Chaotic advection in the ocean

Physics-Uspekhi

Volumn 49, Issue 11, 2006, Pages 1151-1178

  Koshel, K V ^a   Prants, S V ^a  

^a IL ICHEV PACIFIC OCEANOLOGICAL INSTITUTE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

ADVECTION; CHAOTIC SYSTEMS; DYNAMICAL SYSTEMS; FRACTALS; GEOPHYSICS; HYDRODYNAMICS; KINEMATICS; OCEAN CURRENTS;

BAROCLINIC OCEANS; BAROTROPIC OCEANS; CHAOTIC ADVECTION; LAGRANGIAN TRANSPORT;

OCEANOGRAPHY;

EID: 33947653661     PISSN: 10637869     EISSN: None     Source Type: Journal    
DOI: 10.1070/PU2006v049n11ABEH006066     Document Type: Article

References (154)

1. Dijkstra H A Nonlinear Physical Oceanography (Atmospheric and Oceanographie Sci. Library, Vol. 22) (Dordrecht: Kluwer, 2000)
2. Ottino J M The Kinematics of Mixing: Stretching, Chaos, and Transport (Cambridge: Cambridge Univ. Press, 1989)
3. Wiggins S Annu. Rev. Fluid Mech. 37 295 (2005)
4. Sarkisyan A S, Akulichev V A (Eds) Izbrannye Trudy Professora V.F. Kozlova (Selected Papers of Professor V.F. Kozlov) (Izhevsk: Institut Komp'yuternykh Issledovanii, 2006)
5. Dutkiewicz S, Griffa A, Olson D B J. Geophys. Res. 98 16487 (1993)
6. Lichtenberg A J, Lieberman M A Regular and Stochastic Motion (New York: Springer-Verlag, 1983) [Translated into Russian (Moscow: Mir, 1984)]
7. Zaslavsky G M, Sagdeev R Z Vvedenie v Nelineinuyu Fiziku: Ot Mayatnika do Turbulentnosti i Khaosa (Introduction to Nonlinear Physics: from a Pendulum to Turbulence and Chaos) (Moscow: Nauka, 1988);
8. 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)
9. Zaslavsky G M Physics of Chaos in Hamiltonian Systems (River Edge, NJ: Imperial College Press, 1998) [Translated into Russian (Moscow: Institut Komp'yuternykh Issledovanii, 2004)]
10. Arnold V I, Kozlov V V, Neishtadt A I Matematicheskie Aspekty Klassicheskoi i Nebesnoi Mekhaniki (Mathematical Aspects of Classical and Celestial Mechanics) (Itogi Nauki i Tekhniki. Sovremennye Problemy Matematiki. Fundamental'nye Napravleniya, Vol. 3, Ed. R V Gamkrelidze) (Moscow: VINITI, 1985) [Translated into English (Berlin: Springer, 1993)]
11. Aref H J. Fluid Mech. 143 1 (1984)
12. Aref H Phys. Fluids 14 1315 (2002)
13. Arnold V I C.R. Hebd. Seances Acad. Sci. 261 17 (1965)
14. Hénon M C.R. Hebd. Seances Acad. Sci. 262 312 (1966)
15. Eckart C J. Mar. Res. 7 265 (1948)
16. Welander P Tellus 7 141 (1955)
17. Lamb H Hydrodynamics 6th ed. (New York: Dover Publ., 1945) [Translated into Russian (Moscow - Leningrad: OGIZ, 1947)]
18. Poincaré H C.R. Acad. Sci. Paris 123 1224 (1896);
19. Izbrannye Trudy (Selected Papers) Vol. 1,2 (Moscow: Nauka, 1971)
20. Kozlov V V Simmetrii, Topologiya i Rezonansy v Gamil'tonovoi Mekhanike (Symmetry, Topology, and Resonances in Hamiltonian Mechanics) (Izhevsk: Izd. Udm. Gos. Univ., 1995)
21. Mel'nikov V K Tr. Mosk. Mat. Obschestva 12 3 (1963)
22. [Trans. Moscow Math. Soc. 12 1 (1963)]
23. Rom-Kedar V, Leonard A, Wiggins S J. Fluid Mech. 214 347 (1990)
