A perturbation study of particle dynamics in a plane wake flow

Journal of Fluid Mechanics

Volumn 384, Issue , 1999, Pages 1-26

  Burns, T J ^a   Davis, R W ^a   Moore, E F ^a  

^a NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FLUID DYNAMICS; NUMERICAL METHODS; PARTICLES (PARTICULATE MATTER); PERTURBATION TECHNIQUES; PHASE SPACE METHODS; REYNOLDS NUMBER; TRANSPORT PROPERTIES; VORTEX FLOW;

BACKGROUND FLOW FIELD; PARTICLE DYNAMICS; STOKES NUMBER; STUART VORTICES; VON KARMAN VORTEX STREET;

WAKES;

EID: 0032679899     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S002211209900419X     Document Type: Article

References (44)

1. ANDRONOV, A. A., WITT, A. A. & KHAIKIN, S. E. 1966 Theory of Oscillators. Pergamon.
2. AREF, H. 1983 Integrable chaotic and turbulent vortex motion in two-dimentional flows Ann. Rev. Fluid Mech. 13, 345-389.
3. AREF, H. & POMPHREY, N. 1982 Integrable and chaotic motion of four vortices. I. The case of identical vortices Proc. R. Soc. Lond. A 380, 359-387.
4. ARNOLD, V. I. 1963 Small denominators and problems of stability of motion in classical and celestial mechanics. Usp. Mat. Nauk 18, 91-192 (English Transl: Russian Math. Surveys 18, 85-191).
5. ARNOLD, V. I. 1963 Small denominators and problems of stability of motion in classical and celestial mechanics. Usp. Mat. Nauk 18, 91-192 (English Transl: Russian Math. Surveys 18, 85-191).
6. CROWE, C. T., TROUTT, T. R. & CHUNG, J. N. 1996 Numerical models for two-phase turbulent flows. Ann. Rev. Fluid Mech. 28, 11-43.
7. CROWE, C. T., TROUTTT, T. R., CHUNG, J. N., DAVIS, R. W. & MOORE, E. F. 1995 A turbulent flow without particle mixing. Aerosol Sci. Technol. 22, 135-138.
8. DAVIS, R. W. & MOORE, E. F. 1982 A numerical study of vortex shedding from rectangles. J. Fluid Mech. 116, 475-506.
9. DAVIS, R. W., MOORE, E. F. & PURTELL, L. P. 1984 A numerical-experimental study of confined flow around rectangular cylinders. Phys. Fluids 27, 46-59.
10. DRUZHININ, O. A. 1994 Concentration waves and flow modification in a particle-laden circular vortex. Phys. Fluids 6, 3276-3284.
11. DUAN, J. & WIGGINS, S. 1997 Lagrangian transport and chaos in the near wake of a cylinder in the time-periodic regime: a numerical implementation of lobe dynamics. Nonlinear Processes Geophys. 4, 125-136.
12. FENICHEL, N. 1971 Persistence and smoothness of invariant manifolds for flows. Indiana Univ. Math. J. 21, 193-226.
13. FENICHEL, N. 1979 Geometric singular perturbation theory for ordinary differential equations. J. Diffl Equat. 31, 51-98.
14. GRASSBERGER, P. & PROCACCIA, I. 1983 Measuring the strangeness of strange attractors. Physica D 9, 189-208.
15. HAFFNER, T. 1995 Dynamik von Teilchen in einer periodische Wirbelströmung. Diplomarbeit, Department of Mathematics, University of Stuttgart, September 1995.
16. JONES, C. K. R. T. 1995 Geometric singular perturbation theory. In CIME lectures. June 13-22, 1994 Lecture Notes in Mathematics, Vol. 1609. (ed. R. Johnson), pp. 44-120. Springer.
17. LAMB, H. 1932 Hydrodynamics, 6th Edn. Cambridge University Press.
18. MARCU, B. & MEIBURG, E. 1996 The effect of streamwise braid vortices on the particle dispersion in a plane mixing layer. I. Equilibrium points and their stability. Phys. Fluids 8, 715-733.
19. MARCU, B., MEIBURG, E. & NEWTON, P. K. 1995 Dynamics of heavy particles in a Burgers vortex. Phys. Fluids 7, 400-410.
