RSS feeds
РусскийEnglish
Issue 4, 2024
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

2012

 / 

January

←  →

Reviews of topical problems


Ray and wave chaos in underwater acoustic waveguides

 a,  b,  b
a Federal Research Center A.V. Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences, ul. Ulyanova 46, Nizhny Novgorod, 603000, Russian Federation
b Pacific Oceanological Institute, Far-Eastern Division of the Russian Academy of Sciences, Baltiiskaya str. 43, Vladivostok, 690041, Russian Federation

In the 1990s, the study of the chaotic behavior of ray trajectories in inhomogeneous waveguides emerged as a new field in ocean acoustics. It turned out that at ranges on the order of or larger than 1000 km ray chaos is well developed and should be taken into account when describing long-range sound propagation in the ocean. The theoretical analysis of ray chaos and of its finite-wavelength manifestation, wave chaos, is to a large extent based on well-known methods and ideas from the theory of dynamical and quantum chaos. Concrete examples are used to review the results obtained in this field over the last two decades.

Fulltext pdf (3.9 MB)
Fulltext is also available at DOI: 10.3367/UFNe.0182.201201b.0019
PACS: 05.45.−a, 43.30.Bp, 43.30.Cq, 43.30.Dr (all)
DOI: 10.3367/UFNe.0182.201201b.0019
URL: https://ufn.ru/en/articles/2012/1/c/
000303763300002
2-s2.0-84860247076
2012PhyU...55...18V
Citation: Virovlyansky A L, Makarov D V, Prants S V "Ray and wave chaos in underwater acoustic waveguides" Phys. Usp. 55 18–46 (2012)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 15th, March 2011, revised: 29th, April 2011, 29th, April 2011

Оригинал: Вировлянский А Л, Макаров Д В, Пранц С В «Лучевой и волновой хаос в подводных акустических волноводах» УФН 182 19–48 (2012); DOI: 10.3367/UFNr.0182.201201b.0019

References (142) ↓ Cited by (33) Similar articles (20)

