Cantwell, A general classification of three-dimensional flow fields, in: H.K. Moffatt, A. Tsinober (Eds.), Topological Fluid Mechanics, Cambridge University Press, Cambridge, 1990.
9. C. Coulliette, S. Wiggins, Intergyre transport in a wind-driven, quasigeostrophic double gyre: an application of lobe dynamics, Nonlinear Proc. Geophys. 7 (2000) 59-85.
10. A. DiBenedetto, Partial Differential Equations, Birkhäuser, Boston, 1995.
11. R. Doerner, B. Hübinger, W. Martienssen, A. Grossmann, S. Thomae, Stable manifolds and predictability of dynamical systems, Chaos Solitons Fractals 10 (1999) 1759-1782.
12. T. Dombre, U. Frisch, J.M. Greene, M. Hénon, A. Mehr, A.M. Soward, Chaotic streamlines in ABC flows, J. Fluid Mech. 167 (1986) 353-391.
13. A. Dresselhaus, M. Tabor, The kinematics of stretching and alignment of material elements in general flow fields, J. Fluid Mech. 236 (1991) 415-444.
14. M. Feingold, L.P. Kadanoff, O. Piro, Passive scalars, three-dimensional volume-preserving maps, and chaos, J. Statist. Phys. 50 (1988) 529-565.
15. G.O. Fountain, D.V. Khakhar, J.M. Ottino, Visualization of three-dimensional chaos, Science 281 (1998) 683-686.
16. R.D. Frederiksen, J.A. Dahm, D.R. Dowling, Experimental assessment of fractal scale similarity in turbulent flows. Part 2. Higher-dimensional intersections and non-fractal inclusions, J. Fluid Mech. 338 (1997) 89-126.
17. S. Friedlander, M.M. Vishik, Instability criteria for the flow of an inviscid incompressible fluid, Phys. Rev. Lett. 66 (1991) 2204-2206.
18. M. Giona, A. Adrover, Invariant geometric properties of a class of 3D chaotic flows, Physica D 140 (2000) 50-68.
19. G. Haller, A.C. Poje, Finite-time transport in aperiodic flows, Physica D 119 (1998) 352-380.
20. G. Haller, Finding finite-time invariant manifolds in two-dimensional velocity fields, Chaos 10 (2000) 99-108.
21. G. Haller, G. Yuan, Lagrangian coherent structures and mixing in two-dimensional turbulence, Physica D 147 (2000) 352-370.
22. J. von Hardenberg, F. Fraedrich, F. Lunkeit, A. Provenzale, Transient chaotic mixing during a baroclinic life cycle, Chaos 10 (2000) 122-134.
23. M. Hénon, Sur la topologie des lignes de courant dans un cas particulier, C.R. Acad. Sci. Paris A 262 (1966) 312-314.
24. P.J. Holmes, Some remarks on chaotic particle paths in time-periodic, 3D swirling flows, in: J.E. Marsden (Ed.), Fluids and Plasmas - Geometry and Dynamics, Contemp. Math. 28 (1984) 393-401.
25. Y.-T. Lau, J.M. Finn, Dynamics of a three-dimensional incompressible flow with stagnation points, Physica D 57 (1992) 283-310.
26. A. Lifschitz, Essential spectrum and local instability condition in hydrodynamics, Phys. Lett. A 152 (1991) 199-204.
27. J.W. Loder, Y Shen, H. Ridderinkhof, Characterization of three-dimensional Lagrangian circulation associated with tidal reflection over a submarine bank, J. Phys. Oceanogr. 27 (1997) 1729-1742.
28. R.S. MacKay, Transport in 3D volume-preserving flows, J. Nonlinear Sci. 4 (1994) 329-354.
29. I. Mezić, S. Wiggins, On the integrability and perturbation of three-dimensional fluid flows with symmetry, J. Nonlinear Sci. 4 (1994) 157-194.
30. RD. Miller, C.K.R.T. Jones, A.M. Rogerson, L.J. Pratt, Quantifying transport in numerically generated velocity fields, Physica D 110 (1997) 105-122.
31. A.I. Neishtadt, A.A. Vasiliev, Change of the adiabatic invariant at a separatrix in a volume-preserving 3D system, Nonlinearity 12 (1999) 303-320.
32. K.K. Nomura, G.K. Post, The structure of vorticity and rate of strain in incompressible homogeneous turbulence, J. Fluid Mech. 377 (1998) 65-97.
33. J.M. Ottino, The Kinematics of Mixing: Stretching, Chaos, and Transport, Cambridge University Press, Cambridge, 1989.
34. A.M. Rogerson, P.D. Miller, L.J. Pratt, C.K.R.T. Jones, Lagrangian motion and fluid exchange in a barotropic meandering jet, J. Phys. Oceanogr. 29 (1999) 2635-2655.
35. A.C. Poje, G. Haller, Geometry of cross-stream mixing in a double-gyre ocean model, J. Phys. Oceanogr. 29 (1999) 1649-1665.
36. A.C. Poje, G. Haller, I. Mezić, The geometry and statistics of mixing in aperiodic flows, Phys. Fluids A 11 (1999) 2963-2968.
37. A. Provenzale, Transport by coherent barotropic vortices, Ann. Rev. Fluid Mech. 31 (1999) 55-93.
38. H.A. Stone, A. Nadim, S.H. Strogatz, Chaotic streamlines inside drops immersed in steady Stokes flows, J. Fluid Mech. 232 (1991) 629-646.
39. S.L. Ziglin, Dichotomy of the separatrices and the nonexistence of first integrals in systems of differential equations of Hamiltonian type with two degrees of freedom, Math. USSR-Izv. 31 (1988) 407-421.
40. S.L. Ziglin, On the nonintegrability of the ABC flow for A = B, Funct. Anal. Appl. 30 (1996) 80-81.
41. J. Weiss, The dynamics of enstrophy transfer in 2-dimensional hydrodynamics, Physica D 48 (1991) 273-294.
42. S. Winkler, Personal communication, 2000.
43. Y.-T. Lau, J.M. Finn, Dynamics of a three-dimensional incompressible flow with stagnation points, Physica D 57 (1991) 199-204.