Multifractal cascade dynamics and turbulent intermittency

Fractals

Volumn 5, Issue 3, 1997, Pages 427-471

  Schertzer, D ^a,d   Lovejoy, S ^b   Schmitt, F ^c   Chigirinskaya, Y ^a   Marsan, D ^a  

^a SORBONNE UNIVERSITÉ   (France)

^b MCGILL UNIVERSITY   (Canada)

^c ROYAL METEOROLOGICAL INSTITUTE OF BELGIUM   (Belgium)

^d LABORATOIRE DE MÉTÉOROLOGIE DYNAMIQUE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001371711     PISSN: 0218348X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218348X97000371     Document Type: Article

References (136)

1. L. F. Richardson, Weather Prediction by Numerical Processes (Cambridge University Press, Cambridge, 1926).
2. L. F. Richardson, Proc. Roy. Soc. A214, 1 (1926).
3. A. N. Kolmogorov, Dokl. Acad. Sci. USSR 30, 299 (1941).
4. A. M. Obukhov, Dokl. Akad. Nauk. SSSR 32, 22 (1941).
5. M. D. Milliontchikov, Dokl. Akad. Nauk. SSSR, 32, 611 (1941).
6. R. H. Kraichnan, in Second Symposium on Naval Hydrodynamics (Office of Naval Research, Washington, 1958).
7. R. H. Kraichnan, J. Fluid Mech. 5, 82 (1959).
8. D. C. Leslie, Developments in the theory of turbulence (Clarendon Press, Oxford, 1973).
9. M. Lesieur, Turbulence in Fluids (Kluwer, Dordrecht, 1990).
10. D. Forster, D. R. Nelson and M. J. Stephen, Phys. Rev. A16, 732 (1977).
11. J. R. Herring, D. Schertzer, J. P. Chollet, M. Larchevêque, M. Lesieur and G. R. Newman, J. Fluid Mech. 124, 411 (1982).
12. L. Prandtl, Phys. Zs. 11, 1072 (1910).
13. L. D. Landau and E. M. Lifshitz, Fluids Mechanics (Pergamon Press, Oxford, 1987).
14. G. K. Batchelor and A. A. Townsend, Proc. Roy. Soc. A199, 238 (1949).
15. U. Frisch, M. Lesieur and D. Schertzer, J. Fluid Mech. 111, 127 (1979).
16. U. Frisch, The Legacy of A. N. Kolmogorov (Cambridge University Press, 1995).
17. A. N. Kolmogorov, J. Fluid Mech. 83, 349 (1962).
18. A. Obukhov, J. Fluid. Mech. 13, 77 (1962).
19. A. M. Yaglom, Sov. Phys. Dokl. 2, 26 (1966).
20. E. N. Lorenz, J. Atm. Sci. 20, 130 (1963).
21. M. Feigenbaum, Phys. Rev. A16, 732 (1975).
22. P. Grassberger and I. Procaccia, Phys. Rev. Lett. 50, 346 (1983).
23. D. Schertzer and S. Lovejoy, J. Geoph. Res. 92, 9693 (1987).
24. D. Schertzer, S. Lovejoy and F. Schmitt, in Smallscale structures in 3D hydro and MHD turbulence, eds. M. Meneguzzi et al. (Springer-Verlag, Berlin, 1995).
25. D. Schertzer and S. Lovejoy, J. Appl. Meteor. 36(9), 1296 (1997).
26. S. Lovejoy and D. Schertzer, J. Geophys. Res. 95, 2021 (1990).
27. F. Schmitt, D. Lavallée, D. Schertzer and S. Lovejoy, Phys. Rev. Letters 68, 305 (1992).
28. S. Lovejoy, D. Schertzer, in Fractals in Geoscience and Remote Sensing, eds. G. Wilkinson, I. Kanelllopoulous and J. Megier (Office for Official Publications of the European Communities, Luxembourg, 1995).
29. Z. She and E. Leveque, Phys. Rev. Letters 72, 336 (1994).
30. Y. Chigirinskaya and D. Schertzer, in Stochastic Models in Geophysics, eds. A. Molchanov and W. A. Woyczynski (Springer-Verlag, 1996).
31. E. A. Novikov, Phys. Rev. E50, R3303 (1994).
32. B. Dubrulle, Phys. Rev. Letters 73, 959 (1994).
