Particles and fields in fluid turbulence

Reviews of Modern Physics

Volumn 73, Issue 4, 2001, Pages 913-975

  Falkovich, G ^a   Gawedzki K ^b   Vergassola, M ^c  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^b UNIVERSITÉ DE LYON   (France)

^c CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035470905     PISSN: 00346861     EISSN: None     Source Type: Journal    
DOI: 10.1103/RevModPhys.73.913     Document Type: Article

References (253)

1. Abrikosov, A., and I. Ryzhkin, 1978, Adv. Phys. 27, 146.
2. Adzhemyan, L. Ts., and N. V. Antonov, 1998, Phys. Rev. E 58, 7381.
3. Adzhemyan, L. Ts., N. V. Antonov, V. A. Barinov, Yu. S. Kabrits, and A. N. Vasil'ev, 2001, Phys. Rev. E 63, 025303(R).
4. Adzhemyan, L. Ts., N. V. Antonov, M. Hnatich, and S. V. Novikov, 2001, Phys. Rev. E 63, 016309.
5. Adzhemyan, L. Ts., N. V. Antonov, and A. N. Vasil'ev, 1989, Sov. Phys. JETP 68, 733.
6. Adzhemyan, L. Ts., N. V. Antonov, and A. N. Vasil'ev, 1998, Phys. Rev. E 58, 1823.
7. Adzhemyan, L. Ts., N. V. Antonov, and A. N. Vasil'ev, 1999, The Field Theoretic Renormalization Group in Fully Developed Turbulence (Gordon and Breach, London).
