Chaotic advection in three-dimensional unsteady incompressible laminar flow

Journal of Fluid Mechanics

Volumn 316, Issue , 1996, Pages 259-284

  Cartwright, Julyan H E ^a   Feingold, Mario ^b   Piro, Oreste ^a,c  

^a UNIVERSITAT DE LES ILLES BALEARS   (Spain)

^b BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

^c INSTITUTO MEDITERRÁNEO DE ESTUDIOS AVANZADOS   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ADVECTION; CHAOTIC; INCOMPRESSIBLE; LAMINAR FLOW; MODELLING-MATHEMATICAL;

MATHEMATICAL MODELS; NAVIER STOKES EQUATIONS; REYNOLDS NUMBER; THREE DIMENSIONAL; UNSTEADY FLOW; VELOCITY;

CHAOTIC ADVECTION; EULERIAN VELOCITY; INCOMPRESSIBLE FLOW; SPHERICAL COUETTE FLOW;

LAMINAR FLOW;

EID: 0030153058     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112096000535     Document Type: Article

References (49)

1. AREF, H. 1984 Stirring by chaotic advection. J. Fluid Mech. 143, 1-21.
2. AREF, H. & BALACHANDAR, S. 1986 Chaotic advection in a Stokes flow. Phys. Fluids 29, 3515-3521.
3. AREF, H., JONES, S. W., MOFINA, S. & ZAWADZKI, I. 1989 Vortices, kinematics and chaos. Physica D 37, 423-440.
4. ARNOLD, V. I. 1965 Sur la topologie des écoulements stationnaires des fluides parfaits. C. R. Acad. Sci. Paris A 261, 17-20.
5. ARNOLD, V. I. 1978 Mathematical Methods of Classical Mechanics. Springer.
6. ARROWSMITH, D. K. & PLACE, C. M. 1990 An Introduction to Dynamical Systems. Cambridge University Press.
7. BAJER, K. 1994 Hamiltonian formulation of the equations of streamlines in three-dimensional steady flows. Chaos, Solitons & Fractals 4, 895-911.
8. BAJER, K. & MOFFATT, H. K. 1990 On a class of steady confined Stokes flows with chaotic streamlines. J. Fluid Mech. 212, 337-363.
9. BAJER, K. & MOFFATT, H. K. 1992 Chaos associated with fluid inertia. In Topological Aspects of the Dynamics of Fluids and Plasmas (ed. H. K. Moffatt, G. M. Zaslavsky, P. Comte & M. Tabor), pp. 517-534. Kluwer.
10. BÜHLER, K. 1992 Pattern formation of instabilities in spherical Couette flow. In Pattern Formation in Complex Dissipative Systems: Fluid Patterns, Liquid Crystals, Chemical Reactions (ed. S. Kai), pp. 298-302. World Scientific.
11. CARTWRIGHT, J. H. E., FEINGOLD, M. & PIRO, O. 1994a Dynamically diffusive Lagrangian trajectories in time-periodic three-dimensional flows. In Heat Transfer Enhancement by Lagrangian Chaos and Turbulence (ed. H. Peerhossaini & A. Provenzale), pp. 101-107. ISITEM. Univ. Nantes.
12. CARTWRIGHT, J. H. E., FEINGOLD, M. & PIRO, O. 1994b Passive scalars and three-dimensional Liouvillian maps. Physica D 76, 22-33.
13. CARTWRIGHT, J. H. E., FEINGOLD, M. & PIRO, O. 1995 Global diffusion in a realistic three-dimensional time-dependent nonturbulent fluid flow. Phys. Rev. Lett. 75, 3669-3672.
14. CARTWRIGHT, J. H. E. & PIRO, O. 1992 The dynamics of Runge-Kutta methods. Intl J. Bifurcation Chaos 2, 427-449.
15. CHAIKEN, J., CHEVRAY, R., TABOR, M. & TAN, Q. M. 1986 Experimental study of Lagrangian turbulence in Stokes flow. Proc. R. Soc. Lond. A 408, 165-174.
16. CHAIKEN, J., CHU, C. K., TABOR, M. & TAN, Q. M. 1987 Lagrangian turbulence and spatial complexity in a Stokes flow. Phys. Fluids 30, 687-699.
17. CHENG, C.-Q. & SUN, Y.-S. 1990 Existence of invariant tori in three-dimensional measure preserving mappings. Celest. Mech. 47, 275-292.
18. CHIEN, W.-L., RISING, H. & OTTINO, J. M. 1986 Laminar mixing and chaotic mixing in several cavity flows. J. Fluid Mech. 170, 355-377.
19. DOMBRE, T., FRISCH, U., GREENE, J. M., HéNON, M., MEHR, A. & SOWARD, A. M. 1986 Chaotic streamlines in the ABC flows. J. Fluid Mech. 167, 353-391.
20. FEINGOLD, M., KADANOFF, L. P. & PIRO, O. 1987 A way to connect fluid dynamics to dynamical systems: Passive scalars. In Fractal Aspects of Materials: Disordered Systems (ed. A. J. Hurd, D. A. Weitz & B. B. Mandelbrot), pp. 203-205. Materials Research Society.