24. MacKay R S, Meiss J D, Percival I C Physica D 13 55 (1984)
25. Budyansky M V, Prants S V Pis'ma Zh. Tekh. Fiz. 27 (12) 51 (2001)
26. [Tech. Phys. Lett. 27 508 (2001)]
27. Budyansky M V, Uleysky M Yu, Prants S V Zh. Eksp. Teor. Fiz. 126 1167 (2004)
28. [JETP 99 1018 (2004)]
29. Budyansky M V, Uleysky M Yu, Prants S V Dokl. Ross. Akad. Nauk 386 686 (2002)
30. [Dokl. Earth Sci. 387 929 (2002)]
31. Budyansky M V, Prants S V, in Nelineinye Dinamicheskie Protsessy (k 80-letiyu so Dnya Rozhdeniya Uno Kopvillema) (Nonlinear Dynamical Processes (to the 80th Anniversary of Uno Kopvillem)) (Ed. S V Prants) (Vladivostok: Dal'nauka, 2004) p. 63
32. Budyansky M, Uleysky M, Prants S Physica D 195 369 (2004)
33. Budyansky M V, Uleysky M Yu, Prants S V, in Proc. Fifth EUROMECH Nonlinear Dynamics Conf. (Ed. D H van Campen et al.) (Eindhoven: Eindhoven Univ. of Technology, 2005) p. 1489
34. Mitchell K A et al. Chaos 13 880 (2003)
35. Zhurbas V M, Oh I S, Pyzhevich M L Okeanologiya 43 660 (2003)
36. [Oceanol. 43 622 (2003)]
37. Sainz-Trápaga S, Sugimoto T J. Oceanogr. 56 79 (2000)
38. Bower A S, Lozier MS J. Phys. Oceanogr. 24 1399 (1994)
39. Bower A S, Rossby T J. Phys. Oceanogr. 19 1177 (1989)
40. Osborne A R et al. Tellus 41A 416 (1989)
41. Osborne A R, Caponio R Phys. Rev. Lett. 64 1733 (1990)
42. Brown M G, Smith K B J. Phys. Oceanogr. 20 139 (1990)
43. Meyers S D, Magnan J F, O'Brien J J Nonlinear Proc. Geophys. 1 (1) 45 (1994)
44. Özgökmen T M et al. J. Phys. Oceanogr. 31 2691 (2001)
45. Assireu A T et al. Physica D 168-169 397 (2002)
46. Bower A S J. Phys. Oceanogr. 21 173 (1991)
47. Samelson R M J. Phys. Oceanogr. 22 431 (1992)
48. Uleysky M Yu, Budyansky M V, Prants S V Nelineinaya Dinamika 2 (2) 165 (2006)
49. Meyers S D J. Phys. Oceanogr. 24 1641 (1994)
50. Duan J, Wiggins S J. Phys. Oceanogr. 26 1176 (1996)
51. Dutkiewicz S, Paldor N J. Phys. Oceanogr. 24 2418 (1994)
52. Yuan G-C, Pratt L J, Jones C K R T J. Phys. Oceanogr. 34 1991 (2004)
53. Yang H, Liu Z Geophys. Res. Lett. 21 545 (1994)
54. Yang H J. Phys. Oceanogr. 26 115 (1996)
55. Poje A C, Haller G J. Phys. Oceanogr. 29 1649 (1999)
56. Yang H, Liu Z J. Phys. Oceanogr. 27 1258 (1997)
57. Poplvani L M, Wisdom J Phys. Fluids A 2 123 (1990)
58. Dahleh M D Phys. Fluids A 4 1979 (1992)
59. Kozlov V F, Gurulev A Yu Meteorol. Gidrolog. (6) 70 (1994)
60. [Meteorol. Hydrol. (6) 41 (1994)]
61. Kozlov V F Izv. Ross. Akad. Nauk Ser. Fiz. Atm. Okeana 31 245 (1995)
62. [Izv. Atm. Ocean. Phys. 31 229 (1995)]
63. Pedlosky J Geophysical Fluid Dynamics 2nd ed. (New York: Springer-Verlag, 1987)
64. Tikhonov A N, Samarskii A A Uravneniya Matematicheskoi Fiziki (Equations of Mathematical Physics) (Moscow: Nauka, 1997) [Translated into English (New York: Dover Publ., 1990)]
65. Rhines P B, Young W R J. Fluid Mech. 122 347 (1982)
66. Kozlov V F, Gurulev A Yu Izv. Ross. Akad. Nauk Ser. Fiz. Atm. Okeana 34 395 (1998)
67. [Izv. Atm. Ocean. Phys. 34 353 (1998)]
