Fractional Brownian motions and enhanced diffusion in a unidirectional wave-like turbulence

Journal of Statistical Physics

Volumn 100, Issue 5-6, 2000, Pages 1071-1095

  Fannjiang, Albert ^a   Komorowski, Tomasz ^b,c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b MARIA CURIE SK ODOWSKA UNIVERSITY   (Poland)

^c INSTITUTE OF MATHEMATICS   (Poland)

Author keywords

Convection enhanced diffusion; Fractional brownian motions; Wave turbulence

Indexed keywords

EID: 0034343918     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1018738009970     Document Type: Article

References (29)

1. R. J. Adler, Geometry of Random Fields (Wiley, New York, 1981).
2. R. J. Adler, An Introduction to Continuity Extrema and Related Topics for General Gaussian Processes, Inst. of Math. Stat., Hayward Lecture Notes, Vol. 12.
3. M. Avellaneda and A. J. Majda, Mathematical models with exact renormalization for turbulent transport, Comm. Math. Phys. 131:381-429 (1990).
4. P. Billingsley, Convergence of Probability Measures (Wiley, New York, 1968).
5. P. Castiglione, A. Crisanti, A. Mazzino, M. Vergassola, and A. Vulpiam. Resonant enhanced diffusion in time-dependent flow, J. Phys. A 31(35):7197-7210 (1998).
6. I. T. Drummond, Path-integral methods for turbulent diffusion, J. Fluid Mech. 123:59-68 (1982).
7. I. T. Drummond, S. Duane, and R. R. Horgan. Scalar diffusion in simulated helical turbulence with molecular diffusivity, J. Fluid. Mech. 138:75 (1984).
8. A. Fannjiang, Phase diagram for turbulent transport: Sampling drill, eddy diffusivity and variational principles, Physica D 136(1/2):145-174 (1999).
9. A. Fannjiang and T. Komorowski, An invariance principle for diffusion in turbulence, Ann. Prob. 27(2):751-781 (1999).
10. A. Fannjiang and T. Komorowski, Diffusion approximation for particle convection in Markovian flow, Bull. Polish Acad. Sci. 48:253 (2000).
11. A. Fannjiang and T. Komorowski, Fractional-Brownian-motion limit for a model of turbulent transport, Ann. Appl. Probab. (in press).
12. A. Fannjiang and G. Papanicolaou, Convection enhanced diffusion for periodic flows. SIAM J. Appl. Math. 54(2):333-408 (1994).
13. A. Fannjiang and G. Papanicolaou, Convection enhanced diffusion for random flows, J. Stat. Phys. 88(5/6):1033-1076 (1997).
14. G. Gaudron, Scaling laws for the advection-diffusion equation, Ann. of Appl. Prob. 8:649-663 (1998).
15. D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order (Springer-Verlag, Berlin/New York, 1977).
16. M. I. Gordin, On the central limit theorem for stationary processes, Soviet Math. Dokl. 10:1174-1176 (1969).
17. I. S. Helland, Central limit theorems for martingales with discrete or continuous time, Scan. J. Statist. 9:79-94 (1982).
18. M. B. Isichenko, Percolation, statistical topography, and transport in random media, Rev. Mod. Phys. 64(4):961-1043 (1992).
19. H. Kesten and G. Papanicolaou, A limit, theorem in turbulent, diffusion, Comm. Math. Phys. 65:97-128 (1979).
20. E. Knobloch and W. J. Merryfield, Enhancement of diffusive transport in oscillatory Hows, Astrophys. J. 401(1):196-205 (1992).
21. A. J. Majda and P. R. Kramer, Simplified models for turbulent diffusion: Theory, numerical modelling and physical phenomena, Phys. Rep. 314:237-574 (1999).
22. A. Mazzzino and M. Vergassola, Interference between turbulent and molecular diffusion, Europhys. Lett. 37(8):535-540 (1997).
23. I. Mezić, J. F. Brady, and S. Wiggins, Maximal effective diffusivity for time-periodic incompressible fluid flows, SIAM J. Appl. Math. 56(1):40-56 (1996).
24. Yu. A. Rozanov, Stationary Random Processes (Holden-Day, 1967).
25. P. G. Saffman, On the effect of molecular diffusivity in turbulent diffusion, J. Fluid Mech. 8:73 (1960).
26. G. Samorodnitsky and M. S. Taqqu, Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance (Chapman and Hall, New York, 1994).
27. D. Strook, S. R. S. Varadhan, Multidimensional Diffusion Processes (Springer-Verlag, Berlin/Heidelberg/New York, 1979).
28. V. E. Zakharov, V. S. L'vov, and G. Falkovich, Kolmogorov Spectra of Turbulence (Springer-Verlag, Berlin New York, 1992).
29. Q. Zhang and J. Glimm, Inertial range scaling of laminar shear flow as a model of turbulent transport, Comm. Math. Phys. 146(2):217-229 (1992).