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Reviews of topical problems


Vortex ring oscillations, the development of turbulence in vortex rings and generation of sound

,
Central Institute of Aerohydrodynamics, Acoustic Division, ul. Radio 17, Moscow, 105005, Russian Federation

The state of the art in describing the eigen-oscillations of a vortex ring in an ideal incompressible fluid is reviewed. To describe eigen-oscillations, the displacement field is taken as the basic dynamic variable. A vortex ring with the simplest vorticity distribution in the core and with a potential flow in the vortex ring envelope is the commonest approximation used in treating the eigen-oscillations of vortex rings of a more general form. It turns out that allowing for even a very weak degree of core smoothing causes many oscillation modes to lose their stability. It is shown that the instability effect is determined by the sign of the vibration energy. The energies of the ring eigen-oscillations are calculated and two kinds of eigen-oscillations, those with a negative energy and those with a positive energy, are identified, of which it is the former which become unstable when the core vorticity is smoothed. The multiple instabilities of vortex ring oscillations together with the details of the spatial structure of its eigen-oscillations suggest that it is the nonlinear evolution of precisely these processes which might be the origin of vortex ring turbulence. A new method for the study of unsteady processes in turbulent vortex rings, which utilizes the experimental diagnostics of the ring’s sound field, is presented. The structure of the sound field strongly supports the proposed model of the turbulent vortex ring.

Fulltext pdf (1.3 MB)
Fulltext is also available at DOI: 10.1070/PU2000v043n07ABEH000769
PACS: 43.30.−k, 47.27.−i, 47.27.Sd, 47.32.−y (all)
DOI: 10.1070/PU2000v043n07ABEH000769
URL: https://ufn.ru/en/articles/2000/7/b/
000165062700002
Citation: Kop’ev V F, Chernyshev S A "Vortex ring oscillations, the development of turbulence in vortex rings and generation of sound" Phys. Usp. 43 663–690 (2000)
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Оригинал: Копьев В Ф, Чернышев С А «Колебания вихревого кольца, возникновение в нем турбулентности и генерация звука» УФН 170 713–742 (2000); DOI: 10.3367/UFNr.0170.200007b.0713

References (103) ↓ Cited by (39) Similar articles (20)

