Percolation models of turbulent transport and scaling estimates

Chaos, Solitons and Fractals

Volumn 23, Issue 5, 2005, Pages 1703-1731

  Bakunin, O G ^a,b  

^a FOM INSTITUTE FOR PLASMA PHYSICS RIJNHUIZEN   (Netherlands)

^b KURCHATOV INSTITUTE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; APPROXIMATION THEORY; CORRELATION METHODS; DIFFUSION; MAGNETIC FIELDS; MATHEMATICAL MODELS; PERTURBATION TECHNIQUES; RANDOM PROCESSES; TOPOLOGY; TRANSPORT PROPERTIES;

CORRELATION EFFECTS; DRIFT FLOWS; FLOW TOPOLOGY; PERTURBATION AMPLITUDE;

TURBULENCE;

EID: 9644287975     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(04)00435-7     Document Type: Article

References (88)

1. Monin AS, Yaglom AM. Statistical fluid mechanics. Cambridge MA: MIT Press; 1975.
2. Frenkiel FN, editor. Atmospheric diffusion and air pollution. New York London: Academic Press; 1959.
3. Frost W, Moulden TH, editors. Handbook of turbulence. New York, London: Plenum Press; 1977.
4. Frisch U. Turbulence: the legacy of A.N. Kolmogorov. Cambridge: University Press Cambridge; 1995.
5. McComb WD. The Physics of fluid turbulence. Oxford: Clarendon Press; 1994.
6. Isichenko MB. Percolation, statistical topography, and transport in random media. Rev Mod Phys 1992;64:961.
7. Bouchaud JP, Georges A. Anomalous diffusion in disordered media: statistical mechanisms, models and physical applications. Phys Rep 1990;195:127-293.
8. Haus JW, Kehr KW. Diffusion in regular and disordered lattices. Phys Rep 1987;150:263.
9. Balescu R. Statistical dynamics. London: Imperial College Press; 1997.
10. Shiesinger MF, Zaslavsky GM. Levy flights and related topics in physics. Springer; 1995.
11. Metzler R, Klafter J. The random walk's guide to anomalous diffusion: a fractional dynamics approach. Phys Rep 2000;339:1.
12. Zaslavsky GM. Chaos, fractional kinetics, and anomalous transport. Phys Rep 2002;371:461.
13. Avellaneda M, Majda A. Mathematical models with exact renormalization for turbulent transport. Commun Math Phys 1990;131:381.
14. Mandelbrot BB. Fractals: form, chance, and dimension. San Francisco: Freemen; 1997.
15. Mandelbrot BB. The fractal geometry of nature. San Francisco: Freemen; 1982.
16. Feder J. Fractals. New York: Plenum Press; 1988.
17. Moffatt HK. Some developments in the theory of turbulence. J Fluid Mech 1981;106:27.
18. Moffatt HK. Transport effects associated with turbulence with particular attention to the influence of helicity. Rep Prog Phys 1983;46:621.
19. Isichenko MB, Horten W. Stochastic diffusion and Kolmogorov entropy in regular and random Hamiltonians. Phys Fluids B 1992;4:3973.
20. Majda AJ, Kramer PR. Simplified models for turbulent diffusion: theory, numerical modeling, and physical phenomenon. Phys Rep 1999;314:237-574.
21. Falkovich G, Gawedzki K, Vergassola M. Particles and fields in fluid turbulence. Rev Mod Phys 2001;73:913.
22. Kadomtsev BB, Pogutse OP. Plasma physics and controlled nuclear fusion research. In: Proceedings of the 7th International Conference, IAEA Vienna, vol. 1. 1978; p. 649.
23. Zel'dovich YB, Molchanov SA, Ruzmaikin AA, Sokolov DD. Intermittent passive fields in random media. Sov Phys Usp 1985;89:2061.
24. Galeev A, Kuznetsova MM, Zeleny LM. Magnetopause stability threshold for patchy reconnection. Space Sci Rev 1986;44:1.
25. Stauffer D. Introduction to percolation theory. London: Taylor and Francis; 1985.
26. Ziman JM. Models of disorder: the theoretical physics of homogeneously disordered systems. London: Cambridge University Press; 1979.
27. Sokolov IM. Dimensionalities and other geometric critical exponents in percolation theory. Sov Phys Usp 1986;29:924.