8. Andersen, K. H., and P. Muratore-Ginanneschi, 1999, Phys. Rev. E 60, 6663.
9. Antonov, N. V., 1999, Phys. Rev. E 60, 6691.
10. Antonov, N. V., 2000, Physica D 144, 370.
11. Antonov, N. V., and J. Honkonen, 2001, Phys. Rev. E 63, 036302.
12. Arad, I., L. Biferale, A. Celani, I. Procaccia, and M. Vergassola, 2001, Phys. Rev. Lett. 87, 164502.
13. Arad, I., L. Biferale, and I. Procaccia, 2000, Phys. Rev. E 61, 2654.
14. Arad, I., B. Dhruva, S. Kurien, V. S. L'vov, I. Procaccia, and K. R. Sreenivasan, 1998, Phys. Rev. Lett. 81, 5330.
15. Arad, I., V. S. L'vov, E. Podivilov, and I. Procaccia, 2000, Phys. Rev. E 62, 4904.
16. Arad, I., V. S. L'vov, and I. Procaccia, 1999, Phys. Rev. E 81, 6753.
17. Arad, I., and I. Procaccia, 2000, arXiv:nlin.CD/0001067.
18. Avellaneda, M., and A. Majda, 1989, Phys. Rev. Lett. 62, 753.
19. Avellaneda, M., R. Ryan, and W. E, 1995, Phys. Fluids 7, 3067.
20. Avellaneda, M., and M. Vergassola, 1995, Phys. Rev. E 52, 3249.
21. Balkovsky, E., M. Chertkov, I. Kolokolov, and V. Lebedev, 1995, JETP Lett. 61, 1012.
22. Balkovsky, E., G. Falkovich, and A. Fouxon, 1999, arXiv:xhaodyn/9912027.
23. Balkovsky, E., G. Falkovich, and A. Fouxon, 2001, Phys. Rev. Lett. 86, 2790.
24. Balkovsky, E., G. Falkovich, I. Kolokolov, and V. Lebedev, 1997, Phys. Rev. Lett. 78, 1452.
25. Balkovsky, E., G. Falkovich, and V. Lebedev, 1997, Phys. Rev. E 55, R4881.
26. Balkovsky, E., G. Falkovich, V. Lebedev, and M. Lysiansky, 1999, Phys. Fluids 11, 2269.
27. Balkovsky, E., G. Falkovich, V. Lebedev, and I. Shapiro, 1995, Phys. Rev. E 52, 4537.
28. Balkovsky, E., and A. Fouxon, 1999, Phys. Rev. E 60, 4164.
29. Balkovsky, E., A. Fouxon, and V. Lebedev, 2000, Phys. Rev. Lett. 84, 4765.
30. Balkovsky, E., and V. Lebedev, 1998, Phys. Rev. E 58, 5776.
31. Batchelor, G. K., 1959, J. Fluid Mech. 5, 113.
32. Batchelor, G. K., 1969, Phys. Fluids Suppl. II 12, 233.
33. Baxendale, P. H., 1986, in Lyapunov Exponents, Bremen 1984, edited by L. Arnold and V. Wihstutz, Lecture Notes in Math. Vol. 1186 (Springer-Verlag, Berlin), p. 322.
34. Bec, J., 2001, Phys. Rev. Lett. 87, 104501.
35. Bec, J., and U. Frisch, 2000, Phys. Rev. E 61, 1395.
36. Bec, J., U. Frisch, and K. Khanin, 2000, J. Fluid Mech. 416, 239.
37. Belinicher, V. I., and V. S. L'vov, 1987, Sov. Phys. JETP 66, 303.
38. Bensoussan, A., J.-L. Lions, and G. Papanicolaou, 1978, Asymptotic Analysis for Periodic Structures (North-Holland, Amsterdam).
39. Benzi, R., L. Biferale, and A. Wirth, 1997, Phys. Rev. Lett. 78, 4926.
40. Bernard, D., 2000, Europhys. Lett. 50, 333.
41. Bernard, D., and M. Bauer, 1999, J. Phys. A 32, 5179.
42. Bernard, D., and K. Gawȩdzki, 1998, J. Phys. A 31, 8735.
43. Bernard, D., K. Gawȩdzki, and A. Kupiainen, 1996, Phys. Rev. E 54, 2564.
44. Bernard, D., K. Gawȩdzki, and A. Kupiainen, 1998, J. Stat. Phys. 90, 519.
45. Biskamp, D., and U. Bremer, 1994, Phys. Rev. Lett. 72, 3819.
46. Boffetta, G., and A. Celani, 2000, Physica A 280, 1.
47. Boffetta, G., A. Celani, A. Crisanti, and A. Vulpiani, 1998, Phys. Rev. E 60, 6734.
48. Boffetta, G., A. Celani, and M. Vergassola, 2000, Phys. Rev. E 61, R29.
49. Boffetta, G., and I. M. Sokolov, 2000, arXiv:nlin.CD/0009047.
50. Bohr, T., M. H. Jensen, G. Paladin, and A. Vulpiani, 1998, Dynamical Systems Approach to Turbulence (Cambridge University Press, Cambridge, England).