  1. Flatté S M et al. Sound Transmission Through A Fluctuating Ocean (Ed. S M Flatté) (Cambridge: Cambridge Univ. Press, 1979)
  2. Brekhovskikh L M, Lysanov Yu P Teoreticheskie Osnovy Akustiki Okeana (M.: Nauka, 2007); Brekhovskikh L M, Lysanov Yu P Fundamentals Of Ocean Acoustics (New York: Springer, 2003)
  3. Jensen F B et al. Computational Ocean Acoustics (New York: AIP Press, 1994)
  4. Munk W H et al. J. Acoust. Soc. Am. 96 2330 (1994)
  5. Abdullaev S S, Zaslavskii G M Zh. Eksp. Teor. Fiz. 80 524 (1981); Abdullaev S S, Zaslavskii G M Sov. Phys. JETP 53 265 (1981)
  6. Abdullaev S S, Zaslavskii G M Zh. Eksp. Teor. Fiz. 85 1573 (1983); Abdullaev S S, Zaslavskii G M Sov. Phys. JETP 58 915 (1983)
  7. Abdullaev S S, Zaslavskii G M Zh. Eksp. Teor. Fiz. 87 763 (1984); Abdullaev S S, Zaslavskii G M Sov. Phys. JETP 60 435 (1984)
  8. Abdullaev S S, Zaslavskii G M Izv. AN SSSR Fizika atmosfery i okeana 23 724 (1987)
  9. Abdullaev S S, Zaslavskii G M Akust. Zhurn. 34 578 (1988); Abdullaev S S, Zaslavskii G M Sov. Phys. Acoust. 34 334 (1988)
  10. Abdullaev S S, Zaslavskii G M Usp. Fiz. Nauk 161 (8) 1 (1991); Abdullaev S S, Zaslavsky G M Sov. Phys. Usp. 34 645 (1991)
  11. Abdullaev S Chaos And Dynamics Of Rays In Waveguide Media (Langhorne, Pa.: Gordon and Breach, 1993)
  12. Palmer D R et al. Geophys. Res. Lett. 15 569 (1988)
  13. Palmer D R, Georges T M, Jones R M Comput. Phys. Commun. 65 219 (1991)
  14. Smith K B, Brown M G, Tappert F D J. Acoust. Soc. Am. 91 1939 (1992)
  15. Tappert F D, Tang X J. Acoust. Soc. Am. 99 185 (1996)
  16. Simmen J, Flatté S M, Wang G-Y J. Acoust. Soc. Am. 102 239 (1997)
  17. Wolfson M A, Tappert F D J. Acoust. Soc. Am. 107 154 (2000)
  18. Wolfson M A, Tomsovic S J. Acoust. Soc. Am. 109 2693 (2001)
  19. Beron-Vera F J et al. J. Acoust. Soc. Am. 114 1226 (2003)
  20. Worcester P F, Spindel R C J. Acoust. Soc. Am. 117 1499 (2005)
  21. Zaslavskii G M Stokhastichnost’ Dinamicheskikh Sistem (M.: Nauka, 1984)
  22. Gutzwiller M C Chaos In Classical And Quantum Mechanics (New York: Springer-Verlag, 1990)
  23. Reichl L E The Transition To Chaos: Conservative Classical Systems And Quantum Manifestations (New York: Springer-Verlag, 1992); Raikhl L E Perekhod k Khaosu v Konservativnykh Klassicheskikh i Kvantovykh Sistemakh (M. - Izhevsk: RKhD, 2008)
  24. Koshel’ K B, Prants C B Usp. Fiz. Nauk 176 1177 (2006); Koshel K V, Prants S V Phys. Usp. 49 1151 (2006)
  25. Koshel’ K B, Prants C B Khaoticheskaya Advektsiya v Okeane (M. - Izhevsk: RKhD, Inst. komp’yut. issled., 2008)
  26. Zaslavskii G M, Sagdeev R Z Vvedenie v Nelineinuyu Fiziku. Ot Mayatnika do Turbulentnosti i Khaosa (M.: Nauka, 1988); Zaslavsky G M, Sagdeev R Z Nonlinear Physics: From The Pendulum To Turbulence And Chaos (Chur: Harwood Acad. Publ., 1988)
  27. Lichtenberg A J, Lieberman M A Regular And Stochastic Motion (New York: Springer-Verlag, 1983); Likhtenberg A, Liberman M Regulyarnaya i Stokhasticheskaya Dinamika (M.: Mir, 1984)
  28. Brown M G, Viechnicki J J. Acoust. Soc. Am. 104 2090 (1998)
  29. Brown M G et al. J. Acoust. Soc. Am. 113 2533 (2003)
  30. Smirnov I P, Virovlyansky A L, Zaslavsky G M Phys. Rev. E 64 036221 (2001)
  31. Makarov D V, Uleysky M Yu, Prants S V Chaos 14 79 (2004)