28. Rosenbluth MN, Sagdeev RZ, editors. Handbook of plasma physics. Amsterdam: North-Holland; 1984.
29. Krommes JA. Systematic statistical theories of plasma turbulence and intermittency: current status and future prospects. Phys Rep 1997;283:5-48.
30. Krommes JA. Fundamental statistical descriptions of plasma turbulence in magnetic fields. Phys Rep 2002;360:1-352.
31. Yoshizawa A, Itoh S-I, Yokoi N. Turbulence theories and modeling if fluids and plasmas. Plasma Phys Controlled Fusion 2001;43:R1.
32. Similon PL, Sudan RN. Plasma turbulence. Annu Rev Fluid Mech 1990;22:317.
33. Horton W. Drift waves and transport. Rev Mod Phys 1999;71:735.
34. Krommes GA. Plasma transport in stochastic magnetic fields. II: Principles and problems of test electron transport. Suppl Progr Theor Phys 1978;64:137.
35. Krommes JA, Oberman C, Kleva RG. Plasma transport in stochastic magnetic fields. Part 3 Kinetics of test particle diffusion. J Plasma Phys 1983;30:11.
36. Avellaneda M, Elliott F, Apelian C. Trapping, percolation, and anomalous diffusion of particles in a two-dimensional random field. J Stat Phys 1993;72:1227.
37. Grisanti A, Falcioni M, Paladin G, Vulpian A. Anisotropic diffusion in fluids with steady periodic velocity fields. J Phys Math A: Gen 1990;23:3307.
38. Pommois P, Veltri P, Zimbardo G. Kubo number and magnetic field line diffusion coefficient for anisotropic magnetic turbulence. Phys Rev E 2001;63:066405.
39. Fannjiang A, Papanicolaou G. Convection-enhanced diffusion for random flows. J Stat Phys 1997;88:1033.
40. Bohr T, Gensen M, Paladin G, Vulpiani A. Dynamical systems approach to turbulence. Cambridge: Cambridge University Press; 1998.
41. Bifarale L, Crisanti A, Vergassola M, Vulpiani A. Eddy diffusivities in scalar transport. Phys Fluids 1995;7:1725.
42. Celani A, Vergassola M. Statistical geometry in scalar turbulence. Phys Rev Lett 2001;86:424.
43. Ott E, Antonsen TM. Chaotic fluid convection and the fractal nature of passive scalar gradients. Phys Rev Lett 1988;61:2839.
44. Fung JCH, Vassilicos JC. Fractal dimensions of lines in chaotic advection. Phys Fluids A 1991;3:2725.
45. Bakunin OG. Mysteries of diffusion. Physics-Uspekhi 2003;46:323.
46. Taylor GI. Diffusion by continuous movements. Proc London Math Soc 1921;Ser 2(20):196.
47. Tsytovich VN. Theory of turbulent plasma. New York: Plenum Press; 1974.
48. Rosenbluth MN, Sagdeev RZ, Taylor JB. Nucl Fusion 1966;6:297.
49. Jokipii JR, Parker EN. Stochastic aspects of magnetic lines of force with application to cosmic-ray propagation. The Astrophys J 1969;155:777.
50. Dupree TH. Nonlinear theory of drift-wave turbulence and enhanced diffusion. Phys Fluids 1967;10:1049.
51. Dupree TH. Theory of phase space density granulation in plasma. Phys Fluids 1972;15:334.
52. Getmantsev GG. The model of cosmic rays diffusion. Astron Rep 1962;6:477.
53. Zaslavsky GM, Chirikov BV. A universal instability of many-dimensional oscillator systems. Sov Phys Uspekhy 1972;14:549.
54. Rechester AB, Rosenbluth MN. Electron heat transport in a tokamak with destroyed magnetic surfaces. Phys Rev Lett 1978;40:38.
55. Bakunin OG. Correlation and percolation properties of turbulent diffusion. Phys Uspekhi 2003;46:733.
56. Bunde A, Gouet JF. On scaling relations in growth models for percolation clusters and diffusion fronts. J Phys A: Math Gen 1985;18:L285.
57. Saleur H, Duplantier B. Exact determination of the percolation hull exponent in two dimensions. Phys Rev Lett 1987;58:2325.
58. Sapoval B, Rosso B, Gouyet J. On scaling relation in growth models for percolation clusters. J Phys Lett 1985;46:149.
59. Levinshtein ME, Shklovsky BI, Shur MS, Efros AL. On the relation between critical indices and percolation theory. JETP 1976;42:112.