51. Boldyrev, S. A., 1997, Phys. Rev. E 55, 6907.
52. Borue, V., 1993, Phys. Rev. Lett. 71, 3967.
53. Borue, V., and V. Yakhot, 1996, Phys. Rev. E 53, R5576.
54. Bouchaud, J.-P., and A. Georges, 1990, Phys. Rep. 195, 127.
55. Bouchaud, J.-P., and M. Mézard, 1996, Phys. Rev. E 54, 5116.
56. Bowman, J. C., B. A. Shadwick, and P. J. Morrison, 1999, Phys. Rev. Lett. 83, 5491.
57. Brenier, Y., 1989, J. Am. Math. Soc. 2, 225.
58. Burgers, J. M., 1974, The Non-Linear Diffusion Equation (Reidel, Dordrecht).
59. Celani, A., A. Lanotte, and A. Mazzino, 1999, Phys. Rev. E 60, R1138.
60. Celani, A., A. Lanotte, A. Mazzino, and M. Vergassola, 2000, Phys. Rev. Lett. 84, 2385.
61. Celani, A., A. Lanotte, A. Mazzino, and M. Vergassola, 2001, Phys. Fluids 17, 287.
62. Celani, A., and A. Mazzino, 2000, private communication.
63. Celani, A., and M. Vergassola, 2001, Phys. Rev. Lett. 86, 424.
64. Chaves, M., G. Eyink, U. Frisch, and M. Vergassola, 2001, Phys. Rev. Lett. 86, 2305.
65. Chekhlov, A., and V. Yakhot, 1995, Phys. Rev. E 52, 5681.
66. Chekhlov, A., and V. Yakhot, 1996, Phys. Rev. Lett. 77, 3118.
67. Chen, S., and R. H. Kraichnan, 1998, Phys. Fluids 10, 2867.
68. Chertkov, M., 1997, Phys. Rev. E 55, 2722.
69. Chertkov, M., 1998, Phys. Fluids 10, 3017.
70. Chertkov, M., 1999, Phys. Fluids 11, 2257.
71. Chertkov, M., 2000, Phys. Rev. Lett. 84, 4761.
72. Chertkov, M., and G. Falkovich, 1996, Phys. Rev. Lett. 76, 2706.
73. Chertkov, M., G. Falkovich, and I. Kolokolov, 1998, Phys. Rev. Lett. 79, 2121.
74. Chertkov, M., G. Falkovich, I. Kolokolov, and V. Lebedev, 1995a, Phys. Rev. E 51, 5609.
75. Chertkov, M., G. Falkovich, I. Kolokolov, and V. Lebedev, 1995b, Phys. Rev. E 52, 4924.
76. Chertkov, M., G. Falkovich, I. Kolokolov, and M. Vergassola, 1999, Phys. Rev. Lett. 83, 4065.
77. Chertkov, M., I. Kolokolov, and M. Vergassola, 1997, Phys. Rev. E 56, 5483.
78. Chertkov, M., I. Kolokolov, and M. Vergassola, 1998, Phys. Rev. Lett. 80, 512.
79. Chertkov, M., A. Pumir, and B. Shraiman, 1999, Phys. Fluids 11, 2394.
80. Childress, S., and A. Gilbert, 1995, Stretch, Twist, Fold: The Fast Dynamo (Springer, Berlin).
81. Ciliberto, S., and C. Laroche, 1998, J. Phys. (Paris) 8, 215.
82. Cocke, W. J., 1969, Phys. Fluids 12, 2488.
83. Coleman, S., 1977, in New Phenomena in Subnuclear Physics, edited by A. Zichichi (Plenum Press, New York).
84. Corrsin, S., 1951, J. Appl. Phys. 22, 469.
85. Crisanti, A., G. Paladin, and A. Vulpiani, 1993, Products of Random Matrices (Springer, Berlin).
86. Duchon, J., and R. Robert, 2000, Nonlinearity 13, 249.
87. E, W., K. Khanin, A. Mazel, and Ya. G. Sinai, 1997, Phys. Rev. Lett. 78, 1904.
88. E, W., K. Khanin, A. Mazel, and Ya. G. Sinai, 2000, Ann. Math. 151, 877.
89. E, W., and E. Vanden Eijnden, 1999, Phys. Rev. Lett. 83, 2572.
90. E, W., and E. Vanden Eijnden, 2000a, Commun. Pure Appl. Math. 53, 852.
91. E, W., and E. Vanden Eijnden, 2000b, Proc. Natl. Acad. Sci. U.S.A. 97, 8200.
92. Elliott, Jr., F. W., and A. J. Majda, 1996, Phys. Fluids 8, 1052.
93. Ellis, R. S., 1985, Entropy, Large Deviations, and Statistical Mechanics (Springer, Berlin).
94. Eyink, G., 1993, Phys. Lett. A 172, 355.
95. Eyink, G., 1995, Phys. Rev. Lett. 74, 3800.
96. Fairhall, A. L., B. Galanti, V. S. L'vov, and I. Procaccia, 1997, Phys. Rev. Lett. 79, 4166.
97. Falkovich, G., 1994, Phys. Rev. E 49, 2468.
98. Falkovich, G., I. Kolokolov, V. Lebedev, and A. Migdal, 1996, Phys. Rev. E 54, 4896.
99. Falkovich, G., and V. Lebedev, 1994, Phys. Rev. E 50, 3883.
100. Falkovich, G., and V. Lebedev, 1997, Phys. Rev. Lett. 79, 4159.
101. Falkovich, G., V. Lebedev, and V. Kazakov, 1998, Physica A 249, 36.
102. Fannjiang, A., T. Komorowski, and S. Peszat, 2000, Lagrangian dynamics for a passive tracer in a class of Gaussian Markov flows, preprint.