68. Kozlov V F, Makarov V G Okeanologiya 35 658 (1995)
69. [Oceanol. 35 601 (1995)]
70. Kozlov V F, Makarov V G Okeanologiya 36 493 (1996)
71. [Oceanol. 36 453 (1996)]
72. Kozlov V F, Makarov V G Okeanologiya 38 505 (1998)
73. [Oceanol. 38 456 (1998)]
74. Kozlov V F, Koshel' K V Izv. Ross. Akad. Nauk Ser. Fiz. Atm. Okeana 35 137 (1999)
75. [Izv. Atm. Ocean. Phys. 35 123 (1999)]
76. Liu Z, Yang H J. Phys. Oceanogr. 24 1768 (1994)
77. Berloff P S, Meacham S P J. Mar. Res. 55 407 (1997)
78. Meacham S P, Berloff P S J. Mar. Res. 55 523 (1997)
79. Ipatova V M, Filatov A N Izv. Ross. Akad. Nauk Ser. Fiz. Atm. Okeana 33 443 (1997)
80. [Izv. Atm. Ocean. Phys. 33 407 (1997)]
81. Pierrehumbert R T, Yang H J. Atmos. Sci. 50 2462 (1993)
82. Kozlov V F, Koshel' K V Izv. Ross. Akad. Nauk Ser. Fiz. Atm. Okeana 36 119 (2000)
83. [Izv. Atm. Ocean. Phys. 36 109 (2000)]
84. Jones S W, Aref H Phys. Fluids 31 469 (1988)
85. Pierrehumbert R T Geophys. Astrophys. Fluid Dyn. 58 285 (1991)
86. Yang H Int. J. Bifurc. Chaos 3 1013 (1993)
87. Hogg N G J. Fluid Mech. 58 517 (1973)
88. Kozlov V F Modeli Topograficheskikh Vikhrei v Okeane (Models of Topographical Vortices in the Ocean) (Moscow: Nauka, 1983)
89. Zyryanov V N Topograficheskie Vikhri v Dinamike Morskikh Techenii (Topographical Vortices in Sea-Current Dynamics) (Moscow: Inst. Vod. Problem RAN, 1995)
90. Mullineaux L S, Mills S W Deep-Sea Res. Pt. 744 745 (1997)
91. Mikhaǐlik E V, Khanchuk A I Dokl. Ross. Akad. Nauk 394 234 (2004)
92. [Dokl. Earth Sci. 394 19 (2004)]
93. Goldner D R, Chapman D C Deep-Sea Res. Pt. 144 719 (1997)
94. Deese H E, Pratt L J, Helfrich K R J. Phys. Oceanogr. 32 1870 (2002)
95. Sokolovskiy M A, Zyryanov V N, Davies P A Geophys. Astrophys. Fluid Dyn. 88 1 (1998)
96. Carnevale G F, Kloosterziel R C, van Heijst G J J. Fluid Mech. 233 119 (1991)
97. Milne-Thomson L M Theoretical Hydrodynamics 4th ed. (New York: Macmillan, 1960) [Translated into Russian (Moscow: Mir, 1964)]
98. Gledzer A E Izv. Ross. Akad. Nauk Ser. Fiz. Atm. Okeana 35 838 (1999)
99. [Izv. Atm. Ocean. Phys. 35 759 (1999)]
100. Wiggins S Introduction to Applied Nonlinear Dynamical Systems and Chaos (New York: Springer-Verlag, 1990)
101. Wiggins S Chaotic Transport in Dynamical Systems (New York: Springer-Verlag, 1992)
102. Kozlov V F, Koshel' K V Izv. Ross. Akad. Nauk Ser. Fiz. Atm. Okeana 37 378 (2001)
103. [Izv. Atm. Ocean. Phys. 37 351 (2001)]
104. Shevchenko I I Phys. Lett. A 241 53 (1998)
105. Izrailsky Yu G, Kozlov V F, Koshel' K V Phys. Fluids 16 3173 (2004)
106. Krauskopf B, Osinga H J. Comput. Phys. 146 404 (1998)
107. Kozlov V F, Koshel' K V, Stepanov D V Dal'nevostochyi Mat. Zh. 2 (2) 89 (2001)
108. Kozlov V F, Koshel' K V, Stepanov D V Izv. Ross. Akad. Nauk Ser. Fiz. Atm. Okeana 41 242 (2005)
109. [Izv. Atm. Ocean. Phys. 41 217 (2005)]
110. Koshel' K V, Stepanov D V Regul. Chaotic Dyn. 9 (4) 439 (2004)
