Control of transport in a chaotic lattice

Physica D: Nonlinear Phenomena

Volumn 93, Issue 3-4, 1996, Pages 191-209

  Shinbrot, Troy ^a   Bresler, Leo ^a   Ottino, Julio M ^a  

^a Northwestern University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY LAYER FLOW; CHAOS THEORY; CONTROL EQUIPMENT; DIFFUSION; JETS; MATHEMATICAL MODELS; TRANSPORT PROPERTIES;

CHAOTIC LATTICE; FLOW CONTROL DEVICES;

FLOW CONTROL;

EID: 0030169907     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/0167-2789(95)00293-6     Document Type: Article

References (38)

1. H. Lamb, Hydrodynamics, 6th Ed. (Dover, New York, 1932) 221-229.
2. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Dover, New York, 1961) 43-51.
3. G.K. Batchelor, ed., The Scientific Papers of G.I. Taylor, Vol. II (Cambridge University Press, Cambridge, 1958) 190-192.
4. T.H. Solomon and J.P. Gollub, Passive transport in steady Rayleigh-Bénard convection, Phys. Fluids 31 (1988) 1372-1379;
5. R. Camassa and S. Wiggins, Chaotic advection in a Rayleigh-Bénard flow, Phys. Rev. A 43 (1991) 774-797;
6. M.J. Shelley and M. Vinson, Coherent structures on a boundary layer in Rayleigh-Bénard turbulence, Nonlinearity 5 (1992) 323-351.
7. P.K. Newton and E. Meiberg, Particle dynamics in a viscously decaying cat's eye: the effect of finite Schmidt numbers, Phys. Fluids A 3 (1991) 1068-1072;
8. J.T. Stuart, On finite amplitude oscillations in laminar mixing layers, J. Fluid Mech. 29 (1967) 417-440.
9. D. Del Castillo-Negrete and P.J. Morrison, Chaotic transport by Rossby waves in shear flow, Phys. Fluids A 5 (1993) 948-965;
10. J.B. Weiss, Transport and mixing in traveling waves, Phys. Fluids A 3 (1991) 1379-1384.
11. M. Gaster, A simple device for preventing turbulent contamination on swept leading edges, J. Aerosp. Soc. 69 (1965) 788-798;
12. W.J. Jung, N. Mangiavacchia and R. Akhavan, Suppression of turbulence in wall-bounded flows by high-frequency spanwise oscillations, Phys. Fluids A 4 (1992) 1605-1607;
13. F. Laadhari, L. Skandaji and R. Morel, Turbulence reduction in a boundary layer by a local spanwise oscillating surface, Phys. Fluids 6 (1994) 3218-3220.
14. B.J. Cantwell, Organized motion in turbulent flow, Ann. Rev. Fluid Mech. 13 (1981) 457-515;
15. R.D. Joslin and C.L. Streett, The role of stationary cross-flow vortices in boundary-layer transition on swept wings, Phys. Fluids 6 (1994) 3442-3453.
16. C. Scovel, On symplectic lattice maps, Phys. Lett. A 159 (1991) 396-400.
17. J.B. Weiss and E. Knobloch, Mass transport and mixing by modulated traveling waves, Phys. Rev. A 40 (1989) 2579-2589.
18. B.I. Shraiman, Diffusive transport in a Rayleigh-Bénard convection cell, Phys. Rev. A 36 (1987) 261-267.
19. A.L. Bertozzi, Heteroclinic orbits and chaotic dynamics in planar fluid flows, SIAM J. Math. Anal. 19 (1988) 1271-1294;
20. D.S. Broomhead and S.C. Ryrie, Particle paths in wavy vortices. Nonlinearity 1 (1988) 409-434.
21. T.H. Solomon and J.P. Gollub, Chaotic particle transport in time-dependent Rayleigh-Bénard convection. Phys. Rev. A 38 (1988) 6280-6286.
22. A.J. Lichtenberg and B.P. Wood, Diffusion through a stochastic web, Phys. Rev. A 39 (1989) 2153-2159;
23. G.M. Zaslavskii, R.A. Sagdeev, D.K. Chaikovskii and A.A. Chernikov, Chaos and two-dimensional random walk in periodic and quasiperiodic fields, Sov. Phys. JETP 68 (1989) 995-1000.
24. G.M. Zaslavskii, M.Yu. Zakharov, R.Z. Sagdeev, D.A. Usikov and A.A. Chernikov, Stochastic web and diffusion of particles in a magnetic field, Sov. Phys. JETP 64 (1986) 294-303.
25. V.V. Afanasév, R.Z. Sagdeev, D.A. Usikov and G.M. Zaslavsky, Perturbation of a stochastic web, Phys. Lett. A 151 (1990) 276-280.
26. M.W. Browne, Micro-machines help solve intractable problem of turbulence. New York Times (3 January 1995) pp. B5, B8.
27. H.W. Liepmann, The rise and fall of ideas in turbulence, Amer. Scientist 67 (1979) 221-228.
28. R.S. MacKay, J.D. Meiss and I.C. Percival, Transport in Hamiltonian systems, Physica D 13 (1984) 55-81;
29. S. Wiggins, Chaotic Transport in Dynamical Systems (Springer, Berlin, 1992).
30. H. Rising, Application of chaos and dynamical systems approaches to mixing in fluids, Ph.D. Thesis, Univ. of Mass., Amherst, MA 01003 USA (1989).
31. D. Del Castillo-Negrete and P.J. Morrison, Chaotic transport by rossby waves in shear flow, Phys. Fluids A 5 (1993) 948-965.
32. J.E. Howard and J. Humphreys, Nonmonotonic twist maps, Physica D 80 (1995) 256-276.
33. D. Del Castillo-Negrete, J.M. Greene and P.J. Morrison, Area preserving nontwist maps: periodic orbits and transition to chaos, Physica D 91 (1996) 1-23.
34. A. Crisanti, M. Falcioni, A. Vulpiani and G. Paladin, Lagrangian chaos: Transport, mixing and diffusion in fluids, Rivista del Nuovo Cimento 14 (1991) 1-80;
35. G.M. Zaslavskii, M.Yu. Zakharov, A.I. Neishtadt, R.Z. Sagdeev, D.A. Usikov and A.A. Chernikov, Multidimensional Hamiltonian chaos, Sov. Phys. JETP 69(5) (1989) 885-897.
36. J.M. Greene, R.S. MacKay and J. Stark, Boundary circles for area-preserving maps, Physica D 21 (1986) 267-295.
37. D. Del Castillo-Negrete, J.M. Greene and P.J. Morrison, Area preserving nontwist maps: periodic orbits and transition to chaos, Physica D 91 (1996) 1-23..
38. J.D. Meiss, Symplectic maps, variational principles and transport, Rev. Mod. Phys. 64 (1992) 795-848.