103. Fannjiang, A., and G. Papanicolaou, 1996, Prob. Theory Rel. Fields 105, 279.
104. Feigel'man, M. V., 1980, Sov. Phys. JETP 52, 555.
105. Feller, W., 1950, An Introduction to Probability Theory and its Applications (Wiley, New York).
106. Forster, A., D. Nelson, and M. Stephen, 1977, Phys. Rev. A 16, 732.
107. Frachebourg, L., and Ph. A. Martin, 2000, J. Fluid Mech. 417, 323.
108. Frederikson, P., J. L. Kaplan, E. D. Yorke, and J. A. Yorke, 1983, J. Diff. Eqns. 49, 183.
109. Frisch, U., 1995, Turbulence. The Legacy of A. N. Kolmogorov (Cambridge University Press, Cambridge, England).
110. Frisch, U., and J. Bec, 2000, Burgulence, to appear in Les Houches 2000: New Trends in Turbulence, edited by M. Lesieur (Springer EDP-Sciences).
111. Frisch, U., J. Bec, and B. Villone, 2001, Physica D 152-153, 620.
112. Frisch, U., A. Mazzino, A. Noullez, and M. Vergassola, 1999, Phys. Fluids 11, 2178.
113. Frisch, U., A. Mazzino, and M. Vergassola, 1998, Phys. Rev. Lett. 80, 5532.
114. Fung, J. C. H., and J. C. Vassilicos, 1998, Phys. Rev. E 57, 1677.
115. Furstenberg, H., 1963, Trans. Am. Math. Soc. 108, 377.
116. Furstenberg, H., and H. Kesten, 1960, Ann. Math. Stat. 31, 457.
117. Gallavotti, G., and E. G. D. Cohen, 1995, Phys. Rev. Lett. 74, 2694.
118. Gamba, A., and I. Kolokolov, 1996, J. Stat. Phys. 85, 489.
119. Gamba, A., and I. Kolokolov, 1998, J. Stat. Phys. 94, 759.
120. Gat, O., V. S. L'vov, E. Podivilov, and I. Procaccia, 1997, Phys. Rev. E 55, R3836.
121. Gat, O., V. S. L'vov, and I. Procaccia, 1997, Phys. Rev. E 56, 406.
122. Gat, O., I. Procaccia, and R. Zeitak, 1998, Phys. Rev. Lett. 80, 5536.
123. Gat, O., and R. Zeitak, 1998, Phys. Rev. E 57, 5511.
124. Gawȩdzki, K., 1998, in Advances in Turbulence VII, edited by U. Frisch (Kluwer Academic, Dordrecht), p. 493.
125. Gawȩdzki, K., 1999, arXiv:chao-dyn/9907024.
126. Gawȩdzki, K., and A. Kupiainen, 1995, Phys. Rev. Lett. 75, 3834.
127. Gawȩdzki, K., and A. Kupiainen, 1996, in Low-Dimensional Models in Statistical Physics and Quantum Field Theory, ed-ited by H. Grosse and L. Pittner (Springer, Berlin), p. 71.
128. Gawȩdzki, K., and M. Vergassola, 2000, Physica D 138, 63.
129. Geisel, T., J. Nierwetberg, and A. Zachert, 1985, Phys. Rev. Lett. 54, 616.
130. Gibson, C. H., C. A. Freihe, and S. O. McConnell, 1977, Phys. Fluids Suppl. 20, S156.
131. Girimaji, S., and S. Pope, 1990, J. Fluid Mech. 220, 427.
132. Goldhirsch, I., P.-L. Sulem, and S. Orszag, 1987, Physica D 27, 311.
133. Gotoh, T., 1998, Phys. Rev. E 57, 2984.
134. Gotoh, T., and R. H. Kraichnan, 1998, Phys. Fluids 10, 2859.
135. Groisman, A., and V. Steinberg, 2000, Nature (London) 405, 53.
136. Gruzinov, A., S. Cowley, and R. Sudan, 1996, Phys. Rev. Lett. 77, 4342.
137. Gurarie, V., and A. Migdal, 1996, Phys. Rev. E 54, 4908.
138. Gurbatov, S, N., S. I. Simdyankin, E. Aurell, U. Frisch, and G. Tóth, 1997, J. Fluid Mech. 344, 339.
139. Gutman, D., and E. Balkovsky, 1996, Phys. Rev. E 54, 4435.
140. n, preprint.