33. Z. She and E. Waymire, Phys. Rev. Letters 74, 262 (1995).
34. H. Fan, C. R. Acad. Sci. Paris 1308, 151 (1989).
35. P. Brax and R. Pechanski, Phys. Lett. B, 225 (1991).
36. S. Kida J. Phys. Soc. of Japan 60, 5 (1991).
37. M. Feigenbaum, Statistical Physics 46, 919 (1987).
38. T. Tel, Z. Naturforsch. 43, 1154 (1988).
39. H. G. Schuster, Deterministic Chaos: An Introduction (VCH, New York, 1988).
40. D. Schertzer and S. Lovejoy, in Fractals, Physical origins and properties, ed. Pietronero (Plenum Press, London, 1989).
41. D. Schertzer and S. Lovejoy, Phys. Rep. (in press).
42. E. A. Novikov and R. Stewart, Izv. Akad. Nauk. SSSR Ser. Geofiz 3, 408 (1964).
43. B. Mandelbrot, J. Fluid Mech. 62, 331 (1974).
44. U. Frisch, P. L. Sulem and M. Nelkin, J. Fluid Mech. 87, 719 (1978).
45. D. Schertzer and S. Lovejoy, in Turbulence and Chaotic Phenomena in fluids, ed. T. Tatsumi (North-Holland, 1984).
46. R. Benzi, G. Paladin, G. Parisi and A. Vulpiani, J. Phys. A17, 3521 (1984).
47. C. Meneveau and K. R. Sreenivasan, Phys. Rev. Lett. 59, 1424 (1987).
48. S. I. Vainshtein, K. R. Sreenivasan, R. T. Pierrehumbert, V. Kashyap and A. Juneja, Phys. Rev. E50, 1823 (1994).
49. J. Wilson, D. Schertzer and S. Lovejoy Nonlinear Variability in Geophysics: Scaling and Fractals, eds. D. Schertzer and S. Lovejoy (Kluwer, Dordrecht, 1991).
50. D. Schertzer and S. Lovejoy, Phys. Chem. Hyd. J. 6, 623 (1985).
51. S. Pecknold, S. Lovejoy, D. Schertzer, C. Hooge and J. F. Malouin, in Cellular Automata: Prospects in Astronomy and Astrophysics, eds. J. M. Perdang and A. Lejeune (World Scientific, Singapore, 1993).
52. S. Pecknold, S. Lovejoy and D. Schertzer, in Stochastic Models in Geosystems, eds. S. S Molchan and W. A. Woyczynski (Springer-Verlag, Berlin, 1996).
53. P. Brenier, D. Schertzer and S. Lovejoy, Annales Geophysicae Sup. 8, 320 (1991).
54. D. Marsan, D. Schertzer and S. Lovejoy, J. Geoph. Res. 101, 26333 (1996).
55. D. Schertzer and S. Lovejoy, in Space-Time Variability and Interdependence for Various Hydrological Processes, ed. R. Feddes (Cambridge University Press, Cambridge, 1995).
56. th Ed. (Cambridge University Press, Cambridge, 1963).
57. V. I. Arnold, Ann. Inst. Fourier (Grenoble) 16, 319 (1966).
58. A. M. Obukhov, Fluid Dynam. Trans. 5, 193 (1971).
59. A. M. Obukhov and E. V. Dolzhansky, Geoph. Fluid. Dyn. 6, 195 (1975).
60. E. B. Gledzer, Izv. Acad. Nauk USSR Ser. MFG 1, (1980).
61. E. B. Gledzer, E. V. Dolzhansky and A. M. Obukhov, Systems of Fluid Mechanical Type and Their Application (Nauka, Moscow, 1981), (in Russian).
62. Y. Oono, Theor. Phys. Suppl. 99, 165 (1989).
63. B. Mandelbrot, in Turbulence and Stochastic Processes, eds. J. C. R. Hunt et al. (The Royal Society, London, 1991).
64. G. Parisi and U. Frisch, in Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics, eds. M. Ghil, R. Benzi and G. Parisi (North-Holland, 1985).
65. D. Schertzer and S. Lovejoy, Physica A185, 187 (1992).
66. T. C. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia and B. Shraiman, Phys. Rev. A33, 1141 (1986).
67. A. Obukhov, Izv. Akad. Nauk SSSR Geogr. I Jeofiz. 13, 55 (1949).