  32. Smirnov I P, Virovlyansky A L, Zaslavsky G M J. Acoust. Soc. Am. 117 1595 (2005)
  33. Flatté S M (Ed.) Sound Transmission Through A Fluctuating Ocean (Cambridge: Cambridge Univ. Press, 1979); Flatte S (Red.) Rasprostranenie Zvuka vo Fluktuiruyushchem Okeane (M.: Mir, 1982)
  34. Rytov S M, Kravtsov Yu A, Tatarskii V I Vvedenie v Statisticheskuyu Radiofiziku Ch. II Sluchainye Polya (M.: Nauka, 1978)
  35. Virovlyansky A L nlin/0012015
  36. Virovlyanskii A L Akust. Zhurn. 51 90 (2005); Virovlyansky A L Acoust. Phys. 51 71 (2005)
  37. Virovlyanskii A L Luchevaya Teoriya Dal’nego Rasprostraneniya Zvuka v Okeane (N. Novgorod: IPF RAN, 2006)
  38. Leontovich M Izv. AN SSSR Ser. fiz. 8 16 (1944)
  39. Leontovich M, Fok V Zh. Eksp. Teor. Fiz. 16 557 (1946); Leontovich M, Fock V J. Phys. USSR 10 13 (1946)
  40. Tappert F D Lecture Notes Phys. 70 224 (1977)
  41. Kravtsov Yu A, Orlov Yu I Geometricheskaya Optika Neodnorodnykh Sred (M.: Nauka, 1980); Kravtsov Yu A, Orlov Yu I Geometrical Optics Of Inhomogeneous Media (Berlin: Springer-Verlag, 1990)
  42. Landau L D, Lifshits E M Mekhanika (M.: Nauka, 1965); Landau L D, Lifshitz E M Mechanics (Oxford: Pergamon Press, 1976)
  43. Makarov D, Prants S, Virovlyansky A, Zaslavsky G Ray And Wave Chaos In Ocean Acoustics (Singapore: World Scientific, 2010)
  44. Brekhovskikh L M, Godin O A Akustika Sloistykh Sred (M.: Nauka, 1989); Brekhovskikh L M, Godin O A Acoustics Of Layered Media I, II (Berlin: Springer-Verlag, 1990, 1992)
  45. Landau L D, Lifshits E M Kvantovaya Mekhanika. Nerelyativistskaya Teoriya (M: Nauka, 1974); Landau L D, Lifshitz E M Quantum Mechanics. Non-Relativistic Theory (Oxford: Pergamon Press, 1977)
  46. Berman G P, Zaslavsky G M Physica A 97 367 (1979)
  47. Virovlyansky A L, Zaslavsky G M Phys. Rev. E 59 1656 (1999)
  48. Virovlyansky A L, Kazarova A Yu, Lyubavin L Ya Wave Motion 42 317 (2005)
  49. Virovlyansky A L J. Acoust. Soc. Am. 108 84 (2000)
  50. Colosi J A, Brown M G J. Acoust. Soc. Am. 103 2232 (1998)
  51. Garrett C, Munk W Geophys. Fluid Dyn. 3 225 (1972)
  52. Van Uffelen L J et al. J. Acoust. Soc. Am. 125 3569 (2009)
  53. Katsnelson B G et al. J. Acoust. Soc. Am. 126 EL41 (2009)
  54. Badiey M et al. J. Acoust. Soc. Am. 129 EL141 (2011)
  55. Munk W, Wunsch C Deep Sea Res. A 26 123 (1979)
  56. Munk W, Worcester P, Wunsch C Ocean Acoustic Tomography (Cambridge: Cambridge Univ. Press, 1995)
  57. Cornuelle B et al. J. Phys. Oceanogr. 15 133 (1985)
  58. Munk W, Wunsch C Rev. Geophys. Space Phys. 21 777 (1983)
  59. Shang E C J. Acoust. Soc. Am. 85 1531 (1989)
  60. Jones R M, Shang E C, Georges T M J. Acoust. Soc. Am. 94 2296 (1993)
  61. Udovydchenkov I A, Brown M G J. Acoust. Soc. Am. 123 41 (2008)
  62. Wage K E et al. J. Acoust. Soc. Am. 117 1565 (2005)
  63. Worcester P F et al. J. Acoust. Soc. Am. 105 3185 (1999)
  64. Colosi J A et al. J. Acoust. Soc. Am. 105 3202 (1999)
  65. Colosi J A, Tappert F, Dzieciuch M J. Acoust. Soc. Am. 110 163 (2001)
  66. Worcester P F et al. J. Acoust. Soc. Am. 95 3118 (1994)
  67. Colosi J A, Flatté S M, Bracher C J. Acoust. Soc. Am. 96 452 (1994)
  68. Akulichev V A i dr. Dokl. Ross. Akad. Nauk 417 693 (2007); Akulichev V A et al. Dokl. Earth Sci. 417 1432 (2007)