60. Trugman SA. Localization, percolation, and the quantum Hall effect. Phys Rev B 1983;27:7539.
61. Osipenko MV, Pogutse OP, Chudin NV. Plasma diffusion in an array of vortices. Sov J Plasma Phys 1987;13:550.
62. Rosenbluth MN, Berk HL, Doxoas I, Horton W. Effective diffusion in laminar convective flows. Phys Fluids 1987;30:2636.
63. Zeldovich YB. Percolation properties of 2-dimensional random steady magnetic field. JETP Lett 1983;38:57.
64. Isichenko MB, Kalda YL, Tatarinova EV, Telkovskaya OV, Yankov W. Diffusion in vortex flows. Sov Phys JETP 1989;69:517.
65. Gruzinov AV, Isichenko MB, Kalda TL. Two-dimensional turbulent diffusion. Sov Phys JETP 1990;70:263.
66. Zel'dovich YB. Exact solution of the problem of diffusion in a periodic velocity field and turbulent diffusion. Sov Phys Dokl 1982;27:797.
67. Isichenko MB. Effective plasma heat conductivity in "braded" magnetic field - 1. Quasi-linear limit. Plasma Phys Control Fusion 1991;33:795.
68. Isichenko MB. Effective plasma heat conductivity in "braded" magnetic field - II. Percolation limit. Plasma Phys Control Fusion 1991;33:809.
69. Ottaviani M. Test particle transport in a plasma with electrostatic turbulence. Europhys Lett 1992;20:111.
70. Reuss JD, Vlad M, Misguich JH. Percolation scaling for transport in turbulent plasmas. Phys Rev E 1996;54:1857.
71. Zimbardo G, Veltri P, Pommois P. Anomalous, quasilinear, and percolative regimes for magnetic-field-line transport in axially symmetric turbulence. Phys Rev E 2000;61:1940.
72. Yushmanov PN. Neoclassical diffusion in a turbulent plasma. Comment Plasma Phys Control Fusion 1992;14:313.
73. Isichenko MB, Kalda J. Statistical topography. I. Fractal dimension of coastlines and number-area rule for islands. J Nonlinear Sci 1991;1:255.
74. Isichenko MB, Kalda J. Statistical topography II. Two-dimensional transport of a passive scalar. J Nonlinear Sci 1991;1:375.
75. Mitsugu M, Ouchi S, Honda K. On the fractal structure and statistics of contour lines on a self-affine surface. J Phys Sos Jpn 1991;60:2109.
76. Isogami S, Matsushita M. Structural and statistical properties of self-avoiding fractional Brownian motion. J Phys Sos Jpn 1992;61:1445.
77. Kondev J, Henley CL. Geometrical exponents of contour loops on random Gaussian surfaces. Phys Rev Lett 1991;74:4580.
78. Kondev J, Henley CL, Salinas DG. Nonlinear measures for characterizing rough surface morphologies. Phys Rev E 2000;61:104.
79. Kondev J. Critical geometry of two-dimensional passive scalar turbulence. Phys Rev Lett 2001;86:5890.
80. Kalda J. Gradient-limited surfaces: formation of geological landscapes. Phys Rev Lett 2003;90:118501-1.
81. Kalda J. Description of random Gaussian surfaces by a four-vertex model. Phys Rev E 2001;64:020101(R).
82. Bakunin OG, Schep TJ. Multiscale percolation and scaling laws for anisotropic turbulent diffusion. Phys Lett A 2004;322:105.
83. Koch DL, Brady JF. Anomalous diffusion due to long-range velocity fluctuations in the absence of a mean flow. Phys Fluids A 1989;1:47.
84. Dreizin YA, Dykhne AM. Anomalous conductivity of inhomogeneous media in a strong magnetic field. Sov Phys JETP 1973;36:127.
85. Bakunin OG. Diffusion equations and turbulent transport. Plasma Phys Rep 2003;29:995.
86. Bakunin OG. Quasi-diffusion and correlations in models of anomalous transport. Physica A 2004;337:27.
87. Vlad M, Spineanu F, Misguich JH, Balescu R. Diffusion with intrinsic trapping in two-dimensional incompressible stochastic velocity fields. Phys Rev E 1998;58:7359.
88. Vlad M, Spineanu F, Misguich JH, Balescu R. Magnetic line trapping and effective transport in stochastic magnetic fields. Phys Rev E 2002;67:026406.