68. S. Corrsin, J. Appl. Phys. 22, 469 (1951).
69. A. Juneja, D. Lathrop, K. Seenivasan and G. Solovitzky, PRE 49, 5179 (1994).
70. R. Benzi, L. Biferale, A. Crisanti, G. Paladin, M. Vergassola and A. Vulpiani, Physica D65, 352 (1993).
71. A. Marshak, A. Davis, R. Cahalan and W. Wiscombe, PRE 49, 55 (1994).
72. R. Benzi, S. Ciliberto, R. Tripiccione, C. Baudet, F. Massaioli and S. Succi, Phys. Rev. E48, R29 (1993).
73. A. Grossmann and J. Morlet, S.I.A.M. J. Math. Anal. 15, 723 (1984).
74. I. Daubechies, A. Grossmann and Y. Meyer, J. Math. Phys. 27, 1271 (1986).
75. D. Schertzer, S. Lovejoy and D. Lavallée, in Cellular Automata: Prospects in Astronomy and Astrophysics, eds. J. M. Perdang and A. Lejeune (World Scientific, Singapore, 1993).
76. S. Lovejoy, D. Schertzer, P. Silas, Y. Tessier and D. Lavallée, Anna. Geophys. 11, 119 (1993).
77. Y. Chigirinskaya, D. Schertzer, S. Lovejoy, A. Lazarev and A. Ordanovich, Nonlinear Processes in Geophysics 1, 105 (1994).
78. A. Lazarev, D. Schertzer, S. Lovejoy, and Y. Chigirinskaya, Nonlinear Processes in Geophysics 1, 115 (1994).
79. S. Lovejoy, D. Schertzer and A. A. Tsonis, Science 235, 1036 (1987).
80. R. Benzi, S. Ciliberto, C. Baudet, G. R. Chavarria and R. Tripiccione, Europhys. Lett. 24, 275 (1993).
81. R. Benzi, S. Ciliberto, C. Baudet and G. R. Chavarria, Physica D80, 385 (1995).
82. A. N. Kolmogorov, Dokl. Akad. Nuk. SSSR 32, 16 (1941); reprinted in Proc. R. Soc. Lond. A434, 15 (1991).
83. A. N. Kolmogorov, Dokl. Akad. Nuk. SSSR 32, 16 (1941); reprinted in Proc. R. Soc. Lond. A434, 15 (1991).
84. F. Schmitt, D. Schertzer, S. Lovejoy, and Y. Brunet, in Proceedings of the CFIC Conference, ed. M. Giona (World Scientific, Singapore, in press).
85. R. Benzi, L. Biferale, S. Cliberto, M. Sruglia and R. Tripiccione, Physica D96, 162 (1996).
86. V. Carbone, R. Bruno and P. Veltri, Nonl. Proc. Geoph. in press.
87. B. Mandelbrot, in Fractals in the Natural Sciences, eds. M. Fleischman et al. (Princeton University Press, Princeton, 1989).
88. V. G. Gupta and E. C. Waymire, J. Appl. Meteor. 32, 251 (1993).
89. D. Schertzer, S. Lovejoy, D. Lavallée and F. Schmitt, in Nonlinear Dynamics of Structures, eds. R. Z. Sagdeev, U. Frisch, A. S. Moiseev and A. Erokhin (World Scientific, Singapore, 1991).
90. E. Levich and E. Tzvetkov, Phys. Rep. 128, 1 (1985).
91. A. Bialas and R. Peschanski, Nucl. Phys. B273, 703 (1986).
92. R. Grauer, J. Krug and C. Marliani, Phys. Letters A195, 335 (1994).
93. H. Politano and A. Pouquet, Phys. Rev. E52, 636 (1995).
94. E. A. Novikov, Appl. Math. Mech. 35, 231 (1971).
95. U. Frisch, in Turbulence and Stochastic Processes, eds. J. C. R. Hunt et al. (The Royal Society, London, 1991).
96. D. Schertzer and S. Lovejoy, Fractals in the Natural and Applied Sciences, ed. M. M. Novak (North Holland, 1994).
97. P. Bak, C. Tang and K. Weiessenfeld, Phys. Rev. Lett. 59, 381 (1987).
98. P. Bak, C. Tang and K. Weiessenfeld, Phys. Rev. A59, 364 (1988).
99. D. Lavallée, Ph.D. thesis, McGill University, Montreal, Canada (1991).
