Clustering and diffusion of particles and passive tracer density in random hydrodynamic flows

Physics-Uspekhi

Volumn 46, Issue 7, 2003, Pages 667-688

  Klyatskin, V I ^a,b  

^a OBUKHOV INSTITUTE OF ATMOSPHERIC PHYSICS   (Russian Federation)

^b IL ICHEV PACIFIC OCEANOLOGICAL INSTITUTE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

COHERENT PHENOMENA; CONCENTRATION FIELDS; DIFFUSION APPROXIMATIONS; DIFFUSION EQUATIONS; DIVERGENCE FREE; FINITE TIME; HYDRODYNAMIC FLOWS; INERTIAL PROPERTIES; LAGRANGE DESCRIPTION; PARTICLE DYNAMICS; PARTICLE VELOCITIES; PASSIVE TRACERS; STATISTICAL CLUSTERING; STATISTICAL DESCRIPTIONS; VELOCITY FIELD;

DIFFUSION IN SOLIDS; PARTIAL DIFFERENTIAL EQUATIONS; VELOCITY;

FLUID DYNAMICS;

EID: 0242550573     PISSN: 10637869     EISSN: 14684780     Source Type: Journal    
DOI: 10.1070/PU2003v046n07ABEH001600     Document Type: Article

References (104)