111. Borisov A V, Mamaev I S, Sokolovskii M A (Eds) Fundamental'nye i Prikladnye Problemy Teorii Vikhrei (Fundamental and Applied Problems in the Vortex Theory) (Moscow-Izhevsk: Institut Komp'yuternykh Issledovanii, 2003)
112. Rom-Kedar V, Poje A C Phys. Fluids 11 2044 (1999)
113. Zaslavsky G M Stokhastichnost' Dinamicheskikh Sistem (Stochasticity in Dynamical Systems) (Moscow: Nauka, 1984)
114. [Translated into English: Chaos in Dynamic Systems (Chur: Harwood Acad. Publ., 1985)]
115. Koshel K V, Stepanov D V Dokl. Ross. Akad. Nauk 407 542 (2006)
116. [Dokl. Earth Sci. 407 455 (2006)]
117. Shevchenko I I, Mel'nikov A V Pis'ma Zh. Eksp. Teor. Fiz. 77 772 (2003)
118. [JETP Lett. 77 642 (2003)]
119. Koshel' K V, Izrail'skiǐ Yu G, Stepanov D V Dokl. Ross. Akad. Nauk 407 773 (2006)
120. [Dokl. Phys. 51 219 (2006)]
121. Chirikov B V Phys. Rep. 52 263 (1979)
122. Sommeria J, Meyers S D, Swinney H L Nature 337 58 (1989)
123. Behringer R P, Meyers S D, Swinney H L Phys. Fluids A 3 1243 (1991)
124. Solomon T H, Weeks E R, Swinney H L Phys. Rev. Lett. 71 3975 (1993)
125. Shlesinger M F, Zaslavsky G M, Klafter J Nature 363 31 (1993)
126. Weeks E R, Urbach J S, Swinney H L Physica D 97 291 (1996)
127. Hart J E Tellus 37A 286 (1985)
128. Mundt M D, Hart J E, Ohlsen D R J. Fluid Mech. 300 311 (1995)
129. Klein P Fluid Dyn. Res. 5 235 (1990)
130. Danilov S D et al. Chaos 6 297 (1996)
131. Danilov S D et al. Izv. Ross. Akad. Nauk Ser. Fiz. Atm. Okeana 35 810 (1999)
132. [Izv. Atm. Ocean. Phys. 35 733 (1999)]
133. Danilov S D, Dovzhenko V A, Yakyshkin I G Zh. Eksp. Teor. Fh. 118 483 (2000)
134. [JETP 91 423 (2000)]
135. Dolzhanskiǐ F V, Krymov V A, Manin D Yu Usp. Fiz. Nauk 160 (7) 1 (1990)
136. [Sov. Phys. Usp. 33 495 (1990)]
137. Makarov D V et al. Phys. Rev. E 73 066210 (2006)
138. Makarov D V, Uleysky M Yu, Prants S V Chaos 14 79 (2004)
139. Klyatskin V I, Koshel' K V Usp. Fiz. Nauk 170 771 (2000)
140. [Phys. Usp. 43 717 (2000)]
141. Klyatskin V I Diffuziya i Klasterizatsiya Passivnoi Primesi v Sluchainykh Gidrodinamicheskikh Potokakh (Diffusion and Clasterization of Passive Scalars in Random Hydrodynamic Flows) (Moscow: Fizmatgiz, 2005)
142. Tél T et al. Phys. Rep. 413 91 (2005)
143. Kuznetsov L et al. Physica D 191 81 (2004)
144. Knobloch E, Weiss J B Phys. Rev. A 36 1522 (1987)
145. Weiss J B Phys. Fluids A 3 1379 (1991)
146. del-Castillo-Negrete D, Morrison P J Phys. Fluids A 5 948 (1993)
147. Ngan K, Shepherd T G J. Fluid Mech. 334 315 (1997)
148. del-Castillo-Negrete D Phys. Fluids 10 576 (1998)
149. Zaslavsky G M et al. Slabyi Khaos i Kvaziregulyarnye Struktury (Weak Chaos and Quasiregular Patterns) (Moscow: Nauka, 1991) [Translated into English (Cambridge: Cambridge Univ. Press, 1991)]
150. Pierrehumbert R T Phys. Fluids A 3 1250 (1991)
151. Pierce R B, Fairlie T D A J. Geophys. Res. 98 18589 (1993)
152. Bowman K P J. Geophys. Res. 98 23013 (1993)
153. Waugh D W, Plumb R A J. Atmos. Sci. 51 530 (1994)
154. Shuckburgh E, Haynes P Phys. Fluids 15 3342 (2003)