Maximal effective diffusivity for time-periodic incompressible fluid flows

SIAM Journal on Applied Mathematics

Volumn 56, Issue 1, 1996, Pages 40-56

  Mezić, Igor ^a   Brady, John F ^b   Wiggins, Stephen ^c  

^a University of California at Santa Barbara   (United States)

^b California Institute of Technology ^*  (United States)

^c CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Effective diffustivity; Ergodic theory; Homogenization

Indexed keywords

DIFFUSION; PROBLEM SOLVING; TIME VARYING SYSTEMS; VELOCITY;

ERGODIC THEORY; HOMOGENIZATION; MAXIMAL EFFECTIVE DIFFUSIVITY; PECLET NUMBER; STEADY CELLULAR VELOCITY FIELDS; TIME DEPENDENT DUCT VELOCITY FIELDS; TIME PERIODIC INCOMPRESSIBLE FLUID FLOWS; TIME PERIODIC INCOMPRESSIBLE VELOCITY FIELDS;

FLOW OF FLUIDS;

EID: 0030085476     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139994270449     Document Type: Article

References (30)

1. M. AVELLANEDA AND A. J. MAJDA, Stieltjes integral representation and effective diffusivity bounds for turbulent transport, Phys. Rev. Lett., 62 (1989), pp. 753-755.
2. _, An integral representation and bounds on the effective diffusivity in passive advection by laminar and turbulent flows, Comm. Math. Phys., 138 (1991), pp. 339-391.
3. A. BENSOUSSAN, J. L. LIONS, AND G. C. PAPANICOLAOU, Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam, 1978.
4. R. BHATTACHARYA, A central limit theorem for diffusions with periodic coefficients, Ann. Probab., 13 (1978), pp. 385-396.
5. R. N. BHATTACHARYA, V. K. GUPTA AND, H. F. WALKER, Asymptotics of solute dispersion in periodic porous media, SIAM J. Appl. Math., 49 (1989), pp. 86-98.
6. H. BRENNER, Dispersion resulting from flow through spatially periodic porous media, Philos. Trans. Roy. Soc. London Ser. A, A297 (1980), pp. 81-133.
7. L. H. DILL AND H. BRENNER, A general theory of Taylor dispersion phenomena. V. Time-periodic convection, PhysicoChemical Hydrodynamics, 3 (1982), pp. 267-292.
8. _, Dispersion resulting from flow through spatially periodic porous media-III. Time-periodic processes, PhysicoChemical Hydrodynamics, 4 (1983), pp. 279-302.
9. J. G. FRANJIONE AND J. M. OTTINO, Stretching in duct flows, Phys. Fluids A, 3 (1991), pp. 2819-2821.
10. A. FANNJIANG, AND G. C. PAPANICOLAOU, Convection enhanced diffusion for periodic flows, SIAM J. Appl. Math., 54 (1994), pp. 333-408.
11. C. F. F. KARNEY, A. B. RECHESTER, AND R. B. WHITE, Effect of noise on the standard mapping, Physica D, 4 (1982), pp. 425-438.
12. A. I. KHINCHIN, Mathematical Foundations of Statistical Mechanics, Dover, New York, 1949.
13. D. L. KOCH AND J. F. BRADY, The symmetry properties of the effective diffusivity tensor in anisotropic porous media, Phys. Fluids, 30 (1987), pp. 642-650.
14. D. L. KOCH, R. G. Cox, H. BRENNER, AND J. F. BRADY, The effect of order on dispersion in porous media, J. Fluid Mech., 200 (1989), pp. 173-188.
15. A. J. MAJDA AND R. M. MCLAUGHLIN, The effect of mean flows on enhanced diffusivity in transport by incompressible periodic velocity fields, Stud. Appl. Math. 89 (1993), pp. 245-279.
16. R. MAÑE, Ergodic Theory and Differentiable Dynamics, Springer-Verlag, New York, Heidelberg, Berlin, 1987.
17. R. MAURI, Dispersion, convection and reaction in porous media, Phys. Fluids A, 3 (1991), pp. 743-756.
18. I. MEZIĆ AND S. WIGGINS, Birkhoff's ergodic theorem and statistical properties of dynamical systems with applications to fluid mechanical dispersion and mixing, preprint, California Institute of Technology, Pasadena, CA.
19. 2 dispersion of a non-diffusive tracer in incompressible laminar flows, Phys. Fluids A, 6 (1994), pp. 2227-2229.
20. 2 Diffusion in a Class of Volume Preserving Maps, Phys. Rev. E., accepted for publication.
21. _, On the integrability and perturbation of three-dimensional fluid flows with symmetry, J. Nonlinear Sci., 4 (1994), pp. 157-194.
22. J. MOSER, Stable and Random Motions in Dynamical Systems, Princeton University Press, Princeton, NJ, 1973.
23. K. OUCHI AND H. MORI, Anomalous diffusion and mixing in an oscillating Rayleigh-Benard flow, Progress Theoret. Phys., 88 (1992), pp. 467-484.
24. V. ROM-KEDAR AND S. WIGGINS, Transport in two-dimensional maps, Arch. Rat. Mech. Anal., 109 (1989), pp. 239-298.
25. A. M. SOWARD AND S. CHILDRESS, Large magnetic Reynolds number dynamo action in a spatially periodic flow with mean motion, Philos. Trans Roy. Soc. London Ser. A, 331 (1990), pp. 649-733.
26. S. WIGGINS, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-Verlag, New York, Heidelberg, Berlin, 1990.
27. M. WOJTKOWSKI, A model problem with the coexistence of stochastic and integrable behaviour, Comm. Math. Phys., 80 (1981), pp. 453-464.
28. _, On the ergodic properties of piecewise linear perturbations of the twist map, Ergodic Theory Dynamical Systems, 2 (1982), pp. 525-542
29. W. R. YOUNG, P. B. RHINES, AND C. J. R. GARRETT, Shear-flow dispersion, internal waves and horizontal mixing in the ocean, Journal of Physical Oceanography, 12 (1982), pp. 515-527.
30. I. B. ZELDOVICH, Exact solution of the diffusion problem in a periodic velocity field and turbulent diffusion, Dokl. Akad. Nauk SSSR, 266 (1982), pp. 821-826.