1. Monin A S, Yaglom AMStatisticheskaya Gidromekhanika Pts 1, 2 (Statistical Fluid Mechanics) (Moscow: Nauka, 1965, 1967) [Translated into English (Cambridge, Mass.: MIT Press, 1971, 1975)]
2. Csanady G T Turbulent Diffusion in the Environment (Geophys. And Astrophys. Monographs, Vol. 3) (Dordrecht: D. Reidel Publ. Co., 1973)
3. Lesieur M Turbulence in Fluids: Stochastic and Numerical Modelling (Fluid Mechanics and Its Applications, Vol. 1) 2nd ed. (Dordrecht: Kluwer Acad. Publ., 1990)
4. McComb WD The Physics of Fluid Turbulence (Oxford Engineering Sci. Ser., Vol. 25) (Oxford: Clarendon Press, 1990)
5. Okubo A Diffusion and Ecological Problems: Mathematical Models (Biomathematics, Vol. 10) (Berlin: Springer-Verlag, 1980)
6. Dagan G Annu. Rev. Fluid Mech. 19 183 (1987)
7. Gurbatov S N, Malakhov A N, Saichev A I Nelineǐnye Sluchaǐnye Volny v Sredakh bez Dispersii (Nonlinear Random Waves in Nondispersive Media) [Seriya Sovremennye Problemy Fiziki (Current Problems of Physics Series)] Issue 81 (Moscow: Nauka, 1990)
8. [Translated into English: Nonlinear Random Waves and Turbulence in Nondispersive Media: Waves, Rays, Particles (Manchester: Manchester Univ. Press, 1991)]
9. Shandarin S F, Zeldovich Ya B Rev. Mod. Phys. 61 185 (1989)
10. Batchelor G K J. Fluid Mech. 5 113 (1959)
11. Batchelor G K, Howells I D, Townsend A A J. Fluid Mech. 5 134 (1959)
12. Taylor G I Proc. London Math. Soc. Ser. 2 20 196 (1923);
13. Proc. R. Soc. London Ser. A 164 476 (1938)
14. Roberts P H J. Fluid Mech. 11 257 (1961)
15. Kraichnan R H Phys. Fluids 11 945 (1968);
16. Kraichnan R H Phys. Fluids 13 22 (1970);
17. J. Fluid Mech. 64 737 (1974)
18. Saffman P G Phys. Fluids 12 1786 (1969)
19. Chen H, Chen S, Kraichnan R H Phys. Rev. Lett. 63 2657 (1989)
20. Sinai Ya G, Yakhot V Phys. Rev. Lett. 63 1962 (1989)
21. Avellaneda M, Majda A J Commun. Math. Phys. 131 381 (1990)
22. Gao F Phys. Fluids A: Fluid Dyn. 3 511 (1991)
23. Lipscombe T C, Frenkel AL, ter Haar DJ. Stat. Phys. 63 305 (1991)
24. Careta A et al. J. Stat. Phys. 71 235 (1993)
25. Kimura Y, Kraichnan R H Phys. Fluids A: Fluid Dyn. 5 2264 (1993)
26. Majda A J Phys. Fluids A: Fluid Dyn. 5 1963 (1993);
27. J. Stat. Phys. 75 1153 (1994)
28. Kraichnan R H Phys. Rev. Lett. 72 1016 (1994)
29. Klyatskin V I Usp. Fiz. Nauk 164 531 (1994)
30. [Phys. Usp. 37 501 (1994)]
31. Klyatskin VI, Woyczynski WA Zh. Eksp. Teor. Fiz. 108 1403 (1995)
32. [JETP 81 770 (1995)]
33. Klyatskin V I, Woyczynski WA, Gurarie D, in Stochastic Modelling in Physical Oceanography (Progress in Probability, Vol. 39, Eds RJ Adler, PMüller, B Razovskii) (Boston: Birkhäuser, 1996) p. 221;
34. J. Stat. Phys. 84 797 (1996)
35. Saichev A I, Woyczynski W A, in Stochastic Models in Geosystems (The IMA Volumes in Mathematics and Its Applications, Vol. 85, Eds S A Molchanov, W A Woyczynski) (New York: Springer-Verlag, 1997) p. 359
36. Gurarie D, Klyatskin V, in Two-Dimensional Turbulence in Plasmas & Fluids (AIP Conf. Proc., Vol. 414, Eds R L Dewar, RWGriffiths) (Woodbury, NY: American Institute of Physics, 1997) p. 213
37. Klyatskin V I, Saichev A I Zh. Eksp. Teor. Fiz. 111 1297 (1997)
38. [JETP 84 716 (1997)]
39. Klyatskin V I Izv. Ross. Akad. Nauk Ser. Fiz. Atm. Okeana 36 177 (2000)
40. [Izv., Atmos. Ocean. Phys. 36 162 (2000)]
41. Klyatskin V I Statisticheskoe Opisanie Dinamicheskikh Sistem s Fluktuiruyushchimi Parametrami (Statistical Description of Dynamic Systems with Fluctuating Parameters) (Moscow: Nauka, 1975)
42. Saichev A I Dynamic Systems 1 1 (1993)
43. Gurbatov S N, Saichev A I Chaos 3 333 (1993)
44. Klyatskin V I, Gurarie D Usp. Fiz. Nauk 169 171 (1999)
45. [Phys. Usp. 42 165 (1999)]
46. Isichenko MB Rev. Mod. Phys. 64 961 (1992)
47. Klyatskin V I Stokhasticheskie Uravneniya Glazami Fizika. Osnovnye Polozheniya, Tochnye Rezul'taty i Asimptoticheskie Priblizheniya (Stochastic Equations in the Physicist's Eyes: Fundamentals, Exact Results, and Asymptotic Approximations) (Moscow: Fizmatlit, 2001);
48. Dinamika Stokhasticheskikh Sistem. Kurs Lektsiǐ (Dynamics of Stochastic Systems. A Course of Lectures) (Moscow: Fizmatlit, 2002)