20. MARCU, B., MEIBURG, E. & RAJU, N. 1996 The effect of streamwise braid vortices on the particle dispersion in a plane mixing layer. II. Nonlinear particle dynamics. Phys. Fluids 8, 734-753.
21. MARTIN, J. E. & MEIBURG, E. 1994 The accumulation and dispersion of heavy particles in forced two-dimensional mixing layers. I. The fundamental and subharmonic cases. Phys. Fluids 6, 1116-1132.
22. MAXEY, M. R. & RILEY, J. J. 1983 Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26, 883-889.
23. MEIBURG, E. & NEMTON, P. K. 1991 Particle dynamics and mixing in a viscously decaying shear layer. J. Fluid Mech. 227, 211-244.
24. MILNE-THOMSON, L. M. 1968 Theoretical Hydrodynamics. 5th Edn. Macmillan.
25. MOORE, E. F. & DAVIS, R. W. 1986 Numerical computation of particle trajectories: a model problem. Gas-Solid Flows - 1986, ASME-FED Vol. 35, pp. 111-116.
26. NEISHTADT, A. I. 1991 Probability phenomena due to separatrix crossing. Chaos 1, 42-48.
27. OTT, E & TÉL. T. 1994 Chaotic scattering: an introduction Chaos 3, 417-437.
28. OTTINO, J. M. 1989 The Kinematics of Mixing: Stretching, Chaos, and Transport. Cambridge University Press.
29. PERRY, A. E., CHONG, M. S. & LIM, T. T. 1982 The vortex-shedding process behind two-dimensional bluff bodies. J Fliud Mech. 116, 77-90.
30. RUBIK, J, JONES, C. K. R. T. & MAXEY, M. 1995 Settling and asymptotic motion of aerosol particles in a cellular flow field J. Nonlinear Sci. 5, 337-358.
31. SAFFMAN, P. G. 1995 Vortex Dynamics. Cambridge University Press.
32. SAFFMAN, P. G. & SCHATZMAN, J. C. 1981 Properties of a vortex street of finite vortices. SIAM J. Sci. Statist. Comput. 2, 285-295.
33. SHAMPINE, L. F. & WATTS, H. A. 1979 DEPAC - Design of a user oriented package of ODE solvers. SAND 79-2374, Sandia National Laboratories, Albuquerque, NM.
34. SHARIFF, K., PULLIAM, T. H. & OTTINO, J. M. 1991 A dynamical systems analysis of kinematics in the time-periodic wake of a circular cylinder. Lectures in Applied Mathematics, Vol. 28, pp. 613-646, Springer.
35. SOMMERER, J. C, Ku, H.-C. & GILREATH, H. E. 1996 Experimental evidence for chaotic scatttering in a fluid wake. Phys. Rev. Lett. 77, 5055-5058.
36. SOMMERER, J. C., OTT, E. & TÉL, T. 1997 Modeling two-dimensional fluid flows with chaos theory. Johns Hopkins APL Technical Digest 18, 193-203.
37. STUART, J. T. 1967 On finite amitude oscillations in laminar mixing layers. J. Fluid Mech. 29, 417-440.
38. TANG, L., WEN, F., YANG, Y., CROWE, C. T., CHUNG, J. N. & TROUTT, T. R. 1992 Self-organizing particle dispersion mechanism in a plane wake. Phys. Fluid A 4, 2244-2250.
39. TIO, K.-K., GANÁN-CALVO, A. M. & LASHERAS, J. C. 1993a The dynamics of small, heavy, rigid spherical particles in a periodic Stuart vortex flow. Phys. Fluids A 5, 1679-1693.
40. TIO, K.-K., LIÑÁN, A., LASHERS, J. C. & GANÁN-CALVO, A. M. 1993b On the dynamics of buoyant and heavy particles in a periodic Stuart vortex flow. J. Fluid Mech 254, 671-699.
41. VAN DYKE, M. 1982 An Album of Fluid Motion. Parabolic Press, Stanford.
42. WEN, F., KAMALU, N., CHUNG, J. N., CROWE, C. T. & TROUTT, T. R. 1992 Particle dispersion by vortex structures in plane mixing layers. Trans. ASME: J. Fluids Engng 114, 657-666.
43. WIGGINS, S. 1990 Introduction to Applied Nonlinear Dynamicals Systems and Chaos. Springer.
44. WIGGINS, S. 1994 Normally Hyperbolic Invariant Manifolds in Dynamical Systems. Springer.