100. D. Lavallee, S. Lovejoy, D. Schertzer and P. Ladoy, Fractals in Geography, eds. De Cola and L. Lam (Prentice Hall, 1993).
101. D. Lavallée, S. Lovejoy, D. Schertzer and F. Schmitt, in Topological Aspects of the Dynamics of Fluids and Plasmas, eds. K. Moffat, M. Tabor, G. Zalslavsky, M. Tabov and P. Comte (Kluwer, Dordrecht, 1992)
102. A. Arneodo et al. Europhys. Lett. 34, 411 (1996).
103. F. Schmitt, D. Schertzer, S. Lovejoy and Y. Brunet, Nonlin. Proc. Geophys. 1, 95 (1994).
104. G. Ruiz-Chavarria, C. Baudet and S. Ciliberto, Europhys. Lett. 32, 413 (1995).
105. F. Schmitt, D. Schertzer, S. Lovejoy and Y. Brunet, Europhys. Lett. 34, 195 (1996).
106. R. Benzi, L. Biferale and G. Parisi, Europhys. Lett. 18, 213 (1992).
107. J. O. Hinze, Turbulence (McGraw-Hill, New York, 1959).
108. G. Ruiz-Chavarria, C. Baudet and S. Ciliberto, Physica D (in press).
109. R. A. Antonia, E. J. Hopfinger, Y. Gagne and F. Anselmet, Phys. Rev. A30, 2704 (1984).
110. F. Schmitt, D. Schertzer and S. Lovejoy, Geoph. Res. Letters 22, 1689 (1995).
111. G. Taylor, Proc. R. Soc. Lond. A164, 476 (1938).
112. S. Lovejoy and D. Schertzer, in Scaling, Fractals and Non-Linear Variability in Geophysics, eds. D. Schertzer and S. Lovejoy (Kluwer, 1991).
113. I. Zawadski, J. Appl. Meteor. 12, 459 (1973).
114. V. Gupta and E. Waymire, J. Geophys. Res. 92, 9657 (1987).
115. R. K. Crane, J. Geophys. R. 95, 2011 (1990).
116. B. W. Atkinson, Mesoscale Atmospheric Circulations (Academic Press, London, 1981).
117. I. Orlanski, Bull. Amer. Met. Soc. 56, 527 (1975).
118. T. M. Over and V. K. Gupta, J. Geophys. Res. 101, 26319 (1996).
119. R. Lima and R. Vilela Mendes, Phys. Rev. E53, 3536 (1996).
120. M. Bunge, Am. Sci. 49, 432 (1961).
121. A. V. Chechkin, D. Schertzer, A. V. Tur and V. V. Yanovsky, Ukr. J. Phys. 40, 434 (1995).
122. D. Marsan, D. Schertzer and S. Lovejoy, Proceedings of the CFIC Conference, ed. M. Giona (World Scientific, ed. M. Giona, in press).
123. D. K. Lilly in Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics, eds. M. Ghil, R. Benzi and G. Parisi (North-Holland, 1985).
124. P. L. Houtekamer, Ph.D. thesis, University of Wageningen, Holland (1992).
125. E. N. Lorenz, Tellus 21, 289 (1969).
126. C. E. Leith and R. H. Kraichnan, J. Atm. Sci. 29, 1041 (1972).
127. O. Métais and M. Lesieur, J. Atm. Sci. 43, 9 (1986).
128. A. Crisanti, M. H. Jensen and A. Vulpiani, Phys. Rev. Letters 70, 166 (1993).
129. A. Crisanti, M. H. Jensen, G. Paladin and A. Vulpiani, J. Phys. A26, 6943 (1993).
130. Y. Chigirinskaya, D. Schertzer and S. Lovejoy, in Proceedings of the CFIC Conference, ed. M. Giona (Springer, in press)
131. S. Grossmann and D. Lohse, Europhys. Lett. 21, 201 (1993).
132. V. D. Zimin, in Nonlinear Dynamics of Structures, eds. R. Z. Sagdeev et al. (World Scientific, Singapore, 1991)
133. F. Schmitt, D. Schertzer, S. Lovejoy and Y. Brunet, Fractals 1, 568 (1993).
134. A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics: Mechanics of Turbulence, Vol. II (MIT Press, Cambridge, 1975).
135. M. E. Cates and J. M. Deutsch, Phys. Rev. A35, 4907 (1987).
136. J. O'Neil and C. Meneveau, Phys. Fluid A5, 158 (1993).