141. Hinch, E. J., 1977, Phys. Fluids 20, S22.
142. Holzer, M., and E. D. Siggia, 1994, Phys. Fluids 6, 1820; 7, 1519(E), 1995.
143. Holzer, M., and E. D. Siggia, 1994, Phys. Fluids 6, 1820; 7, 1519(E), 1995.
144. Horvai, P., 2000, private communication.
145. Isichenko, M., 1992, Rev. Mod. Phys. 64, 961.
146. Jayesh, and Z. Warhaft, 1991, Phys. Rev. Lett. 67, 3503.
147. Jullien, M-C., P. Castiglione, and P. Tabeling, 2000, Phys. Rev. Lett. 85, 3636.
148. Jullien, M.-C., J. Paret, and P. Tabeling, 1999, Phys. Rev. Lett. 82, 2872.
149. Kardar, M., G. Parisi, and Y. C. Zhang, 1986, Phys. Rev. Lett. 56, 889.
150. Kazantsev, A., 1968, Sov. Phys. JETP 26, 1031.
151. Kida, S., 1979, J. Fluid Mech. 93, 337.
152. Kiffer, Yu., 1988, Random Perturbations of Dynamical Systems (Birkhäuser, Boston).
153. Kloeden, P. E., and E. Platen, 1992, Numerical Solution of Stochastic Differential Equations (Springer, Berlin).
154. Klyatskin, V., and D. Gurarie, 1999, Sov. Phys. Usp. 169, 171.
155. Kolmogorov, A. N., 1941, C. R. Acad. Sci. URSS 30, 301.
156. Kolokolov, I., 1993, JETP 76, 1099.
157. Kraichnan, R. H., 1967, Phys. Fluids 10, 1417.
158. Kraichnan, R. H., 1968, Phys. Fluids 11, 945.
159. Kraichnan, R. H., 1970, The Padé Approximants in Theoretical Physics (Academic, New York).
160. Kraichnan, R. H., 1971, J. Fluid Mech. 47, 525.
161. Kraichnan, R. H., 1974, J. Fluid Mech. 64, 737.
162. Kraichnan, R. H., 1975, Adv. Math. 16, 305.
163. Kraichnan, R. H., 1994, Phys. Rev. Lett. 72, 1016.
164. Krug, J., and H. Spohn, 1992, in Solids Far from Equilibrium, edited by G. C. Godrèche (Cambridge University Press, Cambridge, England), p. 477.
165. Kunita, H., 1990, Stochastic Flows and Stochastic Differential Equations (Cambridge University Press, Cambridge, England).
166. Landau, L. D., and E. M. Lifshitz, 1959, Fluid Mechanics (Pergamon, London).
167. Lanotte, A., and A. Mazzino, 1999, Phys. Rev. E 60, R3483.
168. La Porta, A., G. A. Voth, A. M. Crawford, J. Alexander, and E. Bodenschatz, 2001, Nature (London) 409, 1017.
169. Legras, B., P. Santangelo, and R. Benzi, 1988, Europhys. Lett. 5, 37.
170. Le Jan, Y., 1985, Z. Wahrscheinlichkeitstheor. Verwandte Geb. 70, 609.
171. Le Jan, Y., and O. Raimond, 1998, C. R. Acad. Sci., Ser. I: Math. 327, 893.
172. Le Jan, Y., and O. Raimond, 1999, arXiv:math.PR/9909147.
173. Le Page, E., 1982, in Probability Measures on Groups, edited by H. Heyer, Lecture Notes in Math. Vol. 928 (Springer-Verlag, Berlin), p. 258.
174. Liapounoff, M. A., 1907, Ann. Fac. Sci. Univ. Toulouse Sci. Math. Sci. Phys. 9.
175. Lifshitz, I. M., S. Gradescul, and L. A. Pastur, 1988, Introduction to the Theory of Disordered Systems (Wiley, New York).