  69. Bezotvetnykh V V i dr. Akust. Zhurn. 55 374 (2009); Bezotvetnykh V V et al. Acoust. Phys. 55 376 (2009)
  70. Spindel R C et al. IEEE J. Ocean. Eng. 28 297 (2003)
  71. Baggeroer A B et al. (ATOC Consortium) Science 281 1327 (1998)
  72. Chirikov B V Phys. Rep. 52 263 (1979)
  73. Beron-Vera F J, Brown M G J. Acoust. Soc. Am. 114 123 (2003)
  74. Beron-Vera F J, Brown M G J. Acoust. Soc. Am. 115 1068 (2004)
  75. Morozov A D Rezonansy, Tsikly i Khaos v Kvazikonservativnykh Sistemakh (Izhevsk: RKhD, 2005)
  76. Budyansky M V, Uleysky M Yu, Prants S V Phys. Rev. E 79 056215 (2009)
  77. Uleysky M Yu, Budyansky M V, Prants S V Phys. Rev. E 81 017202 (2010)
  78. Uleiskii M Yu, Budyanskii M V, Prants S V Zh. Eksp. Teor. Fiz. 138 1175 (2010); Uleysky M Yu, Budyansky M V, Prants S V JETP 111 1039 (2010)
  79. Rypina I I et al. Phys. Rev. Lett. 98 104102 (2007)
  80. Brekhovskikh L M i dr. Akust. Zhurn. 36 824 (1990); Brekhovskikh L M et al. Sov. Phys. Acoust. 36 461 (1990)
  81. Goncharov V V, Kurtepov V M Akust. Zhurn. 40 773 (1994); Goncharov V V, Kurtepov V M Acoust. Phys. 40 685 (1994)
  82. Smirnov I P, Karuzers Dzh V, Khil’ko A I Izv. Vuzov Radiofizika 42 982 (1999); Smirnov I P, Caruthers J V, Khil’ko A I Radiophys. Quantum Electron. 42 864 (1999)
  83. Petukhov Yu V Acoust. Phys. 55 785 (2009)
  84. Kudo K, Monteiro T S Phys. Rev. E 77 055203(R) (2008)
  85. Chuprov S D Akustika Okeana. Sovremennoe Sostoyanie (Otv. red. L M Brekhovskikh, I B Andreeva) (M.: Nauka, 1982) p. 71
  86. Grachev G A Akust. Zhurn. 39 67 (1993); Grachev G A Acoust. Phys. 39 33 (1993)
  87. Brown M G et al. J. Acoust. Soc. Am. 117 1607 (2005)
  88. Stöckmann H-J Quantum Chaos: An Introduction (Cambridge: Cambridge Univ. Press, 2000); Shtokman Kh-Yu Kvantovyi Khaos: Vvedenie (M.: Fizmatlit, 2004)
  89. Smirnov I P et al. Phys. Rev. E 72 026206 (2005)
  90. Berman G P, Kolovskii A R Usp. Fiz. Nauk 162 (4) 95 (1992); Berman G P, Kolovskii A R Phys. Usp. 35 303 (1992)
  91. Tatarskii V I Usp. Fiz. Nauk 139 587 (1983); Tatarskii V I Sov. Phys. Usp. 26 311 (1983)
  92. Virovlyansky A L, Zaslavsky G M Chaos 15 023301 (2005)
  93. Bäcker A, Ketzmerick R, Monastra A G Phys. Rev. Lett. 94 054102 (2005)
  94. Heller E J Phys. Rev. Lett. 53 1515 (1984)
  95. Itin A P, Neishtadt A I, Vasiliev A A Physica D 141 281 (2000)
  96. Neishtadt A I Tr. Matem. Inst. Im. V.A. Steklova 250 198 (2005); Neishtadt A I Proc. Steklov Inst. Math. 250 183 (2005)
  97. Neishtadt A, Vasiliev A Nonlinearity 18 1393 (2005)
  98. Vainchtein D L, Neishtadt A I, Mezic I Chaos 16 043123 (2006)
  99. Leoncini X, Neishtadt A, Vasiliev A Phys. Rev. E 79 026213 (2009)
  100. Bogolyubov N N, Mitropol’skii Yu A Asimptoticheskie Metody v Teorii Nelineinykh Kolebanii (M.: Fizmatlit, 1958); Bogoliubov N N, Mitropolsky Y A Asymptotic Methods In The Theory Of Non-Linear Oscillations (Delhi: Hindustan Publ. Corp., 1961)
  101. Makarov D V, Uleysky M Yu Commun. Nonlin. Sci. Numer. Simul. 13 400 (2008)
  102. Makarov D V, Uleiskii M Yu Akust. Zhurn. 53 565 (2007); Makarov D V, Uleyskiy M Yu Acoust. Phys. 53 495 (2007)