21. FEINGOLD, M., KADANOFF, L. P. & PIRO, O. 1988a Diffusion of passive scalars in fluid flows: Maps in three dimensions. In Universalities in Condensed Matter (ed. R. Jullien, L. Peliti, R. Rammal & N. Boccara), pp. 236-241. Les Houches. Springer.
22. FEINGOLD, M., KADANOFF, L. P. & PIRO, O. 1988b Passive scalars, three-dimensional volume-preserving maps, and chaos. J. Statist. Phys. 50, 529-565.
23. FEINGOLD, M., KADANOFF, L. P. & PIRO, O. 1989 Transport of passive scalars: KAM surfaces and diffusion in three-dimensional Liouvillian maps. In Instabilities and Nonequilibrium Structures II (ed. P. Collet, E. Tirapegui & D. Villarroel). Reidel.
24. HABERMAN, W. L. 1962 Secondary flow about a sphere rotating in a viscous liquid inside a coaxially rotating spherical container. Phys. Fluids 5, 625-626.
25. HÉNON, M. 1966 Sur la topologie des lignes de courant dans un cas particulier. C. R. Acad. Sci. Paris A 262, 312-314.
26. JONES, S. W., THOMAS, O. M. & AREF, H. 1989 Chaotic advection by laminar flow in a twisted pipe. J. Fluid Mech. 209, 335-357.
27. KHAKHAR, D. V., FRANJIONE, J. G. & OTTINO, J. M. 1987 A case study of chaotic mixing in deterministic flows. The partitioned pipe mixer. Chem. Engng Sci. 42, 2909-2926.
28. KHAKHAR, D. V., RISING, H. & OTTINO, J. M. 1986 An analysis of chaotic mixing in two chaotic flows. J. Fluid Mech. 172, 419-451.
29. KOSCHMIEDER, E. L. 1993 Bénard Cells and Taylor Vortices. Cambridge University Press.
30. KUSCH, H. A. & OTTINO, J. M. 1992 Experiments on mixing in continuous chaotic flows. J. Fluid Mech. 236, 319-348.
31. LE GUER, Y., CASTELAIN, C. & PEERHOSSAINI, H. 1996 Experimental study of chaotic advection regime in a twisted duct flow. J. Fluid Mech. submitted.
32. MACKAY, R. S. 1994 Transport in 3D volume-preserving flows. J. Nonlinear Sci. 4, 329-354.
33. MEZIĆ, I. & WIGGINS, S. 1994 On the integrability and perturbation of three-dimensional fluid flows with symmetry. J. Nonlinear Sci. 4, 157-194.
34. MUNSON, B. R. 1974 Viscous incompressible flow between eccentric coaxially rotating spheres. Phys. Fluids 17, 528-531.
35. MUNSON, B. R. & JOSEPH, D. D. 1971 Viscous incompressible flow between concentric rotating spheres. Part 1. Basic flow. J. Fluid Mech. 49, 289-303.
36. m, m ≥ 3. Commun. Math. Phys. 64, 35-40.
37. OTTINO, J. M. 1989 The Kinematics of Mixing: Stretching, Chaos, and Transport. Cambridge University Press.
38. PARKER, T. S. & CHUA, L. O. 1989 Practical Numerical Algorithms for Chaotic Systems. Springer.
39. PEARSON, C. E. 1967 A numerical study of the time-dependent viscous flow between two rotating spheres. J. Fluid Mech. 28, 323-336.
40. PIRO, O. & FEINGOLD, M. 1988 Diffusion in three-dimensional Liouvillian maps. Phys. Rev. Lett. 61, 1799-1802.
41. RUELLE, D. & TAKENS, F. 1971 On the nature of turbulence. Commun. Math. Phys. 20, 167-192; 23, 343-344.
42. RUELLE, D. & TAKENS, F. 1971 On the nature of turbulence. Commun. Math. Phys. 20, 167-192; 23, 343-344.
43. SOLOMON, T. H. & GOLLUB, J. P. 1988 Chaotic particle transport in time dependent Rayleigh-Bénard convection. Phys. Rev. A 38, 6280-6286.
44. STONE, H. A., NADIM, A. & STROGATZ, S. H. 1991 Chaotic streaklines inside drops immersed in steady linear flows. J. Fluid Mech. 232, 629-646.
45. SWANSON, P. D. & OTTINO, J. M. 1990 A comparative computational and experimental study of chaotic mixing of viscous fluids. J. Fluid Mech. 213, 227-249.
46. THYAGARAJA, A. & HAAS, F. A. 1985 Representation of volume-preserving maps induced by solenoidal vector fields. Phys. Fluids 28, 1005-1007.
47. WANNIER, G. H. 1950 A contribution to the hydrodynamics of lubrication. Q. Appl. Maths 8, 1-32.
48. YAVORSKAYA, I. M., BELYAEV, Y. N., MONAKHOV, A. A., ASTAF'EVA, N. M., SCHERBAKOV, S. A. & VVEDENSKAYA, N. D. 1980 Stability, non-uniqueness and transition to turbulence in the flow between two rotating spheres. In Proc. XV Intl Congress of Theoretical and Applied Mechanics, pp. 431-443. IUTAM.
49. ZHELIGOVSKY, V. A. 1993 A kinematic magnetic dynamo sustained by a Beltrami flow in a sphere. Geophys. Astrophys. Fluid Dyn. 73, 217-254.