176. Lumley, J. L., 1972, Symp. Math. 9, 315.
177. Lumley, J. L., 1973, J. Polym. Sci., Part D: Macromol. Rev. 7, 263.
178. Majda, A. J., and P. R. Kramer, 1999, Phys. Rep. 314, 237.
179. Matheron, G., and G. de Marsily, 1980, Water Resour. Res. 16, 901.
180. Mazzino, A., and P. Muratore-Ginanneschi, 2001, Phys. Rev. E 63, 015302(R).
181. Mestayer, P. G., 1982, J. Fluid Mech. 125, 475.
182. Moffatt, H. K., 1978, Magnetic Field Generation in Electrically Conducting Fluids (Cambridge University Press, Cambridge, England).
183. Moffatt, H. K., 1986, in Advances in Turbulence, edited by G. Comte-Bellot and J. Mathieu (Springer, Berlin).
184. Molchanov, S., A. Ruzmaikin, and V. Sokolov, 1985, Sov. Phys. Usp. 28, 307.
185. Monin, A. S., 1959, Sov. Phys. Dokl. 4, 271.
186. Monin, A. S., and A. M. Yaglom, 1979, Statistical Fluid Mechanics (MIT, Cambridge).
187. Mordant, N., P. Metz, O. Michel, and J.-F. Pinton, 2001, unpublished.
188. Mydlarski, L., and Z. Warhaft, 1998, J. Fluid Mech. 358, 135.
189. Nam, K., E. Ott, T. M. Antonsen, and P. N. Guzdar, 2000, Phys. Rev. Lett. 84, 5134.
190. Normand, C., Y. Pomeau, and M. G. Velarde, 1977, Rev. Mod. Phys. 49, 581.
191. Obukhov, A. M., 1949, Izv. Akad. Nauk SSSR, Ser. Geogr. Geofiz. 13, 58.
192. Olshanetsky, M. A., and A. M. Perelomov, 1983, Phys. Rep. 94, 313.
193. Onsager, L., 1949, Nuovo Cimento, Suppl. 6, 279.
194. Oseledec, V. I., 1968, Trans. Mosc. Math. Soc. 19, 197.
195. Ottino, J. M., 1989, The Kinematics of Mixing: Stretching, Chaos and Transport (Cambridge University Press, Cambridge, England).
196. Paret, J., M.-C. Jullien, and P. Tabeling, 1999, Phys. Rev. Lett. 83, 3418.
197. Paret, J., and P. Tabeling, 1997, Phys. Rev. Lett. 79, 4162.
198. Paret, J., and P. Tabeling, 1998, Phys. Fluids 10, 3126.
199. Parker, E. N., 1979, Cosmic Magnetic Fields, Their Origin and Activity (Clarendon, Oxford).
200. Polyakov, A. M., 1993, Nucl. Phys. B 396, 367.
201. Polyakov, A. M., 1995, Phys. Rev. E 52, 6183.
202. Pope, S. B., 1994, Annu. Rev. Fluid Mech. 26, 23.
203. Pumir, A., 1994, Phys. Fluids 6, 2118.
204. Pumir, A., 1996, Europhys. Lett. 34, 25.
205. Pumir, A., 1997, Europhys. Lett. 37, 529.
206. Pumir, A., 1998, Phys. Rev. E 57, 2914.
207. Pumir, A., and B. I. Shraiman, 1995, Phys. Rev. Lett. 75, 3114.
208. Pumir, A., and B. I. Shraiman, 2000, private communication.
209. Pumir, A., B. I. Shraiman, and E. D. Siggia, 1997, Phys. Rev. E 55, R1263.
210. Ralston, A., and P. Rabinowitz, 1978, A First Course in Numerical Analysis (McGraw-Hill, New York).
211. Richardson, L. F., 1926, Proc. R. Soc. London, Ser. A 110, 709.
212. Rogachevskii, I., and N. Kleeorin, 1999, Phys. Rev. E 59, 3008.
213. Ruelle, D., 1997, J. Stat. Phys. 86, 935.
214. Rutgers, M. A., 1998, Phys. Rev. Lett. 81, 2244.
215. Saffman, P., 1971, Stud. Appl. Math. 50, 277.
216. Shandarin, S. F., and Ya. B. Zel'dovich, 1989, Rev. Mod. Phys. 61, 185.
217. Shlesinger, M. F., B. West, and J. Klafter, 1987, Phys. Rev. Lett. 58, 1100.
218. Shlesinger, M. F., G. M. Zaslavsky, and J. Klafter, 1993, Nature (London) 363, 31.
219. Shnirelman, A., 1999, Weak solutions with decreasing energy of incompressible Euler equations, IHES/M/99/02 preprint.