  1. Kelvin Lord Philos. Mag. 34 15 (1867)
  2. Kelvin Lord Philos. Mag. 10 155 (1880)
  3. Thomson J J A Treatise On The Motion Of Vortex Rings (London: Macmillan, 1883)
  4. Seffmen F Sovremennaya Gidrodinamika: Uspekhi i Problemy (Pod red. Dzh Betchelor, G Moffat) (M.: Mir, 1984) p. 77
  5. Lamb G Gidrodinamika (M.-L.: Gostekhizdat, 1947)
  6. Betchelor Dzh Vvedenie v Dinamiku Zhidkosti (M.: Mir, 1973)
  7. Villya A Teoriya Vikhrei (M.: ONTI, 1936)
  8. Tung C, Ting L Phys. Fluids 10 901 (1967)
  9. Saffman P G Stud. Appl. Math. 49 (4) 371 (1970)
  10. Lugovtsov B A Nekotorye Problemy Matematiki i Mekhaniki (L.: Nauka, 1970) p. 76
  11. Johnson G M AIAA J. 9 763 (1971)
  12. Maxworthy T J. Fluid Mech. 51 15 (1972)
  13. Maxworthy T J. Fluid Mech. 64 (2) 227 (1974)
  14. Maxworthy T J. Fluid Mech. 81 465 (1977)
  15. Tarasov V F, Yakushev V I Priklad. Mekh. Tekh. Fiz. (1) 130 (1974)
  16. Van-Daik M (Sost.) Al’bom Techenii Zhidkosti i Gaza (M.: Mir, 1986)
  17. Shariff K, Leonard A Annu. Rev. Fluid Mech. 24 235 (1992)
  18. Vladimirov V A, Tarasov V F Dokl. Akad. Nauk SSSR 245 (6) 1325 (1979)
  19. Vladimirov V A, Lugovtsov B A, Tarasov V F Priklad. Mekh. Tekh. Fiz. (5) 69 (1980)
  20. Johari H Phys. Fluids 7 2420 (1995)
  21. Lavrent’ev M A, Shabat B V Problemy Gidrodinamiki i Ikh Matematicheskie Modeli 2-e izd. (M.: Nauka, 1977)
  22. Glezer A, Coles D J. Fluid Mech. 211 243 (1990)
  23. Sallet D, Widmayer R Z. Flugwiss. 22 207 (1974)
  24. Akhmetov D G, Kissarov O P Priklad. Mekh. Tekh. Fiz. (2) 87 (1966)
  25. Weigand A, Garib M Exp. Fluids 22 447 (1997)
  26. Widnall S E, Sullivan I P Proc. R. Soc. London A 332 335 (1973)
  27. Saffman P G J. Fluid Mech. 84 625 (1978)
  28. Widnall S E, Tsai S Y Philos. Trans. R. Soc. London A 287 (1344) 273 (1977)
  29. Uidnell Sh Mekhanika. Novoe v Zarubezhnoi Nauke. №21 Vikhrevye Dvizheniya Zhidkosti (M.: Mir, 1979) p. 126
  30. Vladimirov V A, Tarasov V F Dokl. Akad. Nauk SSSR 253 565 (1980)
  31. Vladimirov V A Nelineinye Problemy Teorii Poverkhnostnykh i Vnutrennikh Voln (Otv. red. Ovsyannikov, V N Monakhov) (Novosibirsk: Nauka, 1985) p. 270
  32. Kopiev V F, Chernyshev S A J. Fluid Mech. 341 19 (1997)
  33. Arnol’d V I Dokl. Akad. Nauk SSSR 162 (5) 975 (1965)
  34. Arnol’d V I PMM 29 (5) 846 (1965)
  35. Holm D D et al. Phys. Rep. 123 1 (1985)
  36. Drazin P G, Reid W H Hydrodynamic Stability (Cambridge: Cambridge University Press, 1981)
  37. Chandrasekhar S Ellipsoidal Figures Of Equilibrium (New Haven, Conn.: Yale Univ. Press, 1969)
  38. Kop’ev V F, Chernyshev S A Izv. AN SSSR Mekh. zhidk. i gaza (5) 99 (1991)
  39. Arnol’d V I Matematicheskie Metody Klassicheskoi Mekhaniki (M.: Nauka, 1974)
  40. Moffatt H K Philos. Trans. R. Soc. London A 333 321 (1990)
  41. Fridman A A Opyt Gidromekhaniki Szhimaemoi Zhidkosti (M.-L.: Gostekhizdat, 1934) p. 367
  42. Miln-Tomson L M Teoreticheskaya Gidrodinamika (M.: Mir, 1964)
  43. Vladimirov V A Priklad. Mekh. Tekh. Fiz. (3) 70 (1986)
  44. Zabusky N J, Hughes M H, Roberts K V J. Comp. Phys. 30 96 (1979)
  45. Dritchel D G J. Fluid Mech. 172 421 (1986)
  46. Benjamin T B J. Fluid Mech. 16 436 (1963)
  47. Stepanyants Yu A, Fabrikant A L Rasprostranenie Voln v Sdvigovykh Potokakh (M.: Nauka. Fizmatlit, 1996)
  48. Kadomtsev V B, Mikhailovskii A B, Timofeev A V Zh. Eksp. Teor. Fiz. 47 2266 (1964)
  49. Sturrock P A J. Appl. Phys. 31 2052 (1960)
  50. Rybak S A Nelineinaya Akustika (Red. V A Zverev, L A Ostrovskii) (Gor’kii: IPF AN SSSR, 1980) p. 176
  51. Kop’ev V F, Leont’ev E A Akust. Zhurn. 29 (2) 192 (1983)
  52. Ostrovskii L A, Rybak S A, Tsimring L Sh Usp. Fiz. Nauk 150 (3) 415 (1986)
  53. Nezlin M V Usp. Fiz. Nauk 120 481 (1976)