49. Nicolis G, Prigogine I Exploring Complexity: an Introduction (New York: W.H. Freeman, 1989)
50. Stokes G G Camb. Trans. 9 8 (1851)
51. Lamb H Hydrodynamics (Cambridge: Univ. Press, 1930) [Translated into Russian (Moscow: Gostekhizdat, 1947)]
52. Landau L D, Lifshitz E M Gidrodinamika (Fluid Mechanics) (Moscow: Nauka, 1986) [Translated into English (Oxford: Pergamon Press, 1987)]
53. Ungarish M Hydrodynamics of Suspensions: Fundamentals of Centrifugal and Gravity Separation (Berlin: Springer-Verlag, 1993)
54. Tory E M (Ed.) Sedimentation of Small Particles in a Viscous Fluid (Advances in Fluid Mechanics, Vol. 7) (Southampton, UK: Computational Mechanics Publ., 1996)
55. Maxey MR, Riley J J Phys. Fluids 26 883 (1983)
56. Maxey MR, Corrsin S J. Atmos. Sci. 43 1112 (1986)
57. Maxey M R J. Fluid Mech. 174 441 (1987);
58. Philos. Trans. R. Soc. London Ser. A 333 289 (1990)
59. Wang L-P, Maxey MR J. Fluid Mech. 256 27 (1993)
60. Maxey M R, Chang E J, Wang L-P Exp. Therm. Fluid Sci. 12 417 (1996)
61. Elperin T, Kleeorin N, Rogachevskii I Phys. Rev. E 53 3431 (1996);
62. Phys. Rev. E 58 3113 (1998);
63. Phys. Rev. Lett. 76 224 (1996);
64. Phys. Rev. Lett. 77 5373 (1996);
65. Phys. Rev. Lett. 81 2898 (1998);
66. Atmos. Res. 53 117 (2000)
67. Balkovsky E, Falkovich G, Fouxon A Phys. Rev. Lett. 86 2790 (2001)
68. Klyatskin V I, Elperin T Zh. Eksp. Teor. Fiz. 122 238 (2002)
69. [JETP 95 282 (2002)]
70. Zirbel C L, Çinlar E, in Stochastic Models in Geosystems (The IMA Volumes in Mathematics and Its Applications, Vol. 85, Eds S A Molchanov, W A Woyczynski) (New York: Springer-Verlag, 1997) p. 459
71. Koshel' K V, Aleksandrova O V Izv. Ross. Akad. Nauk Ser. Fiz. Atm. Okeana 35 638 (1999)
72. [Izv., Atmos. Ocean. Phys. 35 578 (1999)]
73. Klyatskin V I, Koshel' K V Usp. Fiz. Nauk 170 771 (2000)
74. [Phys. Usp. 43 717 (2000)]
75. Mesinger F J. Atmos. Sci. 22 479 (1965);
76. Mon. Weather Rev. 99 15 (1971)
77. Mesinger F, Mintz Y, Technical Report No. 4, No. 5 (Los Angeles, CA: Dep. Meteorology, Univ. of California, 1970)
78. Er-El J, Peskin R L J. Atmos. Sci. 38 2264 (1981)
79. Mirabel' A P, Monin A S Izv. Ross. Akad. Nauk Ser. Fiz. Atm. Okeana 19 202 (1983)
80. Ott S, Mann J J. Fluid Mech. 422 207 (2000)
81. Furutsu K J. Res. NBS D 67 303 (1963)
82. Novikov EA Zh. Eksp. Teor. Fiz. 47 919 (1964)
83. [Sov. Phys. JETP 20 1290 (1965)]
84. Klyatskin V I Stokhasticheskie Uravneniya i Volny v Sluchaǐno- Neodnorodnykh Sredakh (Stochastic Equations and Waves in Randomly Inhomogeneous Media) (Moscow: Nauka, 1980);
85. Ondes et Équations Stochastiques dans les milieus Aléatoirement non Homogènes (Besançon - Cedex: Les Éditions de Physique, 1985)
86. Klyatskin V I, Saichev A I Usp. Fiz. Nauk 162 (3) 161 (1992)
87. [Sov. Phys. Usp. 35 231 (1992)]
88. Gurvich A S, Yaglom A MPhys. Fluids 10 (Suppl.) S59 (1967)
89. Dahm WJ A, Buch K A Phys. Fluids A: Fluid Dyn. 1 1290 (1989)
90. Kerstein A R, McMurtry P A Phys. Rev. E 49 474 (1994)
91. Zaslavskiǐ G M, Sagdeev R Z Vvedenie v Nelineǐnuyu Fiziku: Ot Mayatnika do Turbulentnosti i Khaosa (Introduction to Nonlinear Physics: From Pendulum to Turbulence and Chaos) (Moscow: Nauka, 1988);
92. see also Sagdeev R Z, Usikov D A, Zaslavsky G M Nonlinear Physics: from the Pendulum to Turbulence and Chaos (Chur: Harwood Acad. Publ., 1988)
93. Lichtenberg A J, Lieberman M A Regular and Stochastic Motion (Applied Mathematical Sciences, Vol. 38) (New York: Springer-Verlag, 1983) [Translated into Russian (Moscow: Mir, 1984)]
94. Klyatskin V I, Yakushkin I G Zh. Eksp. Teor. Fiz. 118 849 (2000)
95. [JETP 91 736 (2000)]
96. Weichman P B, Glazman R E Phys. Rev. Lett. 83 5011 (1999);
97. J. Fluid Mech. 420 147 (2000);
98. J. Fluid Mech. 453 263 (2002)
99. Herterich K, Hasselmann R J. Phys. Oceanogr. 12 704 (1982)
100. Sanderson B G, Okubo A J. Geophys. Res. 93 3570 (1988)
101. Walterscheid R L, Hocking WK J. Atmos. Sci. 48 2213 (1991)
102. Klyatskin V I, Elperin T Izv. Ross. Akad. Nauk Ser. Fiz. Atm. Okeana 38 817 (2002)
103. [Izv., Atmos. Ocean. Phys. 38 725 (2002)]
104. Uhlenbeck G E Usp. Fiz. Nauk 103 275 (1971)