220. Shraiman, B. I., and E. D. Siggia, 1994, Phys. Rev. E 49, 2912.
221. Shraiman, B. I., and E. D. Siggia, 1995, C. R. Acad. Sci., Ser. I: Math. 321, 279.
222. Shraiman, B. I., and E. D. Siggia, 1996, Phys. Rev. Lett. 77, 2463.
223. Shraiman, B. I., and E. D. Siggia, 2000, Nature (London) 405, 639.
224. Sinai, Ya., and V. Yakhot, 1989, Phys. Rev. Lett. 63, 1962.
225. Smith, L., and V. Yakhot, 1993, Phys. Rev. Lett. 71, 352.
226. Son, D. T., 1999, Phys. Rev. E 59, 3811.
227. Soward, A. M., 1987, J. Fluid Mech. 180, 267.
228. Sreenivasan, K. R., 1991, Proc. R. Soc. London, Ser. A 434, 165.
229. Sreenivasan, K. R., and R. A. Antonia, 1997, Annu. Rev. Fluid Mech. 29, 435.
230. Stanley, H. E., 1968, Phys. Rev. 176, 718.
231. Stroock, D. W., and S. R. S. Varadhan, 1979, Multidimensional Diffusion Processes (Springer, Berlin).
232. Taylor, G. I., 1921, Proc. London Math. Soc. 20, 196.
233. 't Hooft, G., 1974, Nucl. Phys. B 72, 461.
234. Vergassola, M., 1996, Phys. Rev. E 53, R3021.
235. Vergassola, M., and M. Avellaneda, 1997, Physica D 106, 148.
236. Vergassola, M., B. Dubrulle, U. Frisch, and A. Noullez, 1994, Astron. Astrophys. 289, 325.
237. Vergassola, M., and A. Mazzino, 1997, Phys. Rev. Lett. 79, 1849.
238. Vol'pert, A., 1967, Math. USSR Sb. 2, 225.
239. Voth, G. A., K. Satyanarayan, and E. Bodenschatz, 1998, Phys. Fluids 10, 2268.
240. Warhaft, Z., 2000, Annu. Rev. Fluid Mech. 32, 203.
241. Weiss, J., 1991, Physica D 48, 273.
242. Wiese, K. J., 2000, J. Stat. Phys. 101, 843.
243. Wilson, K., 1969, Phys. Rev. 179, 1499.
244. Woyczyński, W. A., 1998, Burgers-KPZ Turbulence. Göttingen Lectures, Lecture Notes in Mathematics Vol. 1700 (Springer, Berlin).
245. Yaglom, A. M., 1949, Dokl. Akad. Nauk SSSR 69, 743.
246. Yakhot, V., 1997, Phys. Rev. E 55, 329.
247. Yeung, P. K., 1997, Phys. Fluids 9, 2981.
248. Zakharov, V., V. S. L'vov, and G. Falkovich, 1992, Kolmogorov Spectra of Turbulence (Springer, Berlin).
249. Zamolodchikov, A., G. Falkovich, and V. Lebedev, 2000, private communication.
250. Zeman, O., 1990, Phys. Fluids A 2, 178.
251. Zel'dovich, Ya. B., A. Ruzmaikin, S. Molchanov, and V. Sokolov, 1984, J. Fluid Mech. 144, 1.
252. Zel'dovich, Ya. B., A. Ruzmaikin, and D. Sokoloff, 1983, Magnetic Fields in Astrophysics (Gordon and Breach, New York).
253. Zovari, N., and A. Babiano, 1994, Physica D 76, 318.