  54. Kop’ev V F, Leont’ev E A Akust. Zhurn. 31 (3) 348 (1985)
  55. Kop’ev V F, Leont’ev E A Izv. AN SSSR Mekh. zhidk. i gaza 22 (3) 83 (1987)
  56. Moore D W Proc. R. Soc. London A 370 407 (1980)
  57. Hama F R Phys. Fluids 6 526 (1963)
  58. Crow S C AIAA J. 8 2172 (1970)
  59. Widnall S E, Bliss E, Zalay A Aircraft Wake Turbulence And Its Detection (Eds J H Olsen, A Goldburg, M Rogers) (New York: Plenum Press, 1971) p. 305
  60. Klein R, Majda A J Physica D 49 323 (1991)
  61. Basset A B A Treatise On Hydrodynamics With Numerous Examples Vol. 2 (New York: Dover Publ., 1961)
  62. Ladikov Yu P Izv. AN SSSR Mekhanika i mashinostroenie 4 7 (1960)
  63. Saffman P G Vortex Dynamics (Cambridge: Cambridge Univ. Press, 1992)
  64. Gradshtein I S, Ryzhik I M Tablitsy Integralov, Summ, Ryadov i Proizvedenii (M.: Fizmatgiz, 1962)
  65. Kop’ev V F, Chernyshev S A Akust. Zhurn. 44 (3) 373 (1998)
  66. Fraenkel L E Proc. R. Soc. London A 316 29 (1970)
  67. Norbury J J. Fluid Mech. 57 417 (1973)
  68. Fraenkel L E J. Fluid Mech. 51 119 (1972)
  69. Chernyshev S A Kolebaniya Uprugikh Konstruktsii s Zhidkost’yu. VII Simpozium (Novosibirsk: SibNIA, 1992)
  70. Kelvin Lord, Tait P G Treatise On Natural Philosophy Vol. 1 (Cambridge: Cambridge University Press, 1912)
  71. Kochin N E, Kibel’ I A, Roze N V Teoreticheskaya Gidromekhanika Vol. 1 (M.: GIFML, 1963)
  72. Petrov A G Dokl. Ross. Akad. Nauk 359 769 (1998)
  73. Petrov A G PMM 63 (3) 481 (1999)
  74. Chernyavskii V M, Shtemler Yu M Izv. AN SSSR mekh. zhidk. i gaza 5 110 (1991)
  75. Vladimirov V A, Ilin K I Bull. Hong Kong Math. Soc. 1 103 (1996)
  76. Vladimirov V A Dinamika Sploshnoi Sredy. Vyp. 37 (Novosibirsk, 1978) p. 50
  77. Lavrent’ev M A, Shabat B V Metody Teorii Funktsii Kompleksnogo Peremennogo (M.: Nauka, 1973)
  78. Danilov S D Akust. Zhurn. 35 (6) 1059 (1989)
  79. Kop’ev V F, Chernyshev S A Izv. RAN SSSR Mekh. zhidk. i gaza (2000), v pechati
  80. Landau L D, Lifshits E M Teoreticheskaya Fizika T. 6 Gidrodinamika (M.: Nauka, 1986)
  81. Miles J W J. Fluid Mech. 3 (2) 165 (1959)
  82. Petrov A G Dinamika Sploshnoi Sredy. Vyp. 52 (Novosibirsk, 1981) p. 88
  83. Kop’ev V F, Leont’ev E A Akust. Zhurn. 34 (3) 475 (1988)
  84. Zaslavskii G M, Sagdeev R Z Vvedenie v Nelineinuyu Fiziku. Ot Mayatnika do Turbulentnosti i Khaosa (M.: Nauka, 1988)
  85. Aref H J. Fluid Mech. 143 1 (1984)
  86. Rom-Kedar V, Leonard A, Wiggins S J. Fluid Mech. 214 347 (1990)
  87. Kopiev V F et al. Atlas Of Visualization II (Eds-in-Chief Y Nakayama, Y Tanida; Ed. Visualization Soc. Of Japan) (Boca Raton, Fla.: CRC Press, 1996) p. 139
  88. Timofeev A V Usp. Fiz. Nauk 102 (2) 185 (1970)
  89. Kraiton D Sovremennaya Gidrodinamika: Uspekhi i Problemy (Pod red. Dzh Betchelor, G Moffat) (M.: Mir, 1984) p. 359
  90. Lighthill M J Proc. R. Soc. London A 212 564 (1952)
  91. Lighthill M J Proc. R. Soc. London A 222 1 (1954)
  92. Powell A J. Acoust. Soc. Am. 36 (1) 179 (1964)
  93. Howe M S J. Fluid Mech. 71 (4) 625 (1975)
  94. Mohring W J. Fluid Mech. 85 685 (1978)
  95. Obermeier F Acustica 42 56 (1979)
  96. Crow S C Stud. Appl. Math. 49 (1) 21 (1970)
  97. Crighton D G et al. Modern Methods In Analytical Acoustics: Lecture Notes (New York: Springer, 1996)
  98. Kop’ev V F, Chernyshev S A Akust. Zhurn. 41 (4) 622 (1995)
  99. Kambe T J. Fluid Mech. 173 643 (1986)
  100. Obermeier F Doctorate Dissertation (Max-Plank-Institut für Stromungsforschung, 1968)
  101. Blokhintsev D I Akustika Neodnorodnoi Dvizhushcheisya Sredy (M.: Gostekhizdat, 1946)
  102. Zaitsev M Yu, Kop’ev V F i dr. Dokl. Akad. Nauk SSSR 312 (5) 1080 (1990)
  103. Zaitsev M Yu, Kop’ev V F Akust. Zhurn. 39 (6) 1068 (1993)
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