  103. Makarov D V, Kon’kov L E, Uleiskii M Yu Akust. Zhurn. 54 439 (2008); Makarov D V, Kon’kov L E, Uleysky M Yu Acoust. Phys. 54 382 (2008)
  104. Neishtadt A, Vasiliev A Chaos 17 043104 (2007)
  105. Makarov D V, Sosedko E V, Uleysky M Yu Eur. Phys. J. B 73 571 (2010)
  106. Uleysky M Yu, Budyansky M V, Prants S V J. Phys. A Math. Theor. 41 215102 (2008)
  107. Grigorieva N S, Fridman G M, Palmer D R J. Comput. Acoust. 12 355 (2004)
  108. Hegewisch K C, Cerruti N R, Tomsovic S J. Acoust. Soc. Am. 117 1582 (2005)
  109. Kon’kov L E et al. Phys. Rev. E 76 056212 (2007)
  110. Leboeuf P, Voros A J. Phys. A Math. Gen. 23 1765 (1990)
  111. Makarov D V, Kon’kov L E Nelineinaya Dinamika 3 157 (2007)
  112. Makarov D V, Kon’kov L E, Uleysky M Yu Zhurn. Sib. Fed. Un-ta Mat. i fiz. 3 336 (2010)
  113. Keating J P, Prado S D Proc. R. Soc. Lond. A 457 1855 (2001)
  114. Kulkarny V A, White B S Phys. Fluids 25 1770 (1982)
  115. Klyatskin V I, Gurarii D Usp. Fiz. Nauk 169 171 (1999); Klyatskin V I, Gurarie D Phys. Usp. 42 165 (1999)
  116. Froyland G et al. Phys. Rev. Lett. 98 224503 (2007)
  117. Bódai T, Fenwick A J, Wiercigroch M J. Sound Vibr. 324 850 (2009)
  118. Makarov D, Uleysky M J. Phys. A Math. Gen. 39 489 (2006)
  119. Makarov D V et al. Phys. Rev. E 73 066210 (2006)
  120. Gan C, Wang Q, Perc M J. Phys. A Math. Theor. 43 125102 (2010)
  121. Kolovsky A R Phys. Rev. E 56 2261 (1997)
  122. Zaslavskii G M Usp. Fiz. Nauk 129 211 (1979); Zaslavskii G M Sov. Phys. Usp. 22 788 (1979)
  123. Berry M V, Robnik M J. Phys. A Math. Gen. 17 2413 (1984)
  124. Izrailev F M Phys. Rep. 196 299 (1990)
  125. Brody T A Lett. Nuovo Cimento 7 482 (1973)
  126. Berry M V, Keating J P, Prado S D J. Phys. A Math. Gen. 31 L245 (1998)
  127. Berry M V, Keating J P, Schomerus H Proc. R. Soc. Lond. A 456 1659 (2000)
  128. Virovlyanskii A L, Zaslavskii G M Akust. Zhurn. 53 329 (2007); Virovlyanskii A L, Zaslavskii G M Acoust. Phys. 53 282 (2007)
  129. Virovlyansky A L, Kazarova A Yu, Lyubavin L Ya J. Acoust. Soc. Am. 121 2542 (2007)
  130. Virovlyansky A L, Kazarova A Yu, Lyubavin L Ya J. Acoust. Soc. Am. 125 1362 (2009)
  131. Colosi J A, Flatté S M J. Acoust. Soc. Am. 100 3607 (1996)
  132. Virovlyanskii A L Izv. Vuzov Radiofiz. 46 555 (2003); Virovlyansky A L Radiophys. Quantum Electron. 46 502 (2005)
  133. Tikhonov V I, Mironov M A Markovskie Protsessy (M.: Sovetskoe radio, 1977)
  134. Gardiner C W Handbook Of Stochastic Methods For Physics, Chemistry, And The Natural Sciences (Berlin: Springer-Verlag, 1985); Gardiner K V Stokhasticheskie Metody v Estestvennykh Naukakh (M.: Mir, 1986)
  135. Rypina I I, Brown M G J. Acoust. Soc. Am. 122 1440 (2007)
  136. Vadov R A Akust. Zhurn. 52 448 (2006); Vadov R A Acoust. Phys. 52 377 (2006)
  137. Dushaw B D IEEE J. Ocean. Eng. 24 215 (1999)
  138. Spiesberger J L, Metzger K J. Geophys. Res. 96 (C3) 4869 (1991)
  139. Virovlyansky A L J. Acoust. Soc. Am. 113 2523 (2003)
  140. Virovlyanskii A L Akust. Zhurn. 51 330 (2005); Virovlyansky A L Acoust. Phys. 51 271 (2005)
  141. Virovlyansky A L, Zaslavsky G M Chaos 10 211 (2000)
  142. Morozov A K, Kolosi D A Akust. Zhurn. 51 386 (2005); Morozov A K, Colosi J A Acoust. Phys. 53 335 (2007)
© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions